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Self-mediation

This is a section where I hope to find as many things that we can all agree on. Can editors please indicate their agreement or otherwise below. I will add just two items to start, which I hope there will be fairly general agreement on.

Make better use of the two talk pages

This is just a matter of the mechanics of our discussion. This talk page should be reserved for discussion of proposed changes to the article: the general approach and format, what to say, where to put things, what diagrams to have etc. Discussion of the rights and wrongs of different sources, what is conditional and what is not, and other philosophical and mathematical issue around the subject should take place on the arguments page. It is important that this division is voluntary with only the gentlest of reminders to other editors to take their points elsewhere, if needed. Martin Hogbin (talk) 10:16, 5 January 2010 (UTC)

Agree

Martin Hogbin (talk) 10:16, 5 January 2010 (UTC)

Except I don't see why we need to be particularly gentle about it. Rick Block (talk) 16:10, 5 January 2010 (UTC)

Demanding people take their discussions elsewhere does not work and creates ill feeling. Here is the deal as I see it. Everyone agrees to use the two pages properly and engage in discussion on both pages. This means that those who want to keep the article as it is must engage in discussion about the underlying issues on the arguments page, otherwise those that do want change will bring those arguments here. Martin Hogbin (talk) 16:58, 5 January 2010 (UTC)

Except both pages are too long, and I find them hard to work with becaseu of that. JeffJor (talk) 16:38, 5 January 2010 (UTC)

The answer to this is archiving, if somebody knows how to do that. Martin Hogbin (talk) 16:58, 5 January 2010 (UTC)

Have essentially two sections

I think nearly everyone agrees that we should have two sections. In one section we should have the simple non-conditional solution (I think that non-conditional is a useful term in this discussion, which I use to mean not specifically mentioning or discussing conditionality, but not necessarily because the problem is agreed to be unconditional. Maybe the issue is being initially glossed over, in the interests of simplicity and clarity). In the second section we can mention the conditional nature of the problem and other variants and complications.

I am not yet talking about exactly what should go in each section, or what they should be called. I am just trying to get agreement to having a starting section that treats the problem simply, as we now have. Martin Hogbin (talk) 10:16, 5 January 2010 (UTC)

Agree

Martin Hogbin (talk) 10:16, 5 January 2010 (UTC)

The "conditional problem" - i.e., the one that uses Door #1/Door #3 - is a variant that definitely does not belong in the main section. Not only becasue it does not address the actual MHP, but because it does not help the uneducated reader to understand why the unintitive answer is correct. It only confuses him. It is NPOV to do it this way, because it separates the sources that treat different problems into sections that handle their own problems, rather than assuming the sources that handle the originally-intended problem are somehow wrong about what the problem they presented is. JeffJor (talk) 16:38, 5 January 2010 (UTC)

Disagree

I agree the initial section should focus on the fully symmetric problem, but strongly disagree about deferring a conditional probability solution to a subsequent section. IMO, this would not be NPOV. -- Rick Block (talk) 16:13, 5 January 2010 (UTC)

This is roughly chronological order of the sources. None of the sources before Morgan mentions conditional probability, why should we? My main aim (and that of may others I believe) in the first section is to keep it simple. I personally would not object to a footnote stating things might be a bit more complicated. Martin Hogbin (talk) 17:03, 5 January 2010 (UTC)

"None of the sources before Morgan mentions conditional probability"? This is absolutely false. Selvin's second letter [1] has a solution using conditional probability. The MHP was a well-known conditional probability problem in academia years before vos Savant's column. -- Rick Block (talk) 19:16, 5 January 2010 (UTC)

Yes, you are quite right, I was persuaded by the arrogance of the Morgan paper that they had discovered conditional probability. Selvin's second letter does indeed consider the probability with which the host chooses a given door. He, naturally, takes this to be 1/2 (as has already stated that the host will choose randomly when he has a legal choice) and proceeds, without fuss to solve the problem. In the light of this it is hard to see what the Morgan paper adds to the story.

Even so, this is not what I would like to see at the start of this article. I think we need to have a balance between what some see as mathematical correctness and simplicity, so that we can fulfill the basic function of WP of informing our readers. Let me make a proposal below, it is similar to that on Nijdam's development page. Martin Hogbin (talk) 11:34, 6 January 2010 (UTC)

Somewhere in between

Too soon the article is getting complex. The Whitaker question however seems to be most famous, but other well known examples from reliable sources are welcome. My main suggestion would be to use the information which is already in the article, but reshape it:

1. Introduction. (Until "When the above statement". Move the last two paragraphs to the "History" chapter.)
2. Popular solution
3. Conditional solution
4. Aids to understanding
5. History (general)
---similar problems
---Monty Hall
---American Statistician
---Parade
6. Arguments and methods (detailed)
---Conditional or not
---Variants
---Bayesian analysis
7. Links and references
Heptalogos (talk) 21:47, 5 January 2010 (UTC)

Discussion and proposals aimed at reaching a compromise on this subject

This section is intended for discussion of what editors would like to see as the first solution.

I would like to see this as the first solution in the article, with pretty pictures, of course. I also would accept a footnote of some kind to indicate that some people regard this solution as incomplete, exact wording to be negotiated.

You choose a goat		You choose a goat		You choose a car
The host opens a door to reveal a goat		The host opens a door to reveal a goat		The host opens a door to reveal a goat
You Stick	You Swap	You Stick	You Swap	You Stick	You Swap
You get a Goat	You get a Car	You get a Goat	You get a Car	You get a Car	You get a Goat

Rick, could you accept this? Nijdam? Martin Hogbin (talk) 11:47, 6 January 2010 (UTC)

I'm not Rick or Nijdam. I have stated at least twice that the only appropriate way to 'major edit' the article is to start with the current version. That way all adds/deletes/modifies are clearly discernible with a true audit trail. Is this obtuse to anyone? Do I need to rephrase that sentence for clarity? Do you catch my drift? Glkanter (talk) 12:11, 6 January 2010 (UTC)

My suggestion above is not suitable for immediate inclusion in the article because it needs pretty pictures. Everything done on WP is recorded so any agreements made here can be later transferred to the article with an 'audit trail' as you have put it the past. Do you like the suggestion above (with your choice of footnote, including none)? Martin Hogbin (talk) 13:51, 6 January 2010 (UTC)

And the footnote infers that 'Probability' is the only discipline available to solve the puzzle. That is false, and I will not support it's inclusion with the 'probability/logic solutions'. Unless you want to go to 4 distinct solutions in chrono order: The one above from 1975 (with footnote), Selvin's indifferent conditional from 1975, vos Savants probability/logic solution from 1990, and Morgan's non-solution from 1991. Glkanter (talk) 12:46, 6 January 2010 (UTC)

Would you be happy with a different footnote? If so what? Would you like to see the above solution with no footnote? Martin Hogbin (talk) 13:51, 6 January 2010 (UTC)

As an alternative, I suggest again a unified solution section, more or less like #Proposed unified solution section. The first part of this is (I think) pretty much exactly like what you're suggesting. But then instead of a footnote it continues with a conditional solution of the symmetric problem presented as an alternative. Maybe this will be the meat of the mediation, but I don't see how deferring a conditional solution to a later section rather than including one at this point is anything other than POV favoritism. The difference is only one screenful of text and figures, basically one paragraph. -- Rick Block (talk) 14:51, 6 January 2010 (UTC)

Here's another word Rick and I disagree on the meaning of: 'compromise'. Rick thinks (as per his edit summary) that going from 2 separate solution sections (as the article has today) to 1, is a compromise with the guy(s) who want 3 or 4. Another thing we disagree on is that chronological order has a POV. Maybe we should somehow have all the solutions typed on top of each other? To be fair, of course. Glkanter (talk) 15:13, 6 January 2010 (UTC)

If that's going to be your attitude then I see no point in continuing this discussion until we have a mediator. -- Rick Block (talk) 15:21, 6 January 2010 (UTC)

That's not an attitude, it's a statement of fact. I agree, you should stop trying to change the article in opposition to what the consensus wants. I've been trying to move us to formal mediation for weeks now. Glkanter (talk) 15:26, 6 January 2010 (UTC)

Rick, as you say, my proposed diagram (which was taken from 'The Curious Incident of the Dog...') is quite similar to yours but it does not have door numbers which, according to K&W, only confuse people. The footnote has the advantage of allowing us to present a clear diagram, which most people can actually understand, but still be correct. I think you have forgotten how difficult this problem is for most people when they first see it. We need to do all that we can to make the problem and solution simple, at least to start with. The main point of the problem is that the answer is 2/3 and not 1/2. We must get this across first.

I do not think that starting simply and then going into more detail can be regarded as POV. It is how most good text books work. Can we leave what happens after this diagram for the moment. Would you accept the diagram, with an appropriate footnote?

Glkanter, do you like my proposed diagram at all? Would you be happy for the article to start with this?

Finally, I do not think that formal mediation will achieve anything more than we are doing here. Everyone needs to compromise a little. Martin Hogbin (talk) 16:40, 6 January 2010 (UTC)

If the diagram represents the sources accurately, what else is there to say?

OK. Lets compromise. 1st question: Is the contestant ever aware of a host bias? How? Why? 2nd question: How many Solution sections? In what order? 3rd: What about the SoK problem in the Variants - Slightly Modified Problems section? 4th: Other than as part of Morgan's solution, will the probability/logic solutions be describes as 'false'? Will there be a statement that Morgan's view is not universal, more likely a minority opinion?

I think we need the Formal Mediation so that we can go to arbitration on ownership and filibuster issues. Otherwise, the consensus will continue to be improperly restricted from improving the article. Glkanter (talk) 16:55, 6 January 2010 (UTC)

As far as I can see my simple diagram meets all your requirements. Can you confirm that you like it and would be happy for the article to start with it? If not, I am wasting my time with it. Martin Hogbin (talk) 17:03, 6 January 2010 (UTC)

If you feel this would improve the existing article, I encourage you to make such an edit. If you are asking my opinion, I cannot render it out of the context of the existing article. It's a Featured Article. Why would anybody start over at ground zero, rather than add/delete/modify the existing article, or a copy? I've said this countless times, and you guys all just set up sandboxes all over the place. I take no responsibility for how anybody spends their time here, other than for myself. Glkanter (talk) 17:16, 6 January 2010 (UTC)

You thanked me for my support below, how about some from you now. Before I spend my time creating pictures and uploading them, I want to be reasonably confident that I am not wasting my time. I am not starting at ground zero, most of what is currently in the article can stay as far as I am concerned. I just want to start the article with a simple, convincing solution that shows that the player has a 2/3 chance of winning by swapping. This is what is missing, in my view. If I added such a diagram and solution, would you accept it? Martin Hogbin (talk) 17:52, 6 January 2010 (UTC)

Did I?

If I've learned anything from Wikipedia, it's that nothing can be 'assumed'. Until your mods are in the article, or a copy, I can only assume where you're putting it, what else you're changing, etc. And if I do that, then I haven't learned anything after all. Oh, and I don't agree with a footnote, or any other disclaimer. Until Morgan's direct criticism in Morgan's solution section. Glkanter (talk) 20:06, 6 January 2010 (UTC)

I guess I have to leave you to do things your way then. I was trying to reach some kind of consensus here but if you want to try, mediation, arbitration, edit warring, or whatever then go ahead. 86.132.191.65 (talk) 20:23, 6 January 2010 (UTC)

I think your table is quite clear, but I don't think it's easier to understand than the simple pictures in the Popular solution section. Actually I guess it's about the same as the first big picture. What's really different? Heptalogos (talk) 22:25, 7 January 2010 (UTC)

Interesting division in Wikipedia policy: Text - no OR; Images - OR is OK. Glkanter (talk) 22:49, 7 January 2010 (UTC)

What is the argument in support of reporting Morgan's solution prior to the others'?

Why should Morgan's solution 'jump the line' over the other solutions, which were published earlier? It's no 'better' than any other. That would be a NPOV violation. Glkanter (talk) 16:37, 6 January 2010 (UTC)

Where are you getting the notion that anyone is arguing Morgan's solution should be reported prior to any others? Is there a change to the article you're suggesting here, or is this actually a response to something else? -- Rick Block (talk) 19:48, 7 January 2010 (UTC)

LOLZ! We need more humor in all these dry discussions. Thanks, Rick! Glkanter (talk) 03:39, 8 January 2010 (UTC)

This is what happens when hosts/producers share information with contestants.

http://www.huffingtonpost.com/2010/01/08/our-little-genius-kiddie-_n_416440.html

To argue that the host indicating to the contestant where the car is located is consistent with the statement "Suppose you're on a game show..." is contradicted by the facts. Glkanter (talk) 18:32, 8 January 2010 (UTC)

Can you be more explicit in what your exact proposal or criticism is about? Heptalogos (talk) 20:54, 8 January 2010 (UTC)

Sure. Morgan, and others call the simple solutions 'false'. Then they claim to 'prove' this by concocting a host bias, that presumably the contestant is aware of.

Issue #1 is that this is not a valid method of dis-proving a solution, this criticizing problem 'B' as a means to discredit problem 'A'.

Issue #2 is that there can be no such transfer of knowledge, in any way, shape or form from the host/producer to the contestant. As this article demonstrates. I've posted 2 Wikipedia articles on this subject previously. Symmetry prevails by definition.

Morgan and others published it. It goes in the article. Thoughtful editors may choose not to over-emphasize Morgan's critique in the article. Glkanter (talk) 21:18, 8 January 2010 (UTC)

OK, can you please move this to the arguments page first? Heptalogos (talk) 21:28, 8 January 2010 (UTC)

I'm done with it. Besides, it's about how to edit the article. That's what this page is for. Glkanter (talk) 21:37, 8 January 2010 (UTC)

Recent changes and discussions (early Jamuary 2010)

changes

I noticed that the article has changed quite a bit and not all for good.

good

• the current introduction looks good to me it thankfully stays away from Kraus&Wang and the unconditional vs conditional issue. But just state the problem in the parade version which made it famous

not good

• However, this is not the only mathematically explicit version of the problem. Were the names of the doors (the numbers 1, 2, and 3) fixed in advance (painted as huge numerals on each door), or are we naming the doors retrospectively: you choose a door and we call that door 1; then Monty Hall opens a door and we call that door 3; we then give the remaining door the name door 2? This latter appears to have been the intent of Marilyn vos Savant herself. <--- What's that supposed to be? Please no personal speculation of what the problem might be. And in the same manner no (unsourced) speculation of what vos Savant, Morgan or whoever might have had in mind. Stick to summarize what they've actually written.

Source: MvS site. Part of the actual problem statement: "the host opens another door, say #3". "Say" reasonably meaning to give it a random name out of three. This enables the host to say, in the particular event: "Do you want to pick door #2?", also quoted from the statement.

The first similar example described by MvS uses three shells. They are not numbered, reasonably because the chosen one is identified by a finger on top of it, and the other two similarly need no identification other than 'empty or not'.

The second example presents all six possibilities, including openings of door 2, which are counted as valid outcomes. This is probably the most explicitly convincing one.

The third example uses three playing cards in repeated experiment. The cards can't be numbered at all, because the numbers would reveal their value after a few times. This is probably the most implicitly convincing example.

The last example is the experiment actually performed. This one is trying to cover randomness by throwing dices. Three cups are numbered, in reference to the only valid outcomes of the dices. Again, both cups no. 2 and 3 may be lifted and are counted as valid outcomes.

So, it can be reasonably understood that the intent of MvS was not to fix numbers to doors, but rather to identify any possible situation at a certain moment. Heptalogos (talk) 13:11, 9 January 2010 (UTC)

Marilyn herself raised the fact that she was misquoted by Morgan: [2], creating early misimpressions. She accuses Morgan of purposely focussing on semantic issues. She further writes that no additional stated conditions appeared important to a general comprehension of the problem because circumstances in default are reasonably considered random. And finally she states that 'we' (herself and Whitaker?) published no significant reason to view the host as anything more than an agent of chance who always opens a losing door.

Morgan answered that they consider Whitaker's question as an original question, which makes any comment by MvS irrelevant. I don't know if MvS replied to that again, but she ends her letter with the phrase "I have given up on getting the facts across properly and have decided simply to sit back and amuse myself with the reading of it all".

They both make sense and I think this is another example of our need to take distance from opinion, taste and ethics, and present the issues as they arise, anywhere relevant and reliable. Heptalogos (talk) 22:21, 9 January 2010 (UTC)

• Popular solution - 1975. <---Excuse me? None of the sources/descriptions in this section is from 1975 but they are from the 90s onward. Furthermore Selvin (which is the supposed 1975 reference) published a unconditional (=popular) and a conditional solution in 1975. Conclusion this section header complete nonsense.
• Probabilistic solution - 1991. <--- Similarly off as the other section title. All solutions are "probabilistic" if they compute probabilities and use probability theory. That's the case for Gardner, Selvin and later treatments (including that partially that of vos Savant herself). There is also no unconditional vs. conditional difference between 1975 and 1991 if the section header is supposed to allude to that. The only thing that was "new" in 1991 was a generalization of the conditional solution to model different host behaviours.

discussion

Much of the discussion still evolves around "What the real MHP is (according to us)", "What the appropriate or true solution has to look like (according to us)", "What vos Savant thinks the problem means (according to us)", "What Morgan thinks the problem means (according to us)", etc.. While this can be an interesting discussion in its own merit it is largely pointless for the article. For the article we have to provide an accurate/representative summary of he how the problem was defined/solved/treated in reputable literature and that's it. It's not up to us to "decide" whether Morgan or vos Savant or whoever was ultimately "right" or did solve the "real" MHP while the rest was doing something else. If all participants would stick to summarizing all reputable literature in a representative and readable fashion as a goal and stay away from cherry picking sources and pushing their personal view of the problem much of disagreements would vanish.--Kmhkmh (talk) 01:47, 8 January 2010 (UTC)

So, what should the Solutions heading read for the first source that calls the Selvin/vos Savant solutions 'false'? Who gets the credit? What year did that happen? Some long-standing editors of the article seem to think that's a significant point in the history of the puzzle. Do you agree? Glkanter (talk) 22:47, 8 January 2010 (UTC)

You need to decide whether you want to have the chapters being organized by content or chronology. If want to order them by content, then as explained above the current section headers make no sense. If you want to order them chronologically then the headers should be something like 1975 _ Selvin when Selvin posed & solved the problem and coined the term MHP. And 1990 - Parade/Whitaker/vos Savant when the problem became widely known and the "controversy" started. I don't see any particular importance of Morgan in the time line here. He was just the possibly first of string of academic and math publications that followed after the parade affair. The problem with chronological sections however is that you cannot separate the conditional from the unconditional solution (since both are around in 1975). Furthermore we have a chronological overview in the history section anyhow. So if we organize by content the section headers could be something like simple/popular/unconditional solution (essentially with the current content) and conditional solution/detailed mathematical analysis (partially with the current content (conditional solution)m but possibly also the bayesian section and the variants. The header detailed mathematical analysis might also indicate to readers, that people just looking for simple and sufficient explanation do not have to bother, however people interested in various other perspectives or a more "advanced" treatment of the problem might read on.--Kmhkmh (talk) 23:25, 8 January 2010 (UTC)

Is the following structure in compliance with the requirements?:

1. Introduction. (Until "When the above statement". Move the last two paragraphs to the "History" chapter.)

2. Popular solution

3. Conditional solution

4. Aids to understanding

5. History (general & chronological)

• Similar problems
  
• Monty Hall
  
• American Statistician
  
• Parade
  

6. Arguments and methods (detailed)

• Conditional or not
  
• Variants
  
• Bayesian analysis
  

7. Links and references
Heptalogos (talk) 11:47, 9 January 2010 (UTC)

That looks like feasible approach to me, alternatively i'd like to suggest te following structure maybe slightly better suited for a compromise:

1. Introduction (as is)

2.Problem (as is)

3.Solution (unconditional as is)

4.Aids to understanding (as is)

4.1 Why the probability is not 1/2

4.2 Increasing the number of doors

4.3 Chance of Picking Goat With the Assumption of Switching

4.4 Simulation

5.Detailed Mathematical analysis (contains all "advanced"/more complicated mathematical treatments)

5.1 conditional solution (basically the old "Probabilistic solution - 1991" as is)

5.2 Variants - Slightly Modified Problems (as is)

5.2.1 Other host behaviors

5.2.2 N doors

5.2.3 Quantum version

5.3 Bayesian analysis

5.x other math aspects

6. Psychological analysis (here Krauss & Wang, Mueser,Granberg and others could be treated in greater detail)

7. Sources of confusion (can treat math and psychological aspects together or alternatively moved in subchapters of 5 and 6

8. History of the Problem (as is)

9. See also

10. References

11. External links

From my perspective either suggestion might be a starting point for the mediation.--Kmhkmh (talk) 13:01, 9 January 2010 (UTC)

featured status

Given the recent changes in particular, but also the constant quarrel and maybe latent edit warring. I think it is time to review the featured status. This doesn't have to done right now and might be combined with the mediation procedure (or afterwards) but it should be done. Because the current or future article might be somewhat to significantly different from what was reviewed in 2005. Aside from some of problems listed further of the current article stability is also a criteria for a featured article.--Kmhkmh (talk) 01:47, 8 January 2010 (UTC)

I agree to literally all you say. But an accurate/representative summary of how the problem was treated in reputable literature cannot at all be created without a (our) perception of it. So some of your points are literally useless. Let's do it your way, fully objective, consequently, and replace the article by a list of all reliable sources. Not even a choice of quotes of course. You think that's the essence of the featured status? Heptalogos (talk) 12:01, 8 January 2010 (UTC)

Or could it be that you are suffering from the bad symptoms of our inspiration? The same inspiration that created the featured article, while the bad symptoms are almost all in the talk pages. I like your 'not good' stuff, but the 'discussion' paragraph is largely pointless for the article. Heptalogos (talk) 12:11, 8 January 2010 (UTC)

The spirit that created the originally featured article has nothing to do with the endless and ultimately rather boring discussion that followed the 5 years after (in particular the last year, when I paid some attention to it). People are still arguing about changing the article in a way that essentially makes vos Savant or Morgan look "more right", it is just done in more subtle ways. As in "who is mentioned first", "Who is not solving the real MHP", "who should be considered a variant", "what should be moved to separate article", "should both approaches be described in a combined fashion" or for the latest the odd section titles described above. Quite often in the discussion people seem to willfully ignoring or misrepresenting sources not fitting their POV as well as the statements of other participants. If you look at the edit history of some of the involved participants, it also makes you wonder.... Imho the whole thing is as petty and pointless as the original squabble between vos Savant and Morgan, in fact this seems to the wikipedia extension of it.

If you summarize the reputable literature, it is rather obvious that the article needs to contain both, an unconditional and a conditional treatment. Yet here we are, having a year long struggle of how to implement/realize the obvious and having "proxy battles" about marginal differences (section titles, who goes first, etc.). And for intermission we also doubt the obvious by inserting our own WP:OR and giving our own personal version of the real MHP and judge which reputable literature is wrong and which is right according to it. This is Wikipedia at its worst as far as constructive collaboration is concerned. It might be different though if you are here for the show or for sociological research or other reasons.--Kmhkmh (talk) 13:14, 8 January 2010 (UTC)

I agree to most of what you say, but the irony is that everything you write after the 'good' and 'not good' is about the same kind of drama. Try to look at it this way: the article really has improved over the last year. Apart from that, people are learning on the talk pages. At least recreating. Do you maybe know where suggestions can be assigned for a background discussion forum? Heptalogos (talk) 14:39, 8 January 2010 (UTC)

My point is that the article has not significantly (or at all) improved over the last 6 (or even 12) months. The only positive outcome the quarrel has produced are some additional sources, which is arguably good but not that important since the article due to wealth publication tends to rather oversourced than undersourced anyhow. Neglecting some the latest changes it has barely managed not to get worse (probably mostly due due to Rick Block constantly editing out the biggest nonsense). I would agree however that it still has significantly improved over the 2005/2006 version that became a featured article (see [3]). Looking at the early version however I wonder why it got featured at all, presumably the criteria and selection were still somewhat less strict back then. I understand that people learn on discussion pages and that a learning phase might be required in some discussions. However the main or strictly speaking sole purpose of this page is just (constructive) collaboration discussion to improve the article (which i barely see for last 9 months now, though the formal mediation might be bring some difference here). If people just want to discuss/argue their views of the problem, they can do that here Talk:Monty_Hall_problem/Arguments (see template at the top of the page as well), at another internal page created for such a purpose or outside Wikipedia (web fori, usenet, irc, real life), but ideally not on this discussion page. Anyhow just my observation or 2 cents if you will. I do not intend to join the neverending debate for long, aside from maybe helping in the mediation as this would be a more promising constructive attempt.--Kmhkmh (talk) 15:52, 8 January 2010 (UTC)

Wikipedia is intended to work on a consensus basis, recognizing reliable published sources. You have chosen to not be part of the consensus. And the will of the consensus continues to be rebuffed.

I may be the only active editor who came here simply as a reader of the article. In October, 2008, it was horrible. It is orders of magnitude more useful now. And could still be a lot better. FA or not. Glkanter (talk) 15:28, 8 January 2010 (UTC)

I agree with Glkanter. You have chosen not to take part in most of the discussion yet you presume to tell us how the article should be edited. There is strong feeling amongst many editors that the article does not explain the basic puzzle and solution very well. This is a major failing in an encyclopedia for the general public that needs be be addressed.

You refer to 'latent edit warring'. This is how WP is meant to work. Editors should discuss issues to reach a consensus then edit the article appropriately. The fact that you have intentionally absented yourself from this process does not give you any special rights here. Martin Hogbin (talk) 15:57, 8 January 2010 (UTC)

• I'm neither telling anybody how the article should be edited nor I'm claiming any "special rights", but I was outlining what follows directly from the wikipedia guidelines (and common sense actually). There is no problem with editors wanting to have a simple explanation. In fact we have one prominently featured early in the article (though under a questionable section header). There is however a problem with editors wanting to edit out everything other than "their" simple unconditional solution and who in doubt even do not mind to resort to unsourced material and apparently want the article to create the impression that the simple unconditional solution is all that there is to MHP.
• The fact that Wikipedia for the most part primarily targets the general public, does not mean we write a Wikipedia for Dummies and it does not mean WP only contains material "that everybody can understand". WP collects the knowledge of the world and that means a comprehensive treatment of topics. The important thing here is that articles are properly structured, i.e. information/content requiring a different level of background knowledge is in different chapters, with more complicated treatments and extensions towards the end of the article (which we kinda have here as well).
• 'latent edit warring' is not how WP is supposed to work. It is supposed to work by constructive collaboration not by never ending quarrels over essentially the same things and editing things back and forth. It is supposed to work by achieving a reasonable compromise/result which adheres to WP guidelines and then edit the article in agreement. Maybe the mediation will achieve that, we'll see.
• And finally regarding Glkanter's point. Wikipedia is not just some arbitrary consensus by currently active editors somehow using some reliable sources. Wikipedia is a consensus within the WP guidelines and representing the (available) sources appropriately. Or to put it this way there is no such thing in WP as consensus outside the guidelines or that misrepresent sources.

This is only partly true. It may be that 90% of WP is actually arbitrary consensus, while 90% of the editors sees no issues in it and leaves it unquestioned. As long as people agree with it, most people won't bother to request resources. Check this site: Conditional probability. Where do all text and examples come from? What about the definition of the main subject in de second line: "the possible outcomes of the experiment are reduced to B". It's simply an editor's opinion, but most editors simply agree with it. That's WP also. Heptalogos (talk) 21:20, 8 January 2010 (UTC)

• I do however agree that if the current problems are fixed this version can be seen as an improvement over October 2008 and having the unconditional and the conditional solution clearly separated is a plus ("different background knowledge in different chapters"). However this does not mean the criticism of the unconditional can simply be ignored, but it can be discussed in a separate section comparing both approaches or in the section of the conditional solution.

Anyhow I'm off until the mediation assuming we get one anytime soon)--Kmhkmh (talk) 17:20, 8 January 2010 (UTC)

Ugh! More Straw Men. Enough!

We call them Aunt Sallies in the UK. Knhkmh has made up a list of mad things he claims we all want to do just to show how bad we are. Martin Hogbin (talk) 10:44, 9 January 2010 (UTC)

Where does this presumption that the 'consensus' editors respect Wikipedia guidelines less than you, and Rick, and Nijdam (oh, please) come from? I presume everybody is operating in good faith, until they demonstrate, usually via some hipocracy, otherwise. Your interpretation of Wikipedia's guidelines has merit, just like anyone else's. To present it as a fact that some violation has or will occur is hardly appropriate or supported by the writings of any editor, including Glkanter. And it ignores the prevailing Morgan POV of the current article. Glkanter (talk) 17:40, 8 January 2010 (UTC)

How Goes The Formal Mediation Filing?

I tried to sign that I'm willing to go along, or whatever. Is there a place to do this?

Has Nijdam responded? Glkanter (talk) 13:21, 9 January 2010 (UTC)

The request has not been officially filed yet since Nijdam has not responded. I've tried to contact him via email. He hasn't made any edits since Jan 2. I suspect he may be on holiday. I'd like to give him another week or so to respond, but if you're unwilling to wait that long you can certainly file the mediation request yourself (you'd have to rearrange the draft I created a bit). -- Rick Block (talk) 18:07, 9 January 2010 (UTC)

If I filed it without listing Nijdam, is it still valid? Would Nijdam or any other editor be able to claim I had filed a 'biased' request? Glkanter (talk) 18:14, 9 January 2010 (UTC)

I think you are maybe misunderstanding the idea of mediation. The mediator will not try and force an agreement on us, they will just try to help us to work together. So, if Nijdam is happy with the mediation process, it will continue. If anybody says that will have nothing to do with it but they will continue to push for their wishes then it cannot work. I do not have much faith in the process now, after failing to get even one side of the argument to agree, but I am happy to give it a go. Martin Hogbin (talk) 18:30, 9 January 2010 (UTC)

So, it's intractable, then. What official Wikipedia steps remain available to us? Or do we just keep arguing and over-editing each other in the article in a non-3RR manner? Glkanter (talk) 18:39, 9 January 2010 (UTC)

I have done some editing

Having tried in vain to reach any form of consensus I have made a few edits to see what the general reaction is.

I have deleted the unsourced comment about door numbers and replaced it with a comment (citing Seymann) that Morgan address their interpretation of the problem, in that specific doors are identified in the problem statement.

I have added what should be an uncontroversial explanation of the existing diagram. Martin Hogbin (talk) 14:35, 9 January 2010 (UTC)

Kmhkmh's criticism about the unsourced comment is in the 'Recent changes' chapter on this page. I added the source and explanation to that, so I guess we'd better check or discuss it before deleting the entire thing. Heptalogos (talk) 18:44, 9 January 2010 (UTC)

The point is that the section I removed seemed to be a view that is pretty well unique to you, and certainly not one I have seen mentioned in any reliable source. I think the fact that the numbers of the doors may not be intended to be important is better covered by Seymann's comment on the Morgan paper, even though he does not specifically state this.

I think that you are making much the same point but in a different way. Martin Hogbin (talk) 18:53, 9 January 2010 (UTC)

"Unique to you": do you know that Rick added this view? Heptalogos (talk) 20:10, 9 January 2010 (UTC)

Sorry, I though it was you who was promoting this possibility. Martin Hogbin (talk) 21:18, 9 January 2010 (UTC)

What view did I add? -- Rick Block (talk) 01:29, 10 January 2010 (UTC)

I checked the history and thought I saw that you were the one adding the paragraph in the Problem section about 'fixed door numbers'. Isn't that true? Heptalogos (talk) 22:18, 10 January 2010 (UTC)

I found another source. Please check under 'Recent changes'. I may understand your question about Whitaker being a real (third) person. Heptalogos (talk) 22:57, 9 January 2010 (UTC)

With the above changes I am not that unhappy with the article. I would still like to.

1) Rename 'Popular solution - 1975' maybe 'Simple solution' are just 'Popular solution' again.

The year really has no meaning here.

2) Rename 'Probabilistic solution' 'Conditional solution'.

All solutions are probabilistic, this is the conditional solution.

3) Move the 'Aids to understanding' section to be immediately after 'Popular solution'.

If you read this section you will see that none of it relates to the conditional problem/solution

Martin Hogbin (talk) 16:05, 9 January 2010 (UTC)

I've gone ahead and deleted the dates from the headings. It seems clear there's no support for including these dates. -- Rick Block (talk) 16:39, 9 January 2010 (UTC)

How about we do away with the 'History' section, and present the Solution sources chronologically? With headings and sub-headings for clarity? Then, dates would be very useful. Glkanter (talk) 17:25, 9 January 2010 (UTC)

Thanks. Do you see my point about the 'Aids to understanding' section? This is aimed at the general reader, who may not accept or understand the solutions presented. Later sections are for more advanced readers. Martin Hogbin (talk) 17:35, 9 January 2010 (UTC)

I still think we only need one Solution section including both an unconditional style and conditional style of solution. In my opinion, the more you separate the "popular solution" and the "conditional solution" the less NPOV you make it. Please think carefully about your reason for wanting to avoid a conditional solution up front. Is it really because it's a more complicated approach, or is it because it doesn't fit your POV that the problem should be approached unconditionally? -- Rick Block (talk) 17:51, 9 January 2010 (UTC)

My main reason for wanting to change this article has always been that it fails to provide a simple and convincing solution and explanation for the general reader. I think you have lost sight of just how hard it is for most people to understand and accept the simple solution to the non-conditional problem. The last sentence in the lead says, 'Even when given a completely unambiguous statement of the Monty Hall problem, explanations, simulations, and formal mathematical proofs, many people still meet the correct answer with disbelief'. If we just state the facts without making them understood by our readers, no matter how well they are supported by reliable sources, we fail in our job of producing a good encyclopedia. The main point of the MHP is that you can tell people the answer, and still they do not believe you.

My POV is that the issue of conditionality is not that important at the start of the article, although it should be discussed later as it was raised in a published source. That is why I say that I want to treat the problem non-conditionally (meaning just not dealing with that particular issue) rather than unconditionally, to start with. I am happy to continue to discuss the subject of conditional probability on the arguments page with anyone who is interested. Martin Hogbin (talk) 18:22, 9 January 2010 (UTC)

I've mentioned this before (perhaps I should look for a published source supporting this view), but IMO at least one reason many people disbelieve the typical unconditional answer is because it does not have the same form as how people generally interpret the problem - in particular, the fact that the host has opened a particular door completely vanishes. Most people (the K&W study does support this) internalize the question as asking what is the probability in a specific case, e.g. given the player picks door 1 and the host opens door 3. The unconditional solution isn't restricted to this case. I think a solution that addresses BOTH the unconditional situation and the conditional situation is likely to be far more convincing than only an unconditional solution. -- Rick Block (talk) 19:50, 9 January 2010 (UTC)

This really is OR. K&W showed that door numbers generally confused people and that people generally did better when they were not involved. My take on this is that the problem is more easily explained and understood without door numbers. Just as we do now to start with.

I am sure that nobody finds the problem hard just because they think it might matter which door the host opens. Most people miss this point completely, and assume that it cannot possibly make any difference (whereas in truth it could possibly make a difference but does not actually do so, with consistent assumptions). I certainly did not imagine that the door opened by the host could matter, and it is not even mentioned in the 'Three prisoners problem'. More to the point there is no source that I am aware of that claims that this possibility is what makes the problem difficult. Martin Hogbin (talk) 20:14, 9 January 2010 (UTC)

Though I kinda agree with you here, I do on the other hand not mind having 2 different solution sections (unconditional/simple and conditional/detailed mathematical analysis) - in particular if this provides compromise everybody might be live with. If one takes a step back from what he might consider the "optimal" version of article from his perspective but rather thinks of an acceptable or sufficient version (not being optimal to oneself but acceptable to all involved editors and readers in general), then this should be the way to go imho.

Also separating "easy" from the "hard" is definitely good idea. This is a general organizing principle for a well written article/book/whatever anyhow. The fact that this approach might be convenient for Martin potential POV ("it has to be solved unconditional") is irrelevant, since the advantage of that approach are real and having nothing to with Martin. The German probability book, I've mentioned occasionally (Henze) for instance pursues exactly that approach. It mentions MHP in the introduction as an example for probability theory or problems in the public domain and then later gives the unconditional solution. Much later after having laid some theoretical groundwork and having introduced conditional probabilities he revisits the problem for a more detailed analysis and a conditional solution. I see no reason why the our article can't do the same.--Kmhkmh (talk) 20:42, 9 January 2010 (UTC)

Maybe we are moving towards some kind of acceptable compromise here. I wonder what others think? Martin Hogbin (talk) 21:15, 9 January 2010 (UTC)

I agree to most suggestions, especially to the terms 'Simple solution' and 'Conditional solution'. We must remember that the 'Monty Hall problem' is basically a paradox simply solved by the popular solution, and that only specific problem statements, like in Parade, or specific interpretations of them, need conditional solution. This is another argument for starting with the simple solution. Also indeed, 'Sources of confusion' should really be (far) below 'Aids to understanding'. But I am getting into trouble as to where chapters should be, and how they should be structured. It tends to become rather POV or endlessly arguable if we don't use any objective structure. As Glkanter proposes: use chronology. I think it may be good if the whole article is made up that way, which will naturally present the entire scope as it grows in complexity and perspectives. I do understand that most 'normal' subjects are better off with a simple definition and explanation first, but if there's one thing this issue has proven, it is the fact that there is no single truth here. There's lots of different questions with lots of different answers and lots of different methods. The introduction may spend some words on it, to explain the choice for chronology. This should really reduce our disagreements! What is important in this scenario, is to have an exhausting 'contents' tree, from which one can easily jump to the section of choice. The contents section should give enough description to have a fair idea of what it's about. Heptalogos (talk) 22:01, 9 January 2010 (UTC)

Chronological, but none of those 'pointy, POV dates' will be allowed. Glkanter (talk) 22:15, 9 January 2010 (UTC)

Chronology contradicts my suggestion and what Martin seems to be indicating as well. So you cannot support the above (organizing by content and difficulty level) and wanting a chronological organization for the sections, it is either or here. Again I'm getting the impression we are moving 1 step ahead and 2 back. As soon as there seems to be some reasonable common ground, another issue is raised or something rather inconsistent statement is put forward as well. --Kmhkmh (talk) 23:03, 9 January 2010 (UTC)

As a matter of fact I can support changes to the current structure as well as favoring another structure. It's an expression of flexibility which enables reinforcement of common ground, while at the same time offers an opportunity to improve significantly in the long term. Although I am very aware of the extra energy it takes for the time being. If we all keep getting tired, I think we indeed keep getting tired, for a much longer time. Heptalogos (talk) 23:21, 9 January 2010 (UTC)

Why Didn't Whitaker Write To Morgan, et al, Instead?

Because they don't have a general interest column read by millions every week published as a supplement to hundreds of newspapers across America.

In her letter to The American Statistician vos Savant directly tells Morgan her interpretation. She tells them *her* interpretation of Whitaker's letter. But these guys claim to know these things better than vos Savant herself. She had helped to educate over 1,000 PhDs on this paradox, she says. But not this Professor Morgan and his 3 assistants. They are different. Or, having spent 15 months on this article, maybe not so different.

And if Whitaker is fictional? Then vos Savant and her publisher made him up. And they know what they meant to ask.

So, back to the article. How will the article cover the aspect of Morgan calling all simple solutions 'false'? That means Selvin, vos Savant, Adams, Devlin, etc., etc. all are wrong. Sad state of affairs in academia these day. Hasn't been the same since 1991, really. All because Morgan claims a game show host can tell a contestant where the car is.

Will it lead off the solution section? Go last, but bold? Mentioned after each of the other solutions? I want to know. Where else will this revelation be placed in the article? How many times? Because Selvin already did the conditional solution, in 1975. What is it that Morgan's paper is noteworthy for then? The only thing left is calling the simple solutions 'false'. I guess countless Professors, etc. haven't gotten the word on this paper, yet, because they still teach it.

Morgan says this: "...(the producer)...is free to consider a variety of factors in determining how the game will be run." That's correct. Including all applicable laws. Game show hosts and producers do not tell contestants where the car is. Glkanter (talk) 13:55, 10 January 2010 (UTC)

What is YOUR suggestion? -- Rick Block (talk) 14:50, 10 January 2010 (UTC)

What I understand, and why, I have made abundantly clear. I have, and will continue to share my views with the consensus of editors.

But, you're the long-standing defender of Morgan's paper. What do you think are the new issues the paper brought forth in 1991? Why is it significant? Glkanter (talk) 15:39, 10 January 2010 (UTC)

I have just added a section [4] to my Morgan criticism page, which shows the question that Morgan have actually answered. I would be very interested to hear from both of you whether you agree that Morgan's paper actually addresses the question that I have stated. This may stop some pointless argument. Please leave your comments on the associated talk page. The footnotes are simply to address Morgans claim to have given a solution based only on information given in the problem statement. For the moment, do you both agree that the Morgan paper is a fair answer to my stated question? Martin Hogbin (talk) 15:08, 10 January 2010 (UTC)

I agree that your problem statement is one wording of what Morgan et al. calls the "vos Savant" scenario. You might note that Gillman addresses this same problem as well. -- Rick Block (talk) 16:30, 10 January 2010 (UTC)

It looks as if we can agree on the exact question that Morgan actually answer. Martin Hogbin (talk) 17:09, 10 January 2010 (UTC)

You are being rather kind to Morgan though. The fail to mention in their paper that: the car is originally randomly placed, the player chooses randomly, the host can never open the player's originally chosen door, and the host must always offer the swap. Perhaps they take these rules to be somehow transcluded from vos Savant's analysis or elsewhere. Martin Hogbin (talk) 17:43, 10 January 2010 (UTC)

Falk, also. It's one of the versions Krauss and Wang address, too. -- Rick Block (talk) 16:34, 10 January 2010 (UTC)

Glkanter, do you agree that Morgan answer my stated question correctly? Martin Hogbin (talk) 17:11, 10 January 2010 (UTC)

You can find the question that they answered here [5]. Note that I do not claim that this is the MHP. In fact I assert that it is not. Martin Hogbin (talk) 23:53, 10 January 2010 (UTC)

Does anyone object to Formal Mediation?

"Mediation is a voluntary process in which a neutral person works with the parties to a dispute. The mediator helps guide the parties into reaching an agreement that can be acceptable to everyone. When requesting formal mediation, be prepared to show that you tried to resolve the dispute using the steps listed above, and that all parties to the dispute are in agreement to mediate. Mediation cannot take place if all parties are not willing to take part. Mediation is only for disputes about Article Content, not for complaints about user conduct."

Formal Mediation

Please indicate below:

I am willing to take part in Formal Mediation

Glkanter (talk) 15:03, 18 December 2009 (UTC)

Rick Block (talk) 16:03, 18 December 2009 (UTC)

Martin Hogbin (talk) 16:34, 18 December 2009 (UTC)

JeffJor (talk) 16:35, 18 December 2009 (UTC)

Gill110951 (talk) 13:22, 20 December 2009 (UTC)

Colincbn (talk) 02:26, 22 December 2009 (UTC)

Nijdam (talk) 17:13, 11 January 2010 (UTC)

I am not willing to take part in Formal Mediation

Thank you. Glkanter (talk) 15:03, 18 December 2009 (UTC)

Nijdam posted an edit to this page nearly 24 hours ago. How much longer do we wait for him to indicate his decision? Glkanter (talk) 11:56, 21 December 2009 (UTC)

Nijdam posted an edit to this page over 48 hours ago. Still no comment or signature on this Formal Mediation. Can we move on without his signature? Is anybody else ready to move this forward? Glkanter (talk) 13:11, 22 December 2009 (UTC)

I thought we were proceeding. This seems much more important than the RfC below. Martin Hogbin (talk) 13:15, 22 December 2009 (UTC)

Well, we were. But there's no Formal Mediation unless everyone agrees to it. I see us as stuck, for no apparent reason.

Yes, that RfC is a distraction. Unfortunately, for me, anyways, it has to be dealt with seriously. I knew this was coming the minute he vandalized my talk page edit, and begged Dicklyon to let me edit my own section as I had written it. All to no avail. So it goes. Glkanter (talk) 13:23, 22 December 2009 (UTC)

The parties that need to agree are the parties listed in the request for mediation. As far as I know this does not exist yet. After creating such a request you notify the named parties about it, see Wikipedia:Requests for mediation/Guide to filing a case. Pre-agreeing to mediation here is nice, but ultimately irrelevant. The parties named in the informal request were Martin, Jeff, Glkanter, Nijdam, Kmhkmh, Father Goose, and myself. I've been assuming Glkanter or Martin were working on a formal request. If this is not the case I'd be willing to write one up, although if someone else would prefer to do this that's fine with me. I might suggest Martin. -- Rick Block (talk) 17:09, 22 December 2009 (UTC)

It would have been nice of you to present this view either when you signed, or instead of signing, back on the 18th. Why go to all the effort of creating a request until Nijdam, and Kmhkmh indicate they will go along with the decision? I have serious doubts that Nijdam will agree. How hard can it be for them to say? Just more stalling of the inevitable. Excellent job this time, Rick! Glkanter (talk) 17:23, 22 December 2009 (UTC)

Based on the level of hostility you've exhibited toward me, I thought you would prefer someone else write up the mediation request. That's what this edit (from last Thursday) meant, where I provided a link to the appropriate procedure. I assumed you'd read this and that you or Martin were working on it. Per below, Martin is OK with me writing it up. Are you? -- Rick Block (talk) 20:09, 22 December 2009 (UTC)

Martin also wrote this in the very next sentence in the paragraph (below): "If you want me to do it let me know and give me some clues what to do." I like that better, thank you. I don't see myself as hostile. Just honest. And fed up. Glkanter (talk) 20:23, 22 December 2009 (UTC)

Rick, I am not familiar with the procedure, and would be quite happy for you to do it. If you want me to do it let me know and give me some clues what to do. Martin Hogbin (talk) 17:56, 22 December 2009 (UTC)

Informal mediation still a possibility

I note that User:K10wnsta has offered to serve as an informal mediator for the case at Wikipedia:Mediation_Cabal/Cases/2009-12-06/Monty_Hall_problem#Discussion.

If nobody had an objection to proceeding with the case at that venue, it would probably allow things to get under way sooner.--Father Goose (talk) 04:19, 24 December 2009 (UTC)

Re: Wikipedia:Mediation_Cabal/Cases/2009-12-06/Monty_Hall_problem

In my brief overview (I haven't delved into archives), the discussion appears to have remained civil and, more important, cooperative in seeking a means of negotiation. If everyone is willing to excuse the sluggish response to your request for informal mediation (blame it on the holidays ;) ), I'd be happy to work with you in resolving the dispute. However...
You waited over two weeks for assistance at MedCab and, procedurally, are justified in pursuing formal mediation. If someone has already applied significant effort in preparing for that, I understand if you wish to continue in that direction.
--K10wnsta (talk) 20:29, 25 December 2009 (UTC)

There are 11 archives to this discussion, covering 6 years. While technically 'civil', it is very contentious. I appreciate your offer to help, but I'm not sure there would be a result worth the time investment you would need to make. Honestly, if I may, your original comment about this puzzle being 'mathy' did not create confidence in this reader. And I'm the least Mathematics educated person on this talk page.

But, this is just one person's opinion, offered in good faith. I'd hope I can support whatever the consensus decides on your generous offer. Glkanter (talk) 17:33, 26 December 2009 (UTC)

Hehe, well, the 'mathy' description stemmed from reading about a dispute involving 'mathematical sources' and 'conditional probability' in what appeared to be an article about the host of a campy game show. I couldn't fathom how the subjects were related (and even questioned my recall of the host's name). It was certainly not intended to express any personal disdain for mathematics - in fact, I enjoy and excel in most math-related fields (notably algebra, geometry, and statistics).
--K10wnsta (talk) 21:07, 28 December 2009 (UTC)

As one of the long term involved editors I would welcome some mediation. I am not sure what your understanding of maths and probability is like but the Monty Hall problem has been described as the world's most tenacious brain teaser. It will therefore be necessary for you to first get your head round the basic problem, if you are not already familiar with it. Note that nobody here disagrees with the basic numerical answer under the 'standard rules'.

If you proceed with mediation, it would be interesting for you to start by reading the article (or possibly a previous version ) through to see how good an understanding of the problem it gives you before consulting other sources or talking to anyone about it, as the debate is essentially about how well this article addresses the basic problem. You currently have the advantage of seeing this article as a newcomer but once you have been drawn into the debate you will quickly lose that viewpoint. This suggestion is not intended to be an attempt to 'get in early' with my POV. Perhaps someone on the 'other side' could confirm that they would be happy for you to take this approach. Martin Hogbin (talk) 11:02, 28 December 2009 (UTC)

I have read the article and now understand how Monty Hall could be associated with conditional probability (see my reply above). I haven't yet delved into the actual dispute as I prefer remaining sequestered from it until we get past the informal formalities (eg. all interested parties agreeing to participate in the mediation process).
--K10wnsta (talk) 21:07, 28 December 2009 (UTC)

Formal mediation

The informal mediator bailed, so the next step is formal mediation. The guts of the request are the sections I've put up at User:Rick Block/DraftMed. Before filing the request, I'd suggest anyone who's interested take a look. There are separate sections for issues the "filer" is asking to be mediated as opposed to issues other parties want mediated (feel free to add whatever you'd like). I don't care who actually files it (it really shouldn't matter), but have filled this out as if I'll be the one doing the filing. If anyone strongly objects to this we can rearrange things so someone else will be listed as the "filer" (but then whoever this is will have to actually file it at Wikipedia:Requests_for_mediation/File, and notify the involved parties). -- Rick Block (talk) 02:48, 5 January 2010 (UTC)

Unlike informal mediation, formal mediation will be rejected unless all parties named as involved parties agree to mediation. Please indicate here whether you consider yourself to be an involved party, and whether you're willing to participate in mediation. For more on what is involved, please see Wikipedia:Mediation Committee/Policy. If you consider yourself to be an involved party and refuse to participate, the mediation committee will refuse to take the case. At a minimum, I consider myself, Glkanter, Martin Hogbin, and JeffJor to be "involved parties", although Nijdam, and Kmhkmh have been fairly involved in the past as well. Naming more, particularly anyone who is not willing to participate in the process is extremely counterproductive. -- Rick Block (talk) 05:22, 5 January 2010 (UTC)

Well, it's a 'chicken or the egg' kind of thing. Just because you listed someone doesn't mean he will participate/accept the results. I tried to do a 'pre-agree' and after a few days passed, you said that wasn't how it works. The people I added have been participants in the last month or two, and should be offered the chance to be involved. Almost all of them were either part of the consensus or agreed to take part in the formal mediation when I asked.

But I agree, we don't want a named person bringing the formal mediation to a halt. Has Nijdam indicated his willingness to participate to you? Glkanter (talk) 13:08, 5 January 2010 (UTC)

Nijdam has not indicated anything to me. Any pre-agreement is not official. I've trimmed the list back to those who previously indicated a willingness to participate, plus Nijdam and Kmhkmh (I'll ask them both directly). If neither of them indicate they're willing we should talk about how to proceed. -- Rick Block (talk) 14:37, 5 January 2010 (UTC)

I'm willing to take part in formal mediation. Nijdam (talk) 16:43, 11 January 2010 (UTC)

I have posted an edit at Seems selective regarding the invitee list. Glkanter (talk) 16:21, 6 January 2010 (UTC)

I cannot claim to be involved. Although I wanted to participate, lately I have found myself so busy with other things that I have not had the time to dedicate to trying to help with this thorny problem. Good luck and good grace to all, though.--Father Goose (talk) 08:08, 5 January 2010 (UTC)

I'm not sure (and it perhaps depends on the mediator and/or the case), but I think even if you're not listed as an involved party you can generally participate. -- Rick Block (talk) 14:37, 5 January 2010 (UTC)

I would like to participate. Heptalogos (talk) 20:03, 5 January 2010 (UTC)

Do we need it?

Despite continuing discussion and some disagreement, I think there has been a move towards increased understanding between all the parties involved. We should also all congratulate ourselves on keeping the discussions civil and avoiding edit warring.

Now is the time to move on and start improving the article. Some of us have written down our objectives for the article for the mediator and they do not look that far apart. With goodwill and some concessions on both sides we should be able to make considerable progress. We all need to give a little and be prepared to drop some of the finer points of our arguments. For example, I believe that there is no rule telling us that the K&W formulation must be treated conditionally (and I am happy to continue this discussion on the 'arguments' page) however, I am prepared to accept a statement along the lines of, 'strictly speaking this problem is one of conditional probability', if appropriately placed.

I appreciate that I am not a neutral party in all this but I am going to start a new section below, which I will call 'Self-mediation', just to see if we can find things that we agree on. Martin Hogbin (talk) 09:59, 5 January 2010 (UTC)

What EXACTLY was the original Parade problem statement?

It seems there is some variations in what the actual problem said. RussAbbott had recently changed the wording of the problem in a minor way, apparently to make it read better to him. Since it is supposed to be a quote, I went off to the "external link" for MvS's web site, as listed at the bottom of the article, and cut-and-pasted what she lists as the original question. Here that is, verbatim:

Suppose you're on a game show, and you're given the choice of three doors. Behind one door is a car, behind the others, goats. You pick a door, say #1, and the host, who knows what's behind the doors, opens another door, say #3, which has a goat. He says to you, "Do you want to pick door #2?" Is it to your advantage to switch your choice of doors?

I did post that change with it a snide comment, referring to how Morgan had significantly changed the meaning of the problem by rewording it. I guess Rick took offense, and "changed" it back to what he says appears in a "copy of the column as it was published." That consisted of some insiginicant changes: two in puncuation (the first period becomes a colon, and the first comma in the second sentence becoems a semicolon), and using "No." instead of "#" to mean "number." But two minor wording changes were also included, inserting the words "then" in "He then says to you," and removing "of doors" from the end.

The problem is, I don't have a copy of the column (it would be helpful to post it, Rick) but I have seen numerous variations in the alleged "quotations" of this problem in literature. And what I consider to be the best source amid conflicting ones, MvS quoting herself, agrees with my version:

1. MvS's book The Power of Logical Thinking is exactly as I listed it, except it uses "number" instead of "#". I consider that to be just a change in editorial style, maybe even done without her knowledge.
2. Rosenhaus quotes that exactly; but does attribute it to the book, and not the column.
3. Grinstead and Snell substitute "Monty Hall's Let's make a Deal!" for "a game show," and "Monty" for "he" later on. They also move "You're given a choice of three doors" to the second sentence, separating it from what I listed with a comma. And they don't use any form of "#", just listing the bare number.
4. Krauss and Wang use a semicolon where Rick did, and capitalized "Number" wherever it appears in place of "#". But they also added Rick's "then" and changed "pick door #2" to "switch to Door Number 2".
5. Morgan takes significant liberties with the quote, which are discussed elsewhere. They include using "No." and Rick's "then."
6. Are there any others?

My question is, is there an internet source to verify the actual (not quoted) version? And if not, shouldn't we trust MvS's own quote of herself over all others, since there seems to be a inexplicible tendency to misquote it? JeffJor (talk) 17:54, 8 January 2010 (UTC)

Oh for Christ's sake, you think I'm LYING? I have a printout from a microfilm reader of the Sept 9, 1990 edition of Parade Magazine (as published with the Knoxville News Sentinel). The quote as it has been in the article for quite a long time is exact (including punctuation and capitalization). I am NOT going to scan the copy I have and post it. If you don't believe me, you can verify this for yourself (go find a library that has a microfilm copy of a newspaper that included the supplements). -- Rick Block (talk) 03:00, 9 January 2010 (UTC)

No, I don't think you are lying, Rick. I said no such thing, and had no intent to imnply it. But I had actually cut-and-pasted my version from a direct source, so I felt about the same way you do about the edit you made. And I didn't go on to accuse you of calling me a liar. The fact that I didn't put it back to what that source says, and asked for verification and discussion, shows that I am exhibiting a great deal more integrity than you are blaming me for.

And, I do think (1) That microfilm of a newspaper can be mis-read when it comes to the difference between a comma and a semi-colon; (2) That sometimes we see what we want to see even if it isn't there, and (3) that it just might be possible that some editors - like, say, those in Knoxville - "corrected" what they thought was incorrect usage. We actually have evidence of these sorts of thing, since Morgan grossly misquoted it and the internet reference and the on-line version of MvS' book contain at least one such change. Again, I'm not accusing you of any of these things, I'm saying we can't know unless we can all see your source.

The point is, I don't know what was originally published; but we have an easily-verifiable source that anybody can see, and that doesn't require looking at microfilm and/or wondering if some phantom editor changed something. And since you were the one who took it upon yourself to make those insignificant changes (unless you think there is a significance?), yes I do think the onus is on you to prove it is correct when MvS herself quotes it differently. We can change the reference to her book, which is about the column, if you desire, and remove all these difficulties. Or keep it as is, and reference Parade Magazine, as published in the Knoxville News Sentinel.

And this digression kinda echos the entire problem with this article. It seems there are multiple versions of "truth," and the discussion tends to be more centered on "Why can't all you idiots see the truth the way I do?" rather than handling the different "truths" for what they are - truths that are based on different sets of assumptions. Morgan, et al, did solve an actual ptoblem; but it clearly (sources, including MvS, say so, Rick; and the only significant difference in their interpretation is whether door numbers are important, unless you know of anoither. Everything else they criticze is what they say MvS assumed, which is not a difference in interpretation) isn't the one Marilyn intended, or what her problem (which she formatted, not Craig Whitaker) sematically says. JeffJor (talk) 17:15, 11 January 2010 (UTC)

I agree that it is important that we get this right. Just out of interest, does anyone know if Craig Whitaker was a real person? If so has he ever made any comment about the subject? Martin Hogbin (talk) 18:22, 8 January 2010 (UTC)

Per above, if you think it's not right feel free to verify it yourself. Craig Whitaker is (well, at least was) a real person. My understanding from a reliable source (that I will not divulge, which means it's not a "fact" as far as Wikipedia is concerned) is that some reporter (surprisingly, not John Tierney from the NY Times) tracked him down and that what appeared in Parade is not exactly what he wrote (if that's where you're going) but omitted that he thought the answer could be 1/2 or 1/3 depending on what was assumed. -- Rick Block (talk) 03:00, 9 January 2010 (UTC)

Since I, too, live in Columbia Maryland, I looked him up in the phone book. I found no Craigs. And I didn't want to bother the ten-or-so Whitaker families to ask, since it is likely he graduated from one of our High Schools about fifteen years ago. And if we know it isn't exactly what Craig wrote (as per Rick Block's recollection), we need to remove his name from the reference list and make it refer to MvS. Quote her, quoting Craig, and don't imply Craig is an expert at anything. JeffJor (talk) 17:15, 11 January 2010 (UTC)

I was asking just as a matter of interest, I do not doubt any of what you say. I just thought that, if he could be contacted, it would have been interesting to ask him what exactly he had in mind. It did just occur to me that he might have been someone made up by the editor or vS. It is good to know that he is real. I wonder what the makes of the furore that his question created.

Similarly I do not think that Jeff was accusing you or anyone else of anything. Because the exact question is important in statistics, both Jeff and I think that it is necessary to get the original question exactly right. Thank you for confirming this. The matter is of particular importance to some of us because of the way that, in our opinion, Morgan morphed the question into a different one. Martin Hogbin (talk) 10:34, 9 January 2010 (UTC)

What is the best internet source available? Is it the MvS site? Is the Parade edition available in a public library? Do we have arguments about difference between both? If so, what is the WP policy about reliability of non-internet sources? Heptalogos (talk) 14:11, 9 January 2010 (UTC)

Not every citation needs an online source although I agree this is desirable. The article currently cites Whitaker's letter in Parade as this is the definitive source. Martin Hogbin (talk) 15:52, 9 January 2010 (UTC)

The policy regarding sources is Wikipedia:Verifiability with more detailed guidelines at Wikipedia:Reliable sources, and you basically have your question backwards. From Wikipedia:Reliable sources#Quotations: Quotations should be cited to the original source if possible. Parade is a magazine supplement published with hundreds of newspapers (in the U.S.). Microfilm copies of newspapers are available in many public and university libraries. For a long time this quote was indirectly referenced ("as cited by") to an article by Bohl et al. in the 1995 edition of Journal of Recreational Mathematics. As part of the last featured article review I did a large amount of referencing work (one of the concerns was "Huge sections of unsourced content") and as part of this chased down an actual copy of the Sept 9, 1990 edition of Parade (as I mention above).

This entire thread is grossly insulting. I reverted Jeff's change because it was wrong, not because I took offense to his snide comment about Morgan. I really couldn't care less what he thinks about Morgan (or, at this point, pretty much anything else). What I said in my edit summary was "revert to the actual quote - I'm looking at a copy of the column as it was published". In this thread he's both attributing a motivation for my change that he simply made up (which is bad enough) and calling me a liar. Martin echoed Jeff's insult "I agree that it is important that we get this right" (what about "I'm looking at a copy of the column as it was published" is not clear???). And you (Heptalogos) are questioning what the sourcing policy is (as if any internet source could possibly be more reliable than the actual magazine).

I'm trying very hard not to say something grossly insulting in return here. Let's just say that I think all three of you should apologize. -- Rick Block (talk) 16:25, 9 January 2010 (UTC)

+1 I agree that this thread is entirely pointless and somewhat surreal. I'd suggest to simply ignore it.--Kmhkmh (talk) 00:42, 10 January 2010 (UTC)

I can see why Rick has taken exception. His edits, his research, and his very integrity have, in his mind, been attacked, without provocation or fact-based support.

Welcome to my world, Rick! Rather than get an apology, I had 2 guys file an RfC on me for a much more offensive situation than this. Aint Karma a b----, Rick? Glkanter (talk) 16:45, 9 January 2010 (UTC)

Yes, there's an RfC open on your behavior. Your post here is yet another example of your bad behavior. I invite anyone reading this to add their opinions to Wikipedia:Requests for comment/Glkanter. -- Rick Block (talk) 17:28, 9 January 2010 (UTC)

Rick, you are taking this far too personally. I, and I suspect Jeff, just thought that there was some doubt as to the exact wording of the problem, looking at the various sources on the subject. You have confirmed that the current wording is exactly as it is in Parade magazine, some good work on your part. That is the end of the matter as far as I am concerned.

Heptalogos was, I think, just suggesting that some online references would be good (if there are any for the exact quote) so that readers and future editors can verify the problem statement for themselves. Martin Hogbin (talk) 17:48, 9 January 2010 (UTC)

Since the reference is to the printed magazine, it can't be verified definitively against any online source, and so the question of what online source is the best to use to verify the quote is correct is meaningless. At this point, Wikipedia is as good as any other online source - actually, IMO, better since anyone is free to verify it with their own eyes (as I have done) and then correct what it says. In addition, it's a featured article meaning many editors have closely looked at the entire article so the chances that someone has actually verified the quote here is correct are quite high (this applies to any featured article, not just this one).

And, as far as taking it personally, I think I'm taking it in the spirit in which it was intended. -- Rick Block (talk) 18:54, 9 January 2010 (UTC)

Let's stay with the facts and strip them from complex emotions. This is what I understand of it:
1. The Whitaker quote in this article is different from the quote on the MvS site, which is claiming to be an original Parade publishment.
2. A WP-editor, senior Admin, claims to have seen the original Parade article which is exactly the same as in the article.
3. Quotations should be cited to the original source if possible.
4. Any internet source is less reliable than the actual magazine.
5. We have two internet sources quoting the original source: senior Admin and MvS.com.
6. Senior Admin is more explicit in the claim that his quote is very exact.
7. In absence of written policy, do we have any decisional law (jurisdiction) on this? Heptalogos (talk) 20:03, 9 January 2010 (UTC)

It seems to me now, from this source, that Marilyn is about just as explicit in her claim of excellent quoting. An interesting sentence in that, which may even give a hint towards the cause of apparent disparity, is: "Here are both (question and reply), as they first stood". Indeed, MvS site introduction states: "This material in this article was originally published in PARADE magazine in 1990 and 1991". Rick, is the Sept 9, 1990 edition of Parade Magazine, the first one about the problem? Heptalogos (talk) 22:45, 9 January 2010 (UTC)

'...then perhaps we would' and the page stops! What?! We would 'what'?!? I gotta know!

These guys are sorry excuses for whatever it is they are. And we've got the 5th Beatle right here on Wikipedia. Glkanter (talk) 23:05, 9 January 2010 (UTC)

Hard to find the complete PDF, but here's another interesting source: [6]. Heptalogos (talk) 23:45, 9 January 2010 (UTC)

The initial column was Sept 9, 1990. Well, at least, that's what I'm claiming. How about if you verify what the magazine actually says yourself? Just go to a library and look it up. There's a list of newspapers that currently carry it here. Call your local public library and ask if they have microfilm of any of these newspapers (from 1990), including the Sunday supplement sections (specifically Parade Magazine). And, yes, I'm saying in her reply to Morgan et al. vos Savant (like Morgan et al.) trivially misquoted her column. She used a comma rather than semicolon following "Behind one is a car", used "#" rather than "No.", and dropped "then" and added "of doors" in the last sentence.

JSTOR makes only the first page of the references it carries available for free. I have the next page of this one as well. I could tell you what it says, but given how absurd this thread has become I suggest you go to a library (probably a university library for this one) and look it up yourself. -- Rick Block (talk) 01:27, 10 January 2010 (UTC)

On my first visit to the US I might take a look in Parade. In that case I should sign the source witness list, because when I leave here, another editor may ask the same question. I am trying to understand how WP works. But you are convincing and the change seems to be a cosmetic improvement. It makes sense. Marilyn is a proud lady. Heptalogos (talk) 10:18, 10 January 2010 (UTC)

You could try to obtain a reprint of the Parade column as well, see [7]. However, I'm not sure if a reprint obtained this way would necessarily be identical to what was originally published. Another idea would be to find a library (possibly a university library) that might have microfilm of a major US newspaper that carries the magazine. Possible examples would be the Chicago Tribune or the Los Angeles Times. If you're a student or faculty member at a university I'm sure your university library could obtain a copy for you, and if you're not at a university then the reference librarian at any decent public library should be able to help. -- Rick Block (talk) 17:07, 10 January 2010 (UTC)

Rick, I have to take issue with one point you make above. You say, '...vos Savant (like Morgan et al.) trivially misquoted her column...'. I agree that vos Savant's misquotation was trivial but Morgan's was not. It was part of a subtle process that changed the question into something different.

Anyone who has studied the MHP, either here or elsewhere, must know that the exact question is important. Things which at first sight might seem irrelevant turn out to make a critical difference, for example, most people are surprised to be told that it makes a difference whether Monty knows where the car is.

The Morgan misquotation starts to move the problem statement from saying that the host opens a door with and explanation of what that might mean, to the host opens door 3, where it is clearly the intention of the question to specify which door the host opened. These things are important in probability problems and Morgan's misquotation is quite inexcusable. Martin Hogbin (talk) 10:45, 10 January 2010 (UTC)

This New Archiving Taking Place

I just took a look at archive #12. I think sections are being moved, but not in the order they were created. So the archive does not preserve the original discussions as they took place.

Would anyone mind confirming this? Is this the way archiving should work? Glkanter (talk) 13:05, 11 January 2010 (UTC)

I've asked the bot owner. See user talk:Misza13#Archive order. -- Rick Block (talk) 19:48, 11 January 2010 (UTC)

Thanks for doing that, Rick. I just read his response. He says that's the way it's supposed to work. I'm only experienced in 'data' archiving, not 'conversation' archiving. I really don't know, but it seems like it defeats the purpose. It never occurred to me that MHP archives 1 - 11 were built that way. Glkanter (talk) 00:39, 12 January 2010 (UTC)

Door numbers matter

Consider the following game. Roll a (fair) dice, call the outcome X. Put as many white balls as the outcome in an urn and complete with black balls till 6 balls all together. Then before you draw a ball from the urn, predict its colour. Then draw a ball; if your prediction was right you win a car, otherwise a goat. What will be your prediction? Nijdam (talk) 17:04, 11 January 2010 (UTC)

I suggest that we continue this on the arguments page, I have copied your question there. Martin Hogbin (talk) 17:43, 11 January 2010 (UTC)

So, What Are The Significant Events, And Why, Of The Monty Hall Problem Paradox

Some people certainly didn't like the chronology I posted on the this talk page. Heck, it was vandalized, then they put up an RfC/U on me because of it.

And when I added the year to the Solution sections, an edit war damn near broke out. And editors turned on editors.

So, who, what, where, when, and why? But especially this Morgan paper. It seems its only contribution is to use an unimaginably wide paint brush to call the unconditional solutions false. Glkanter (talk) 13:32, 11 January 2010 (UTC)

Glkanter, if you would answer whether you think Morgan have answered this question correctly, it might throw some light on the subject. Martin Hogbin (talk) 13:47, 11 January 2010 (UTC)

I looked at it earlier this morning. First, I would need to know why it even matters. Otherwise, I just can't bend my brain to comprehend that stuff. 6 footnotes? Sorry, it's just not an area I'm strong in, or that I have much interest in. Nor do I think my opinion on that OR is relevant to editing the article Glkanter (talk) 13:59, 11 January 2010 (UTC)

Ignore the footnotes for the moment, just read the question. I am trying to reach some kind of resolution over your, often repeated point, 'Suppose you're on a game show'. Note that my question does not suggest that perspective, it simply asks you to solve a problem based only on the information given in the problem statement. Do you agree that Morgan have answered that question correctly? Martin Hogbin (talk) 14:19, 11 January 2010 (UTC)

What's the point? Who are you trying to influence? And why? Just look at Nijdam's newest contribution to the discussion. But they won't give a straight answer to 'Is The Contestant Aware?' or 'How Can Huckleberry Do Better By Knowing The Equal Goat Door Constraint?'. I prefer to expose intellectual dishonesty, rather than enable it. Glkanter (talk) 17:12, 11 January 2010 (UTC)

See Monty Hall problem#History of the problem. Morgan et al. is one of the "Over 40 papers have been published about this problem in academic journals and the popular press". Although the history section doesn't say this, it is (to my knowledge) the first paper specifically addressing the problem published in an academic peer reviewed statistics journal. -- Rick Block (talk) 19:55, 11 January 2010 (UTC)

I guess it's also the only published paper on the issue that vos Savant publicly replied to. Heptalogos (talk) 20:47, 11 January 2010 (UTC)

How do both of your answers correspond to either advancing MHP Paradox knowledge, or following Wikipedia principals? I don't see them doing much of either. Glkanter (talk) 21:20, 11 January 2010 (UTC)

I'm quite sure that my obvious answer to you will be of no benefit, so I'll leave it here. Heptalogos (talk) 22:05, 11 January 2010 (UTC)

Not if you don't post it. I have no idea whatsoever you might reply. Glkanter (talk) 22:49, 11 January 2010 (UTC)

Yes, I was anticipating your response, Rick. But you chose not to answer this back then. So, tell me now, how and why is Morgan the Uber-Monty-Hall-Problem-Wikipedia-article-source? Glkanter (talk) 21:31, 11 January 2010 (UTC)

Glkanter, I hate the Morgan paper as much as you do, but unfortunately we are stuck with it to some degree, for the reasons given above. The important thing to me is to see it for what it is, a solution to a somewhat contrived and restrictive formulation of the problem that does not represent the MHP as most people understand it. Martin Hogbin (talk) 23:01, 11 January 2010 (UTC)

Of course. It's published. I said that just yesterday. It has no new point to make (except 'as we contrive it, all unconditional solutions are false'), and with all the article's flaws there's no rationale for it being the focus of, and the 800 lb gorilla looming over every aspect of the article. Martin, we're unnecessarily just arguing with ourselves. By now you know that I understand that Morgan is published, and that gives Rick the ability to cling to it. We're being stifled from our legitimate ability to edit the article as the editorial consensus. What's left to say on the various talk pages, by either 'side'? Nobody is budging, clearly, and the article remains confusing and cluttered to the Wikipedia readers. Glkanter (talk) 23:18, 11 January 2010 (UTC)

(outindent) How is this paper "the focus of, and the 800 lb gorilla looming over every aspect of the article"? I said before (toward the end of #What If Morgan Had Used A Different Variant?) "As far as I can tell the only mention of this POV is in the "Probabilistic solution" section, the 4th paragraph in "Sources of confusion" and a paragraph in "Variants"." and you said "It's in every word except the intro and the Simple solution section." Perhaps we should go through the article paragraph by paragraph starting with "Sources of confusion". Here's a list (based on this version - current as I'm typing).

Sources of confusion, paragraph 1: no Morgan et al.

Sources of confusion, paragraph 2: no Morgan et al.

Sources of confusion, paragraph 3: no Morgan et al.

Sources of confusion, paragraph 4: a mention of Morgan et al.

Why the probability is not 1/2: no Morgan et al.

Increasing the number of doors, paragraph 1: no Morgan et al.

Increasing the number of doors, paragraph 2: no Morgan et al.

Increasing the number of doors, paragraph 3: no Morgan et al.

Chance of picking goat with the assumption of switching: no Morgan et al.

Simulation, paragraph 1: no Morgan et al.

Simulation, paragraph 2: no Morgan et al.

Simulation, paragraph 3: no Morgan et al.

Simulation, paragraph 4: no Morgan et al.

Simulation, paragraph 5: no Morgan et al.

Other host behaviors, paragraph 1:no Morgan et al.

Other host behaviors, paragraph 2:no Morgan et al.

Other host behaviors, paragraph 3:a mention of Morgan et al.

Other host behaviors, table:one of nine cases mentions Morgan et al.

N doors, paragraph 1: no Morgan et al.

N doors, paragraph 2: no Morgan et al.

Quantum version: no Morgan et al.

History of the problem, paragraph 1: no Morgan et al.

History of the problem, paragraph 2: no Morgan et al.

History of the problem, paragraph 3: no Morgan et al.

History of the problem, paragraph 4: no Morgan et al.

History of the problem, paragraph 5: no Morgan et al.

History of the problem, paragraph 6: no Morgan et al.

History of the problem, paragraph 7: no Morgan et al.

History of the problem, paragraph 8: no Morgan et al.

History of the problem, paragraph 9: no Morgan et al.

Bayesian analysis, paragraph 1: no Morgan et al.

Bayesian analysis, paragraph 2: no Morgan et al.

Bayesian analysis, paragraph 3: no Morgan et al.

Bayesian analysis, paragraph 4: no Morgan et al.

Bayesian analysis, paragraph 5: no Morgan et al.

Bayesian analysis, paragraph 6: no Morgan et al.

Bayesian analysis, paragraph 7: no Morgan et al.

Bayesian analysis, paragraph 8: no Morgan et al.

Bayesian analysis, paragraph 9: no Morgan et al.

Bayesian analysis, paragraph 10: no Morgan et al.

Bayesian analysis, paragraph 11: no Morgan et al.

Bayesian analysis, paragraph 12: no Morgan et al.

Let's count, shall we? I come up with 42 paragraphs (starting with "Sources of confusion") and 3 references to Morgan et al. Does this make it "the focus of, and the 800 lb gorilla looming over every aspect of the article" and "It's in every word except the intro and the Simple solution section"? If you're not suggesting eliminating Morgan et al. completely from the article (which you keep claiming is NOT what you're suggesting), then what are you suggesting? -- Rick Block (talk) 15:03, 12 January 2010 (UTC)

Last February I wrote that 5% of the article added value, the other 95% was waste. I understand Wikipedia's policy's better now, so I'm willing to double it. Make it 10%.

The very existence (and certainly the content) of Aids and Sources shows a pre-disposition to Morgan's claim that the simple solutions are all false and/or inadequate. The existence of all the variants, except the Forgetful (Random) Monty sprout from Morgan. Morgan gave license to these other contrivances you call variants that are more appropriate for a shell game than a game show. Only the forgetful Monty informs the contestant at the same time as the observer, by revealing the car. All the others rely on collusion or ESP.

So Selvin came up with simple and conditional in 1975. vos Savant came up with random (essentially Deal or No Deal) in 1990. Morgan contrives his stuff to claim the simple solutions are false in 1991. Bayesian? I have no comment. History? Shows that a poor job was done earlier in the article. Just call everything after the Solutions sections 'Diversions'. Glkanter (talk) 16:19, 12 January 2010 (UTC)

So, you're suggesting deleting the entire article following the Solution section? Is this the change you think there's a consensus for that you keep complaining you're being prevented from making? -- Rick Block (talk) 19:31, 12 January 2010 (UTC)

Nope. Not at all. The consensus of the editors agreed on the various benefits of the 3 proposals. I'll be one voice of that consensus that makes changes, eventually. Even Dicklyon made note in his comments of Wikipedia violations of UNDUE in the article.

So, why is Morgan significant? The paper strikes me like Paris Hilton. She's celebrated for being a celebrity. Morgan's paper is, in your estimation, anyways, important for where it was published. Not many of us share that POV. I don't believe Wikipedia's policies support that either. Glkanter (talk) 21:32, 12 January 2010 (UTC)

You apparently have a fundamental misunderstanding of Wikipedia:Consensus. Consensus applies to edits, not editors. It is definitely NOT the case that the article will be "open for editing" ONLY to some set of "consensus" editors. If this is what you're looking for you will never get it, by any process at Wikipedia. I keep asking you about specific changes, because that is the ONLY thing consensus applies to. This will perhaps become more clear to you if/when we get to formal mediation. -- Rick Block (talk) 15:32, 13 January 2010 (UTC)

Another Straw Man, aka Aunt Sallie. Don't you have anything better to do with your time? Glkanter (talk) 16:08, 13 January 2010 (UTC)

I'm just trying to understand what you're talking about. You say the article is rife with a pro-Morgan POV and at least imply you think everything after Solutions might as well be deleted. I asked if this is indeed what you are suggesting. Your reply says you're not talking about deleting everything but that you'll be part of a consensus that makes changes, making it sound like some "consensus of editors" will have carte blanche to make whatever changes they collectively want. What I'm saying is that this is not how it works and you're at least implying you know that. OK. So please say what specific changes you are suggesting. Take any one (or more) section I've listed above. Say "I, Glkanter, would like the pro-Morgan POV in section blah blah blah to be eliminated by changing <something> to <something else>". Thank you. -- Rick Block (talk) 18:08, 13 January 2010 (UTC)

Sure. Right after you answer the subject of this section's heading, 'So, What Are The Significant Events, And Why, Of The Monty Hall Problem Paradox', with special emphasis on Morgan, who did not come up with the conditional argument. Or 'Is the Contestant Aware of a Host Bias?'. Or tell me how your 'FCC guy' answer relates to 'How Would The Equal Goat Door Constraint Benefit Huckleberry?', and how it's relevant to the MHP Paradox article. It seems you're more eager to write what you think I think, rather than what you think. Glkanter (talk) 18:25, 13 January 2010 (UTC)

Significant events:

1) Selvin publishes the problem in a letter to American Statistician., giving an unconditional solution. In a second letter Selvin responds to mail he's received suggesting he's wrong, clarifying his assumptions (the host knows where the prize is and chooses randomly if it comes up) and includes a conditional solution.

2) Others publish the same problem. It becomes a standard example of conditional probability in statistics textbooks.

3) vos Savant publishes a version in Parade, and defends her answer with an unconditional solution and then, in response to continued criticism, clarifies all of her assumptions except that the host chooses randomly if given the chance (and says nothing about conditional vs. unconditional)

4) Morgan et al. publish what is apparently the first peer reviewed paper on the problem, in American Statistician (no one has ever claimed this as far as I know, but I suspect it's not a coincidence that this is the same journal Selvin's problem originally appeared in), making the point that the problem is inherently conditional and criticizing vos Savant's solution/clarification as well as other unconditional solutions, noting that "The distinction between the conditional and unconditional situations here seems to confound many". The paper is fairly lighthearted since the problem has been well known in academia for years and is mathematically rather trivial. Since vos Savant ignored (or simply missed) the effect a potential host preference has on the player's chance of winning, the paper explores this specific aspect of the problem concluding that the player should switch regardless of any host preference (since the probability of winning by switching is between .5 and 1 even assuming a host preference). The conditional probability is 2/3 which is the same as the unconditional probability assuming the host picks randomly between two goats.

5) Gillman publishes a note (presumably without knowing about the Morgan paper) that says essentially the same thing as the Morgan paper

6) popular sources continue to publish unconditional solutions, saying the probability is 2/3 and (following vos Savant's lead) ignoring the issue of host preference and the distinction between the conditional and unconditional situations (which seems to continue to confound many).

7) numerous academic papers examine all aspects of the problem, ranging from what assumptions people make and how they understand it to esoteric variations (e.g. the quantum version)

8) the problem continues to be a standard example of conditional probability in many statistics textbooks. At least some (such as Grinstead and Snell) say the unconditional solution doesn't exactly answer the problem that is asked.

NOW will you please say how you're suggesting the "pro-Morgan POV" might be eliminated from any of the sections that you're complaining about? -- Rick Block (talk) 02:28, 14 January 2010 (UTC)

Imho you need to reverse 2) and 3) though, to my knowledge it mostly became a standard example in probability textbooks at large after the parade affair.--Kmhkmh (talk) 05:11, 14 January 2010 (UTC)

I think 2) should probably come after 4). Text books seem to use Morgan terminology. Are there any textbooks, making a big issue of the conditionality, dating before the Morgan paper? Martin Hogbin (talk) 10:05, 14 January 2010 (UTC)

What about 'Is The Contestant Aware Of A Host Bias' and 'How Can Huckleberry Do Better From Knowing The Equal Goat Door Constraint'? Glkanter (talk) 06:58, 14 January 2010 (UTC)

I thought you said "or". I'm getting the distinct impression you either don't have a suggestion or don't want to say what it is. Mediation will presumably help this. -- Rick Block (talk) 14:50, 14 January 2010 (UTC)

Once again, you spend more time on what you think I'm thinking than what you, yourself have to contribute. So, what about 'Is The Contestant Aware Of A Host Bias' and 'How Can Huckleberry Do Better From Knowing The Equal Goat Door Constraint'? These both demonstrate that Morgan, despite being published in the same journal as Selvin, has contributed nothing of value. But it's published, so it goes in. Glkanter (talk) 15:41, 14 January 2010 (UTC)

It's already in, in a way I'm comfortable with. I'm not the one saying the article needs to be changed in this regard. So are we OK here, or would you like to see it in, in some other way? And, if so, how? Again, I'm getting the distinct impression you either don't have a suggestion or don't want to say what it is. -- Rick Block (talk) 15:51, 14 January 2010 (UTC)

Well, what can I say, Rick? You put up an RfC/U on me for not editing the article often enough. Then I very lightly edit the article for clarity, and I touch off a near-edit war, and am accused of violating NPOV with the 2 'POINTy' dates I added to the headers. Then I tell you I look forward to being one of the consensus of editors, and you jump all over me for that. I've updated my concerns on the mediation request. They're consistent with my statements of 15 months now.

So, tell me how you intellectually justify Morgan's claims in light of 'Is The Contestant Aware Of A Host Bias?' and 'How Can Huckleberry Do Better By Knowing The Equal Goat Door Constraint?'? Glkanter (talk) 16:01, 14 January 2010 (UTC)

So your suggestions are at Wikipedia:Requests for mediation/Monty Hall problem#Additional issues to be mediated. Thank you. That's all I was asking for. These are concrete things we can work on (except for the "blather" comment). Regarding your questions - there is no reason whatsoever that I or anyone else should have to justify Morgan's claims to your satisfaction. They're published in a VERY reliable source backed up by similar (if not identical) claims made in other reliable sources. You apparently do not personally agree with them. Fine. Nobody says you have to. -- Rick Block (talk) 16:47, 14 January 2010 (UTC)

I have moved the 'Aids to understanding section'

I have moved the 'Aids to understanding section' to immediately follow the 'Popular solution section to see how it looks.

In my opinion it makes more sense there for the following reasons:

The section mentions nothing about conditional probability or the specific door that the host opens.

The article now has a logical sequence from simple to complicated.

The move does not affect Morgan's claim in the 'Probabilistic solution' section that conditional probability must be used.

Nobody who does not understand the basic problem is going to make and sense of the Morgan paper and subsequent discussions of conditional probability.

No doubt not everyone will like this but there seemed be be something of a consensus forming that it might be a better way to organise things. Note that I have not changed any wording, just moved a section, although I do notice many uncited claims and statements in the 'Aids to understanding section. This should be addressed regardless of the position of the section. Martin Hogbin (talk) 20:23, 13 January 2010 (UTC)

I strongly object to this, and as I've said think that it is not in keeping with WP:NPOV. We're going to talk about this in formal mediation (Nijdam has agreed). I'll file the request today. -- Rick Block (talk) 02:33, 14 January 2010 (UTC)

Why do you object? Have you read the article as it is now? It makes perfect sense and does not discredit the conditional solution in any way. If you could accept this change, which is just of order and not content, I do not think we would need mediation. I think most editors would be happy with the major content and structure of the article. I cannot see how moving the sections into a logical order without any other changes can be described as POV.

I do not know if you filed your formal mediation request in response to my action or not. I have agreed to it anyway. Remember that the mediator does not attempt to impose a view on us. My action was rather bold but it was a genuine attempt to bring this dispute to a close. The change it would be a major step in the right direction, if you could accept it. If not please give reasons. Martin Hogbin (talk) 09:58, 14 January 2010 (UTC)

I note that my change has been reverted with no reason other than to 'wait for mediation'. There is much support for this cgange and no logical reason against it has been proposed. These changes should be discussed here, as I am trying to do. Martin Hogbin (talk) 15:00, 14 January 2010 (UTC)

I said above I object on the basis of WP:NPOV. In more detail, this change presents the problem and then presents an unconditional solution as "the solution". The alternative conditional solution and the POV (of the sources we all know by now) that the unconditional solution does not exactly address the problem as they see it are buried in the article. This creates an "anti-Morgan" POV in the structure of the article. Unlike the Bayesian analysis, which is highly technical and arguably of little interest to a general readership, the conditional solution is well within the grasp of a general readership. Rather than bury this in the article I think we should actually go the other way and have a SINGLE solution section that presents both an unconditional and conditional solution. Per Wikipedia:Make technical articles accessible the marginally simpler unconditional solution should be presented first, but to comply with WP:NPOV I think an alternative conditional solution should immediately follow.

Regarding mediation - my impression is Glkanter wants mediation with or without this change. I filed the request in response to his continued insistence about this, not specifically because of this change. -- Rick Block (talk) 15:32, 14 January 2010 (UTC)

Formal mediation request filed

I've filed the request for formal mediation and informed all the users listed as involved parties, see Wikipedia:Requests for mediation/Monty Hall problem. If you are listed as an involved party please go to the request page and indicate your official agreement to participate in this process. If you think there are other issues to be mediated, please add them to the "Additional issues to be mediated" section. Wikipedia:Requests for mediation/Common reasons for rejection has some helpful comments that may be relevant. Thank you. -- Rick Block (talk) 03:01, 14 January 2010 (UTC)

Has Nijdam Invoked A 'Freeze' On MHP Article Editing?

His only comment I could find anywhere supporting his revert of Martin's edit was his edit comment 'Wait for mediation'. Does he have this unilateral power as an editor? Mediation might not be accepted, and we probably won't know for over a week. Interesting that his action immediately follows his agreement to take part in the Formal Mediation. Glkanter (talk) 14:18, 14 January 2010 (UTC)

He has as much and as little "power" as Martin or anyone else. The "normal" editing cycle is described at WP:BRD. If anyone makes a change that someone else reverts, the revert is a direct indication that this change does NOT have consensus. Making a change to "test the waters" is fine. Reverting such a change is fine. Reverting a revert is NOT fine. -- Rick Block (talk) 15:00, 14 January 2010 (UTC)

Consensus does not mean unanimity. There is, I think, much support for the change. I do not want to start edit warring but if there are no logical arguments presented as to why the change is wrong, I think it would be quite reasonable of me to revert again. I cannot see how changing the order of sections to make the article read better can be described as POV. I have given full reasons above as to why the change is an improvement. Why do you think it is not? Martin Hogbin (talk) 15:35, 14 January 2010 (UTC)

See above. -- Rick Block (talk) 15:39, 14 January 2010 (UTC)

If one doesn't want to wait for the mediation, than I can say I'm strongly against the proposed change. I want the "simple solution" directly being followed by the correct one, together with the critical notes about the simple solution, so anyone reading the article will guaranteed (I hope) see this. Nijdam (talk) 16:33, 14 January 2010 (UTC)

I would say that until the reader has understood the simple solution they have little chance of understanding the issues involved in conditional probability. In fact many readers will not be able to understand this anyway and many will not be interested. We cannot make our readers read something that they do not want to. The essence of the MHP is its simplicity. Martin Hogbin (talk) 17:00, 14 January 2010 (UTC)

Well, it's clear that keeping it the way it had been would be supporting Nijdam's pro-Morgan POV. We can't have that. Tell me Nijdam, how do you intellectually justify Morgan's claims in light of 'Is The Contestant Aware Of A Host Bias?' and 'How Can Huckleberry Do Better By Knowing The Equal Goat Door Constraint?'?

What we can't have is POV is either direction. You apparently think the current article has a pro-Morgan POV. The fix for this cannot be to make it POV in the other direction. A mediator might help us reach a better solution. -- Rick Block (talk) 18:18, 14 January 2010 (UTC)

Nijdam wrote, "I want the "simple solution" directly being followed by the correct one..." He gives no other reasons. I think it's correct to classify his justification solely as pro-Morgan. You've made similar POV conclusions based on a whole lot less. Glkanter (talk) 18:35, 14 January 2010 (UTC)

And maybe you could clarify for us exactly what you and Boris resolved before he left the discussion? Glkanter (talk) 17:12, 14 January 2010 (UTC)

I would also ask Nijdam to prove on the arguments page that any method of solving the symmetrical problem that does not involve conditional probability must be wrong. Martin Hogbin (talk) 17:21, 14 January 2010 (UTC)

IMO, these questions are asking for WP:OR. It doesn't matter what Boris and Nijdam resolved or whether or not Nijdam can prove anything. The only thing that matters is what reliable sources say. You and Glkanter seem to be having a great deal of trouble with the basic concept of saying what reliable sources say without injecting your own POV. This is another issue a mediator might help with. -- Rick Block (talk) 18:27, 14 January 2010 (UTC)

Please, Rick. You've posted on these pages for what, 6 years now? I've read plenty of your personal interpretations and offers to try various game simulations and slightly different problems. There's a difference between Wikipedia policies and intellectual honesty. And there's a difference between how an article is edited and what good faith editors discuss on talk pages. Glkanter (talk) 18:35, 14 January 2010 (UTC)

What there's a difference between is trying to help people understand what the article says (which I've done plenty of) and suggesting edits based on whether or not an editor can "prove" something (which is what you and Martin seem to be doing). The latter has no place in Wikipedia. Edits are based on what reliable sources say, not on what editors can prove. Again, I think this is an issue a mediator might help with. -- Rick Block (talk) 18:50, 14 January 2010 (UTC)

Nijdam and you are the ones asserting that an unconditional solution must always be wrong, you must therefore prove this. There is one reliable source which makes a similar claim (for their interpretation of the question) but as I say below, there is another source which says that they might have misunderstood the question. Martin Hogbin (talk) 18:57, 14 January 2010 (UTC)

My interpretation is that Nijdam is asserting his personal view here, and on the /Arguments page, that the problem is inherently conditional. Although his view matches that of some of the sources, I don't think he's insisting the article take this as its POV. It's not supposed to matter but you are aware that he's a professor of mathematics (right?). I'm asserting there are multiple reliable sources that say the unconditional solutions don't exactly address the Parade version of the problem statement and want (insist) the article fairly represent this POV. -- Rick Block (talk) 21:37, 14 January 2010 (UTC)

Face the facts, Rick. In a peer reviewed journal, Morgan claims all the simple solutions are false. That's the entirety of Morgan's contribution to the literature. Morgan's paper has many flaws, including misquotes and math errors (you could ask Nijdam about this aspect), has a disclaimer from Seymann attached to it, and his claim has not been acclaimed by the professional community in the 19 ensuing years. Plus, it's inconsistent with the problem statement, 'Suppose you're on a game show...' What's left? The peer-reviewed journal part? How is the fact that it is in a peer reviewed journal of any utility or interest to the Wikipedia reader? It's published. It goes in. Why not chronologically? Glkanter (talk) 18:47, 14 January 2010 (UTC)

Rick, this seems to be the line that you resort to when you are beaten in logical argument. As you well know, there are plenty of reliable sources that treat the problem unconditionally, there are also reliable sources which treat it conditionally. There is one source (Morgan) that suggests that the unconditional treatment is incorrect, there is one, equally reliable, source (Seymann) that suggests that Morgan may have misunderstood the question. All these sources are, quite rightly, reflected in the article. Our job as editors is to decide the best way to do this, for the benefit of our readers. No source tells us how to do that. Martin Hogbin (talk) 18:51, 14 January 2010 (UTC)

This is the line I resort to when it becomes obvious further logical argument is pointless. The fact is many sources, not just Morgan, say the problem as it appeared in Parade asks a conditional probability question and that unconditional solutions are not directly responsive to this question. Our job as editors is to insure the article is written (per WP:NPOV) "from a neutral point of view, representing fairly, proportionately, and as far as possible without bias, all significant views". No source tells us how to do that, but since you personally "hate" (your quote above, and your "criticism" page, etc.) the Morgan et al. paper you have a clear bias. Of course this doesn't necessarily mean you can't edit in an unbiased fashion, but you do seem to be having trouble with this. Yet again, I think this is an issue a mediator might help with.-- Rick Block (talk) 19:18, 14 January 2010 (UTC)

Nijdam reverted Martin's 'Aids to Understanding' placement edit solely because of his pro-Morgan POV and bias. He wants the allegedly only 'correct' answer encountered by the reader as soon as possible in the article. That violates NPOV. Badly. Glkanter (talk) 19:06, 14 January 2010 (UTC)

Is it his statement (that this is the only correct answer) that you are saying violates NPOV, or his edit? As long as he doesn't edit the article to say or imply the conditional solution is the only correct solution he's free to think whatever he wants (as are you). We all have our own personal POV. What NPOV says is we have to make sure the article doesn't have a POV. This is something else I think a mediator might help with.-- Rick Block (talk) 19:41, 14 January 2010 (UTC)

I am happy to try mediation but please remember that it is not the mediator's job to enforce rules or decide who is right. They can only help us to agree amongst ourselves. Martin Hogbin (talk) 20:23, 14 January 2010 (UTC)

Right. A mediator would also help us communicate (would, in fact, probably lay down some pretty strict rules about how we should say things and interact with each other) and presumably would be happy to explain relevant policies and guidelines. My impression is Glkanter is not happy with my attempts at explaining policies. -- Rick Block (talk) 21:37, 14 January 2010 (UTC)

Glkanter will express again that you should spend less time thinking and conjecturing and writing about what I'm thinking. I'm not shy about letting you all know what I'm thinking. Glkanter (talk) 22:21, 14 January 2010 (UTC)

I'm sorry, but I find getting a straight answer out of you for what seem to me to be simple direct questions (for example, per the thread somewhat above where you insisted I answer certain questions before you would deign to respond) to be nearly impossible. I sincerely hope a mediator can help us communicate. -- Rick Block (talk) 23:27, 14 January 2010 (UTC)

Martin made an edit and explained his non-POV reasons why. Nijdam reversed it giving ONLY his Morgan-POV reason shy. Seems clear to me where NPOV is being violated. Strange that you can't see that, Rick. Glkanter (talk) 20:53, 14 January 2010 (UTC)

We all know you're being snide here. Please stop it. This is something else a mediator could help with. -- Rick Block (talk) 23:27, 14 January 2010 (UTC)

Yes, Rick. Quoting people in context is 'snide'. And dates are 'POINTy'. And we continue to disagree on nearly ever topic broached in the last 15 months on these talk pages. Glkanter (talk) 02:03, 15 January 2010 (UTC)

To clarify, what I'm referring to as snide is "Strange that you can't see that, Rick". -- Rick Block (talk) 03:28, 15 January 2010 (UTC)

Let us give it a try, but remember, both sides will have to give something to reach a consensus, mediator or not. Martin Hogbin (talk) 23:37, 14 January 2010 (UTC)

Logical and scientifical solutions

The popular solution is actually a logical solution, while the probabilistic solution is a scientific solution. It is quite clear that within science several sources explicitly state the problem to be conditional and therefore the unconditional to be wrong, while no scientific source states the opposite (including Seymann). Some scientific sources used logic in fact, and were corrected by their colleagues. They did not respond to that, nor did any of them criticize the conditional approach.

The 'conditional' scientists all corrected their colleagues, because the latter were not practicing pure science, even though they may have been fully right logically. The problem with the last option is that logic just can't be proven. although logical sources have certain reliability too. I don't see any other possible interpretation.

This is yet another attempt to agree on this matter, because as I said before, we are all right basically. There is no wrong or right, but within disciplines. Logic can only be beaten logically, while science can only be beaten scientifically. They are both as well superior as inferior to another, and this very extreme paradox cannot simply be positioned objectively. Heptalogos (talk) 22:20, 14 January 2010 (UTC)

What does "The problem with the last option is that logic just can't be proven." mean? It sounds like it contradicts the academic teachings of 'logical proofs'. Glkanter (talk) 22:26, 14 January 2010 (UTC)

When so called logic is proven, it becomes law. Any logic outside the law is unproven. As a result, no proven logic exists. Suppose you use logic to create and claim law. The law should be defined as generally true (provable), to some degree. However, when the law is proven, there is no automatic proof for the logic behind it. Unless you use the same logic to create several proven laws. "The same logic" must then be clearly defined and becomes law.

Some principles may be or seem so clearly logical, but not existing as law (yet). On the other hand, as they don't exist as law, are they really that logical? At the moment, there is no law on practicing conditional solution other than to use any exact given information as a condition. Even if all intelligent people in the world would agree on a specific exception, as logically true, it's not scientifically true. These people could maybe create and claim a new general law, which may be proven, after which even the most consequent scientists will agree on this 'logic', but only because it has become law. And they are right, not beaten, because they're still being as consequent as they should, scientifically. So these are really different dimensions. Heptalogos (talk) 08:49, 15 January 2010 (UTC)

The discussion between Morgan and Marilyn didn't make any sense. They were in different dimensions. Their argue is one of historic value! Most famous paradox, most intelligent person, and most consequent scientists ever. It may be a pitty that the original paradox has been kidnapped for this, but on the other hand this 'new issue' is what it made even bigger. So I think both issues really deserve a prominent position in the article, as long as we can clearly separate them, starting of course with the original paradox. Heptalogos (talk) 09:40, 15 January 2010 (UTC)

Something else to add to the mediation list

One of the points of the three fundamental content policies (WP:V, WP:OR, and WP:NPOV) is to avoid the sorts of arguments that have been raging on this page and the /Arguments page. In total, what these policies mean is all we need to agree on is what sources are reliable (WP:RS makes that pretty easy), whether these sources say what we respectively are claiming they say (nothing too difficult there), and how much weight to give what each source say. That's it. The first two should be easy as pie (alright, maybe easy as pi) since whether we agree with what any of the reliable sources say shouldn't even come up. We simply need to agree whether the article is representing what the sources say "fairly, proportionately, and as far as possible without bias" (this quote is from WP:NPOV). The last one (weight) is trickier and sometimes leads to heated arguments. On this page, we've mostly been arguing about the stuff that is supposed to be EASY. I hope mediation will help this, although I fear that the discussion will then morph into a heated discussion about how much weight we should give specific sources. Assuming mediation happens, while we're there we should make sure we explicitly address the weight issue as well. -- Rick Block (talk) 04:13, 15 January 2010 (UTC)

Rather than wikilawyering we should concern ourselves with the overriding objective to improve the article, for the intended readership, which is a wide section of the general public. Although we are entitled to WP:ignore the rules to improve the article, I am not necessarily suggesting that we do that, just that the rules should not in any way direct us to write the article in a way that will not be useful to most of the general public. Martin Hogbin (talk) 10:48, 17 January 2010 (UTC)

Martin - you are at least implying the article can violate WP:NPOV if doing so would make it more useful to most of the general public. IMO, you are completely wrong about this. I would say if we can't write an article that is both useful to the general public and complies with NPOV we are simply incompetent editors, but if we have to pick one we have to pick NPOV. From WP:NPOV: The principles upon which these policies [NPOV, OR, and V] are based cannot be superseded by other policies or guidelines, or by editors' consensus. -- Rick Block (talk) 17:50, 17 January 2010 (UTC)

N, I am not suggesting we abandon NPOV, although, in the end, everything on WP, including policies, is decided by consensus. The question we have to address is the exact interpretation of those policies and my suggestion is that we do this in order to meet the fundamental purpose of WP which is to inform. Martin Hogbin (talk) 11:24, 18 January 2010 (UTC)

"Wikilawyering", I love it. They've seen it all, haven't they? In my opinion, some good things came out of the discussions of the last couple days:

1. The real items for mediation have made themselves known. How much weight to give Morgan, and is the 'host bias' conditional problem statement consistent with the information given in either Selvin's or Whitaker/vos Savant's MHP?

2. All those "let's start fresh and try to make a compromise article" attempts were destined to fail.

3. Rick's threats of the consensus "violating NPOV" were bluster, unsupported by Wikipedia policy.

Glkanter (talk) 13:20, 17 January 2010 (UTC)

Your point #1 is half right. One of the issues is how much weight to give the viewpoint expressed by Morgan et al. However the second half of this ("is the 'host bias' conditional problem statement consistent ...") is not for us to decide. Sources have decided this. And, for many many sources the decision is clear. I have no idea what you're talking about with your second point. Regarding your third point: I have made no threats, "the consensus" is not a group of people, and this point is yet more low level harrassment directed my way entirely consistent with the objectionable behaviors described here. Please just stop it. -- Rick Block (talk) 17:50, 17 January 2010 (UTC)

The problem of NPOV in MHP

It is NOPV to chronologically:

• Start with the original paradox and explain it fully, logically as well as mathematically.
• Describe the complex issues within science to solve particular statements.

It is also NPOV to:

• Start with the most famous particular statement of the MHP, which is from Parade.
• Explain this one logically as well as mathematically.
• Which will at the mathematical solution already start the complex issues, because of the particular Parade statement.

So, how do we solve this? Heptalogos (talk) 10:11, 15 January 2010 (UTC)

For practical reason, I think we all agree on the Parade statement to start with? A problem description is initially needed, reflecting a mundane situation, instead of basic formula. Any mundane problem description should come from reliable sources and be significant. So without an alternative, there's not much of a discussion here. Heptalogos (talk) 10:31, 15 January 2010 (UTC)

As the Parade statement is particular in a certain way, the mathematical solution has an enormous tail of complexities. What if we do it like this: logical explanation of the paradox first, as it is now. Next the mathematical solutions, again the same, but this section not being significantly bigger (in text) than the logical section. Because that would not be NPOV either. This section should preferably describe the unconditional and conditional scientific solutions, and mention the issue of scientific consensus in favour of the conditional method. Then it may direct to a lower section in the article to give a full description of all scientific sources and arguments. This seems to me as a reasonable compromise, because Nijdam is justly being served at the issue of common readers being aware of the essential criticism on the unconditional method, while Martin and Glkanter are being served at the issue of having the "aids to understand" section above all detailed sources and arguments of science. Heptalogos (talk) 10:51, 15 January 2010 (UTC)

This is exactly the structure I favor. Further, I don't see any particular reason to separate the "logical" solution and the "scientific" solution into different sections. It doesn't seem to me to be that difficult to do both in one section per the proposal above (see #Proposed unified solution section). For a time, I thought there was good progress being made on that solution. -- Rick Block (talk) 15:19, 15 January 2010 (UTC)

This does not address the problem that will be raised for the vast majority of our readers. As Glkanter has pointed out, none of the thousands of letters that vos Savant received was concerned with which door the host opened, they were all about why the answer is not 1/2. This is the question that we must answer first. Martin Hogbin (talk) 15:33, 15 January 2010 (UTC)

Rick, I don't like the unified solution because it spends only a few lines on the paradox that confuses so many people and is then already starting to mention Morgan et al. The scientific solution is very complex, which is the reason to describe it separately. Heptalogos (talk) 19:53, 15 January 2010 (UTC)

Martin - even in the unconditional case you have to talk about the door the player picked, the door the host opened, and the other door. You might as well call these "door 1", "door 3", and "door 2" (respectively). Do you want to add "for example" before every door number to clarify that the initial unconditional solution is only using door numbers as examples (which, btw, is true of the conditional solution as well)? Player picks door 1, host opens door 3, and player can now switch to door 2 is used as the representative example of the general case in nearly all sources. You seem to be saying that using the door numbers in this solution means we're limiting the response to only those players who have picked door 1 and have seen the host open door 3. This is not what ANY of the sources who discuss the solution in terms of these door numbers are intending. Your refusal to see this point mystifies me.

Your table (#Discussion and proposals aimed at reaching a compromise on this subject) is incredibly confusing. Why are there two identical columns for "you choose a goat"? You don't KNOW what you chose. What you initially know is the car is behind your door, or one of the other two doors, and then you find out the car is NOT behind the door the host opens. So, you start with 3 doors (not car, goat, goat - for example, what if rather than goats the losing doors are simply empty?). This model (door centric, rather than car/goat/goat centric) is exactly the basis of vos Savant's case analysis solution (go look at it). This approach matches the example in the problem description (yours doesn't).

I am incredibly tired of arguing about this. How about if we start talking exclusively about how sources handle this. My claim is the unconditional case is handled by vos Savant and nearly all other popular sources using the door numbers given as examples in the problem statement. If you'd like to argue whether this is what popular sources do or not, we can presumably put together a list and go look. Would you like to offer up a source that does not use door numbers? -- Rick Block (talk) 18:29, 15 January 2010 (UTC)

I am not sure exactly what Heptalogos is suggesting. The order I want is U/C solution, Aids to understanding, C solution, Causes of confusion, Variants etc. Martin Hogbin (talk) 15:36, 15 January 2010 (UTC)

I am suggesting about the same as you do, while also offering a comment, within the U/C section, about scientific consensus in favor of the conditional approach. Apart from that I think it's better to replace U/C by L/S meaning logic/scientific. Heptalogos (talk) 19:53, 15 January 2010 (UTC)

No, Martin is disagreeing with you. He wants an initial section that only discusses what you're calling the Logical solution with no mention of conditionality and no mention of scientific consensus, and then an entire section on "aids to understanding" this "logical" solution, and only then a section on the "scientific" solution. -- Rick Block (talk) 21:27, 15 January 2010 (UTC)

It's about the same. He also doesn't want the Morgan battle in between the logical solution and the aids to understand it better. But then again I agree with you that the conditional (scientific) approach should really be mentioned and explained basically right after the logical approach (NPOV), but with a reference to another section to go in detail. Heptalogos (talk) 21:45, 15 January 2010 (UTC)

Unfortunately, we cannot have it both ways, or everyone would be happy and there would be no argument. I want the 'Aids to understanding' section to follow the simple solution section. This is not to intentionally downgrade the conditional solution but simply because most of the reader's difficulties in understanding will be with the simple solution, just as it was for vos Savant. People insisted that the answer was 1/2, not that the host goat door choice was important. Martin Hogbin (talk) 00:12, 16 January 2010 (UTC)

Please read through the current 'Aids to understanding' you will see that it refers only to the issue that I have described above. There is no mention of the host's choice of goat door. Martin Hogbin (talk) 00:15, 16 January 2010 (UTC)

I know what you want, but others also have justified wishes. So what is specifically wrong with the compromise that I propose? Heptalogos (talk) 09:52, 16 January 2010 (UTC)

Summary

See Talk:Monty Hall problem/Arguments. Nijdam (talk) 14:34, 15 January 2010 (UTC)

Let's Discuss, As Per Rick's Comment On Wikipedia Policy, How Much 'Weight' Each Source Receives In The Article

I love this topic! It's what I've been arguing about for months. Sure, Morgan is published in a peer reviewed journal. So what? What do they have to say that's new? The article has at least three gaping errors. Only with the errors can they make the contrived claim that all simple solutions are false. I wonder, even ones that hadn't been published yet?

Here's Rick's diff.

How about Selvin? I added '1975' to the Popular solution section. Someone pointed out that Selvin's 1975 paper isn't even referenced there. And his conditional paper of the same year isn't in the Probabilistic solution section.

This is what real life editors do! They 'weigh' the newsworthiness of various articles from various sources. And they discuss it. With ideas, and logic, and facts.

So, perhaps more Selvin, and less Morgan POV? Glkanter (talk) 18:50, 15 January 2010 (UTC)

I would suggest we wait until mediation for this because it is going to immediately get into Wikipedia policy issues that I think would be best explained by someone you would perceive as a neutral party (i.e. not me). I will say that this is an area that takes editorial judgment, which means it's not nearly as black and white as "is X a reliable source". -- Rick Block (talk) 19:29, 15 January 2010 (UTC)

You may choose to participate or not, Rick. I'm sure there are others like me who will get bored waiting another week or so. Now that you agree 'weight' does not equate to 'biased POV', we can have this discussion again.

So, we can talk about how to edit the article, and actually edit it, or we can offer more urns puzzles, formal probability notations, and narratives on 'truth'. Or, some may wait for the mediator. Glkanter (talk) 19:50, 15 January 2010 (UTC)

Morgan's weight:

• Very explicit arguments against many (unconditional) methods used so far. (are they the first?)
• Very explicit arguments against the method Vos Savant is using. (are they the first?)
• Very first attempt to solve the problem without making assumptions. (are they the only ones?)
• 'Scientifically' published and peer reviewed. (did any unconditional solution?)
• The only scientists to have an extensive debate with Vos Savant.

About the errors: that's POV and it doesn't even really matter in the weight issue.

Please suggest something about Selvin 1975. Do you have his letters? Heptalogos (talk) 20:11, 15 January 2010 (UTC)

The errors are not POV. They are real. The paper discredits itself. Misquotes, math errors found by Martin and Nijdam, treating the host and the car placer differently, assigning 'bias' and transferring this to the contestant on a game show... Much like 'the Earth is flat' doesn't get much emphasis, neither should 'the host, but not the car placer, has a bias known by the contestant' Glkanter (talk) 14:44, 16 January 2010 (UTC)

I think before anyone can talk about this, they need to go read WP:WEIGHT. Weight and POV are different, but related, issues. -- Rick Block (talk) 21:24, 15 January 2010 (UTC)

Certainly. Why your comment? Heptalogos (talk) 21:49, 15 January 2010 (UTC)

Because we all need to able to talk about the issues that will come up using the same terminology. The appropriate weight relates to (from the link I provided) "prevalence in reliable sources, not its prevalence among Wikipedia editors or the general public" (emphasis in the original). Weight also relates to viewpoints as opposed to specific sources. These are things I'm fully expecting to argue with Glkanter and Martin about, but I want there to be a shared understanding of what weight means before we start arguing specific issues (or else I will certainly be accused of "filibustering" or trying to subvert the will of the masses or whatever).

I would truly prefer to defer this discussion until we're in mediation so that I don't have to both help people understand Wikipedia policy and also argue one "side" of this. Doing this apparently tends to make the policy clarifications sound like partisan arguing. -- Rick Block (talk) 23:59, 15 January 2010 (UTC)

OK, I understand. I was basically trying to convince Glkanter personally about the significance of Morgan, nothing more. But I can define the same arguments a little bit different to present the viewpoints in proportion to the prominence of each in the sources. First of all I think Morgan is mentioned a lot in other reliable sources, while it's already most reliable because it was published within scientific media. Then they spent much energy in disproving others, including Vos Savant, on which they published another article. Another (the) prominent part in their main article is their solution without assumptions. The only aspects now missing are Morgan being the first ones, which is probably indeed not relevant, except for Glkanter and myself personally.

I don't see the problem of you switching roles as soon as mediation starts. Is there any Admin responsibility conflicting with that? Heptalogos (talk) 10:55, 16 January 2010 (UTC)

There is no actual conflict. Anyone is free to try to clarify Wikipedia policies during a discussion (although this sometimes leads to Wikipedia:Wikilawyering). As far as content disagreements are concerned admins have no more and no less authority than anyone else - specifically admins can't take administrative actions to enforce their preference of content, i.e. cannot block users or protect a favored version of an article. What I would like is for policy issues to be brought up by an acknowledged neutral party, and thus keep the "meta" (policy) issues distinct from any conflict we might have about content. -- Rick Block (talk) 18:07, 16 January 2010 (UTC)

Regarding a couple of questions raised above. Glkanter asks about Selvin's letters. These letters to the editor (they're not "papers") are referenced in the "History" section. They're not referenced elsewhere since they are being treated here as primary sources. Please see the first bullet at Wikipedia:Reliable sources# Scholarship.

Heptalogos asks

• Is Morgan et al. the first to explicitly argue against many (unconditional) methods used so far? I believe so.
• Is Morgan et al. the first to explicitly argue against the method vos Savant uses? I'd say they were technically the first, although Gillman is effectively simultaneous (the Morgan et al. paper was published in November of 1991, Gillman's in January of 1992).
• Is Morgan et al. the only attempt to solve the problem without making assumptions? Specifically meaning not making assumptions about the host preference between goats, Gillman approaches the problem in exactly the same way. This same approach is one of several presented by Krauss and Wang. At least several others (all presumably assuming initial random car placement) show the same result, i.e. the chance of winning by switching given a host preference p for the door that has been opened (meaning the host opens this door with probability p if there are two goats to pick from) is 1/(1+p).
• Are any unconditional solutions "scientifically" published and peer reviewed? I'm not sure exactly what you mean by this, but assuming you mean a source that acknowledges the difference between the unconditional and conditional questions and then uses an "unconditional" solution to rigorously address the conditional case (like Gill's WP:OR, below) I don't know of such a source.
• Are they the only scientists to have an extensive debate with Vos Savant? I believe the sense of what you're saying is true, although "extensive debate" seems like an overstatement. They published a paper. She wrote a letter to the editor in response. They published a rejoinder.

As mentioned in the "History" section, Barbeau's book contains a survey of the academic literature through about 2000. He published an earlier version of this survey in 1993, it's the Barbeau 1993 reference in the article. -- Rick Block (talk) 20:31, 16 January 2010 (UTC)

Thanks for the answers Rick. Those are the exact answers I was aiming for. Heptalogos (talk) 22:40, 16 January 2010 (UTC)

Do any of these sources criticize the simple solutions based only on the information given in the various forms of the problem statement? Or do they all contrive a 'host preference', then criticize the simple solution for not solving this different problem? Do any of them also contrive a 'car placer preference'? Glkanter (talk) 21:37, 16 January 2010 (UTC)

I've provided quotes from Morgan et al., Gillman, and Grinstead and Snell before (see above #What If Morgan Had Used A Different Variant?) - what they're all saying is that the "simple" (unconditional) solutions don't address the problem as they interpret it, so yes they are criticizing these solutions based on the problem statement. The fully conditional solution in Grinstead and Snell accommodates a 'car placer preference' although they (explicitly) assume the initial car placement is random. These sources don't "contrive" a host preference but say the probability of winning depends on it, and if you don't know what this preference is or don't assume a value for it you can't exactly say what your probability is of winning by switching. Krauss and Wang include a discussion of this as well. They consider the "two door scenario", where the door the player picks as well as the door the host opens are given, to be the "standard version" and say "... one has to make assumptions about what Monty Hall would do in A1 [the case where the player has initially picked door 1 and the car is behind door 1] and estimate the probability that Monty Hall would open Door 3 rather than Door 2." -- Rick Block (talk) 23:55, 16 January 2010 (UTC)

Do any of these sources reason why they do assume e.g. random car placement (etc.), but not random host behavior? Heptalogos (talk) 11:23, 17 January 2010 (UTC)

Morgan et al. are clearly trying to match vos Savant's assumptions - they even call it the "vos Savant scenario". She (and they) assume initial random car placement, that the host always opens a door revealing a goat, and that the host always makes the offer to switch. They mention at the end of the paper that it would also be possible to consider non-uniform probabilities of car placement. Assuming they overlooked or ignored this case is (IMO) simply willful misinterpretation of what they wrote.

Gillman restates the problem (does not quote the Parade version) and explicitly states the initial car location is to be taken as random.

Grinstead and Snell quote the Parade version as reprinted in vos Savant's book "Ask Marilyn" (I haven't checked whether their quote matches this version - what they quote is definitely not the same as the original Parade version) and explicitly say (without rationale) they're assuming the car is initially located randomly.

One might surmise that making this assumption focuses the problem on the effect of the host opening a door. By making this assumption, the probability before the host opens a door is clearly 1/3 and the question becomes what is the probability after the host opens a door. For editing purposes, my claim is we don't care why this assumption is made. The fact is this assumption is made. If the sources don't say why, then the article can't say why and, unless there are other sources that explain or question this assumption, the article can't either. -- Rick Block (talk) 21:04, 17 January 2010 (UTC)

Rick, very clear, thank you. It's quite a mess. However, it triggers me to find the exact relations between sources. Heptalogos (talk) 11:58, 18 January 2010 (UTC)

How Richard Gill110951 sees things now

I distinguish three Monty Hall problems, and I think they are all legitimate problems to discuss; they have all been discussed in the literature of brain-teasers, mathematics, psychology...

There is no law saying that exactly one of these three is "the" Monty Hall problem

Here they are:

0: Marilyn vos Savant's question "would you switch?"

1: A mathematician's question "what is the unconditional probability that switching gives the car?"

2: A mathematician's question "what is the conditional probability that switching gives the car?"

Please specify the sources for 1 and 2, otherwise there's no use in discussing it here. Heptalogos (talk) 11:31, 16 January 2010 (UTC)

Whitaker. Sorry, misread the comment above. I agree that Whitaker should be interpreted as 0. Martin Hogbin (talk) 15:02, 16 January 2010 (UTC)

The following analysis gives the right answers to the questions 1 and 2 under the assumptions conventionally thought to be appropriate. I use Boris Tsirelson's beautiful trick ("symmetry") to deduce the answer to question 2 from the answer to question 1. I finally make some comments on question 0.

My set-up:

The quizteam hides the car, the player chooses a door, the quizmaster opens a door.

Three random variables taking values in {1,2,3}.

I don't care what your interpretation of probability is (subjective or frequentist or ...).

I don't care (for the time being) whose probabilities we are talking about at which stage of the game.

Notation:

C = door where Car is hidden

P = door first chosen by Player

Q = door opened by Quizmaster

Assumptions: with certainty,

Q unequal to P

Q unequal to C

Because of the first assumption we may define

S = door which follows by Switching = unique door different from P and Q

1) Short solution to problem 1:

If Prob(P=C)=1/3 then Prob(S=C)=2/3, since the two events are complementary.

2) Short solution to problem 2:

In this problem, the door chosen by the player is fixed, P= x, say.

We are to compute Prob(S=C|Q=y) for a further specific value y unequal to x. Let y' denote the remaining door number, besides x and y.

Assume that (given the chosen value of P), C is uniform, and the distribution of Q given C is uniform.

So by assumption Prob(P=C)=1/3 and therefore as in Problem 1, Prob(S=C)=2/3.

The latter probability is the weighted average of the two probabilities Prob(S=C|Q=y) and Prob(S=C|Q=y'), weighted by the probabilities Prob(Q=y) and Prob(Q=y').

Since the distribution of C gives equal probabilities to y and y' and since Prob(Q=y|C=x)=Prob(Q=y'|C=x)=1/2, nothing is changed by exchanging y for y' and vice-versa.

Thus the two conditional probabilities Prob(S=C|Q=y) and Prob(S=C|Q=y') are equal, and equal to their (weighted) average 2/3.

0) Short solution to problem 0.

I don't know what strategy the quizteam and quizmaster use, so naturally I had chosen my door uniformly at random, independently of the car's actual location.

Since I know game theory I know that "always switching" is the minimax strategy. It guarantees me a 2/3 (unconditional) chance of winning the car.

I don't care a damn what my conditional probability of winning is, given my specific initial choice: say door 1, and the quizmasters' specific choice: say door 3.

I don't know this probability anyway, since I don't know the strategy used by quiz-team and quiz-master.

I only know that Monty Hall always opens a door revealing a goat.

Gill110951 (talk) 11:03, 16 January 2010 (UTC)

This belongs on the arguments page. Heptalogos (talk) 14:12, 16 January 2010 (UTC)

Gill, I have shown much the same thing on my analysis page using fixed door numbers.

What is your opinion on the order of sections within the article? I would like to see the 'Aids to understanding' immediately follow the 'Popular solution' section as this is the section that most people cannot understand. Martin Hogbin (talk) 15:08, 16 January 2010 (UTC)

@Gill: as I wrote in my mail, once the problem is well stated, the soluton is (must be) obvious. Now your points 0, 1 and 2 do not clearly state the problem. I will ask you to go to the arguments page under Talk:Monty Hall problem/Arguments#Summary, where I also tried to formulate the different views on the MHP, and specify your versions 0, 1 and 2, and if possible relate them to my versions A, B and C.Nijdam (talk) 11:29, 17 January 2010 (UTC)

@Nijdam, @Martin, @Heptalogus, thanks for your comments. Let me explain what I am trying to do here. Problem 0) is supposed to be the question exactly as posed by Marilyn vos Savant, i.e., in her own words. Problems 1) and 2) are what people around here call the unconditional and the conditional problems respectively. They are two different ways in which mathematically inclined people have converted Marilyn's verbal problem into a formal mathematical problem. For each of the three problems the solution is immediate. I wrote it down in explicit, respectable mathematics (especially after I cut a lot of crap out of my first try at problem 2). The point I am trying to make is that Marilyn vos Savant asked whether or not one should switch doors, NOT what some probability was. Her problem was not a maths problem. It is only if you decide that the right way to make your final choice of door is by computing a probability, that you arrive at problems 1) and 2) - the "conventional" unconditional and conditional variants of the problem, which people spend their time here fighting about. I think that, if you think Marilyn is asking you for a probability, then whether 1) or 2) is closer to the question she is asking is a question of interpretation of American-English idiom. Did she refer to the actual door numbers painted on the doors in advance of the show, or did she mean that we decide to call the door which the player chooses "door 1"? Anyway my point is, she did not ask for a probability, she asked for a strategy. The usual *solution* to the conditional problem, problem 2, requires one to make all kinds of assumptions which are not justified by the problem as originally phrased. However, lots of people have talked about it, so it should be on wikipedia, since we are not supposed to be presenting *our* opinion as to what the MH problem ought to be, but merely writing down what it has been to various people. My own humble opinion is that the most satisfactory treatment of the problem uses the language of game-theory, i.e., we explicitly take account of any strategy which might be used by the quiz-team & quiz-master. We don't make unwarranted assumptions about it, whose raison d'etre is merely that they are designed to deliver the answer 2/3. Gill110951 (talk) 20:52, 17 January 2010 (UTC)

Gill, I completely disagree with you about game theory, this, in my opinion adds further complicationto an already difficult problem. If you want to discuss that further, I suggest that we do so on the arguments page. Martin Hogbin (talk) 21:01, 17 January 2010 (UTC)

Gill, I completely agree with you about game theory. If you want to discuss that further, I suggest that we do so on the arguments page, until you come up with a reliable source suggesting this method to solve the MHP. Heptalogos (talk) 22:26, 17 January 2010 (UTC)

I spoke to some game theorists who said they "know" the game theoretic solution to the Monty Hall problem. And any way, it really *is* an easy exercise after you have done Game Theory 101! Probably there exists a published discussion somewhere. Sometime I will post a combination, and condensation of my notes so far (see references Gill 2009a, 2009b, and since an hour ago also **** 2010 ****) to arXiv.org and submit to a light-weight but respectable peer-reviewed journal (more respectable than the American Statistician). BTW I think that Morgan et al. is a very poor paper. It is solving a Statistics 101 problem in a pompous and arrogant way, as well as being definitely un-scholarly in being dogmatic about their version being "the" version; for which purpose they even misquote earlier works. In the meantime my job is to go on looking for reliable sources, creating reliable sources if necessary, and learning from what people say here. In particular I must check what wikipedia already has on game theory. Game-theory ought to be more accessible and more well-known. Personally, I find a game-theoretic approach illuminating. In fact I find it essential since it is the only way as far as I know to give a decent argument for always switching, whatever the conditional probabilities..., without making articial assumptions about the quizmaster. @Martin and @Heptalogus, I am happy to discuss this with anyone, anywhere they like, I have tried to provide information which anyone can use to figure it out for themselves. Anyone who wants to erase anything I put on wikipedia can go ahead. No problem. Gill110951 (talk) 18:01, 18 January 2010 (UTC)

Game Theory 101: von Neumann's (1928) minimax theorem. References:

The minimax theorem (von Neumann, 1928), http://en.wikipedia.org/wiki/Minimax_theorem#Minimax_theorem

Von Neumann's seminal contributions to game theory: http://en.wikipedia.org/wiki/John_von_Neumann#Economics_and_game_theory

What game theory is nowadays: http://en.wikipedia.org/wiki/Game_theory

Honestly, I don't think that the minimax theorem complicates matters. It simplifies matters because we know there is a minimax solution and once we have guessed it, it is easy to check that we were right. And the two party's minimax strategies are exactly the player's and the quiz-master's "symmetric" probability distributions, used to randomize their choices. The probability distributions which turn up all over the place on these pages.

Gill110951 (talk) 19:45, 18 January 2010 (UTC)

I have no objection at all to a section about game theory and the MHP. What I would not want to see is game theory replacing the simple solution of the problem in which the car placement, the player's initial choice, and the host's legal door choice are all assumed to be uniform at random, as is the standard in mathematical puzzles.

After the discussion about the affect of a known or suspected host door opening policy (per Morgan), a section on game theory would be most welcome in my opinion, especially as it shows that, if both the player and the host take the game seriously and competitively, the chances of winning by switching are back to 2/3 again. This puts Morgan's 1-q twaddle back in its proper place. Martin Hogbin (talk) 22:24, 18 January 2010 (UTC)

In some ways the Morgan paper can be seen as a dismally failed attempt to discuss game theory. Martin Hogbin (talk) 22:26, 18 January 2010 (UTC)

A question for the 'conditionalists'.

The MHP is notoriously difficult for most people to understand and many peope do not accept the solution even when it is clearly explained to them. In the lead we state, 'Even when given a completely unambiguous statement of the Monty Hall problem, explanations, simulations, and formal mathematical proofs, many people still meet the correct answer with disbelief'.

Does anyone here think that the above statement does not apply to the unconditionally stated problem, such as that given by Morgan, You will be offered the choice of three doors, and after you chose the host will open a different door, revealing a goat. What is the probability that you win if your strategy is to switch. ?

In other words, does anyone here think that the unconditional problem is not the MHP because it is too easy? Martin Hogbin (talk) 11:00, 17 January 2010 (UTC)

Nijdam, would you care to comment? You say above, 'once the problem is well stated, the soluton is (must be) obvious'. Martin Hogbin (talk) 15:54, 17 January 2010 (UTC)

What is there to be commented?Nijdam (talk) 16:59, 17 January 2010 (UTC)

I take it that you do believe that the solution to the unconditional problem is obvious. Is that right? Martin Hogbin (talk) 20:18, 17 January 2010 (UTC)

Martin - this is the "no-door" version discussed by Krauss and Wang. They consider it an easier version of the MHP, but not the "standard" version. Perhaps it should be discussed in the "Variants" or "Aids to understanding" section. -- Rick Block (talk) 18:03, 17 January 2010 (UTC)

Rick, I understand what the problem is and there is no ulterior motive behind my question. I am just trying to understand your POV. Do you think that the solution to the unconditional problem is obvious? Martin Hogbin (talk) 20:18, 17 January 2010 (UTC)

Why do you care what I think? For editing purposes we actually have a highly reliable source (in fact, a psychology source) that discusses this very question. They say it's an easier version. They say it's not the standard version. My (irrelevant) opinion is that they're right although I doubt that it is a significantly easier version. IMO (more irrelevance) most people would still try to solve this version by thinking about a specific example case - e.g. hmmm, let's say I pick Door 1 and the host opens Door 3, then there would only be two doors left but I still wouldn't know where the car is, so after the host opens a door there's one car and two doors and the chances must be 50/50. -- Rick Block (talk) 20:38, 17 January 2010 (UTC)

I care what you think because I want to resolve this dispute. I am trying to find out why a bunch of, I guess, reasonably intelligent people cannot agree. Both sides seem to keep saying the same thing over and over again but making no impression on the other side. What are we missing? Why do we continue to talk past one another? That is what I am trying to find out.

Nijdam, it would seem, does think that a solution to the well-defined unconditional problem statement is obvious. I have continued this point on the arguments page as I think this may be an important cause of disagreement. Martin Hogbin (talk) 20:56, 17 January 2010 (UTC)

Richard Gill also thinks that the solution to the well-defined unconditional problem is obvious. If the door you first chose has the car behind it with probability 1/3, then switching gives you the car with the complementary probability 2/3, since switchers get the car whenever stayers don't get the car, and vice-versa. He is furthermore really pleased with Boris Tsirelson's proposal to solve the conditional problem under the supplementary condition of *symmetry*, by using *symmetry*. Thus: if after you have chosen door 1 the probability the car is behind each other door is the same, therefore 1/3, and if the quizmaster opens a door by tossing a fair coin when he has a choice, then doors 2 and 3 are exchangeable. Therefore Prob(car is behind 2|player chose 1, quizmaster opened 3)=Prob(car is behind 3|player chose 1, quizmaster opened 2) and both are equal to the unconditional probability Prob(car is behind the remaining closed door|player chose 1, quizmaster opened a door)=2/3. All of this verbal maths argument can be converted into formulas, as I did yesterday. Gill110951 (talk) 21:16, 17 January 2010 (UTC)

When you say obvious, do you mean that most people would be able to spot this solution? 86.132.191.65 (talk) 22:50, 17 January 2010 (UTC)

Yes, spot the solution, or at the very least, quickly understand and accept it when it is presented to them. Martin Hogbin (talk) 11:16, 18 January 2010 (UTC)

Lots of people *do* spot the solution to the unconditional problem. And certainly most people accept it once they have heard it. The exception being lawyers, as was discovered by a survey at the University of Nijmegen. Everyone initially gives the wrong answer (including lawyers), afterwards everyone agrees with the right answer (except lawyers). Gill110951 (talk) 17:28, 18 January 2010 (UTC)

Do you have any more information on what proportion spot the solution without help, and are these results published anywhere. Martin Hogbin (talk) 00:36, 19 January 2010 (UTC)

Explicit assumptions

The 'probabilistic solution' in the article states that "This analysis depends on the constraint in the explicit problem statement that the host chooses randomly which door to open after the player has initially selected the car." Why not mention the other assumptions implicitly made?

This section starts with "Morgan state that many popular solutions are incomplete, because they do not explicitly address their interpretation of the question". And it ends with a solution which does the same. It doesn't make sense. Heptalogos (talk) 12:15, 17 January 2010 (UTC)

This is probably the result of arguments being played out on the page. The best way to correct the problem depends on who you are. I would like to change the first quote to, "Conditional analysis of the problem is only required if it is known that the host may not choose randomly which door to open after the player has initially selected the car." Others may not agree. Martin Hogbin (talk) 12:59, 17 January 2010 (UTC)

Yes (others may not agree). IMO, the article is at this point kind of a mess directly as a result of the senseless bickering on this page. Rather than actually improve the article by presenting a peacefully coexisting (per Boris) pair of unconditional and conditional solutions to the fully symmetric problem, these are being presented (and discussed here) as incompatible solutions. For the symmetric problem these solutions are essentially two sides of the same coin. The unconditional solution says the average probability of winning by switching is 2/3. The conditional solution says the conditional probability of winning by switching in any example case is also 2/3 (which of course means the average must also be 2/3). There is NO conflict between these approaches. You may not think the conditional approach is necessary, but it is certainly not wrong. You may not think the unconditional approach exactly answers the question, but it certainly says what the average probability is. These are both useful solutions, and it is also useful to understand the difference. And, unsurprisingly, this is exactly how most sources (at least most academic sources) treat the problem. -- Rick Block (talk) 18:30, 17 January 2010 (UTC)

I see you both react from your political programs. But I am not at all trying to continue the same discussion from yet another angle. Within the conditional section, which is a valid one as we all agree, I noticed some defects. How can we repair? Heptalogos (talk) 19:35, 17 January 2010 (UTC)

Mo comment was not intended to be political or to be supporting my view. I was just pointing out that, unless we can reach agreement on how to structure the article there is unlikely to be a solution to the problem that you have found. Maybe mediation will help. Martin Hogbin (talk) 20:15, 17 January 2010 (UTC)

An actual suggestion for an improvement rather than continued bickering? WHAT ARE YOU THINKING?  :)

I'd suggest revising the section to be more or less like the relevant paragraph out of the proposed unified solution section, above, which at least is intended to present the conditional approach as an alternative solution without introducing the POV that the unconditional solution is wrong. I think others may disagree that it accomplishes this goal, but I think it's an improvement over what's there now and by working on it together we can make incremental changes toward this goal. -- Rick Block (talk) 20:23, 17 January 2010 (UTC)

As a temporary solution, until we can reach a consensus on how to move forward, I am not fussed. Martin Hogbin (talk) 20:38, 17 January 2010 (UTC)

I like a lot of what Rick Block says above. I would like to underline that there is now a fantastic opportunity to simplify the whole article by presenting the answer to the conditional problem (with the supplementary assumption of symmetry between remaining two doors given player's first choice) as a corollary to the answer of the unconditional problem (with the assumption only that the first choice has probability 1/3 of being correct). My POV is furthermore that since both conditional and unconditional problems are interesting in their own rights and frequently discussed in the literature, both by "amateurs" and by "professionals", both problems need to be treated on the encyclopaedia page. Finally I want to repeat again that Marilyn vos Savant's simply asked "would you switch", she didn't ask for a probability, let alone specifying a conditional or unconditional probability. Personally I think that her problem is a sensible problem and as far as it looks like a math problem, it looks to me more like a problem of game theory than a problem of probability theory, since what the player ought to do depends on what the player believes the quizmaster is doing. Perhaps a sensible player prefers not to follow the advice of a calculation based on a specific assumption about the behaviour of the quizmaster. Perhaps the player would be happy just to discover that by starting with a uniform random choice of door and thereafter always switching (s)he gets the car 2/3 of the time, whatever the quizmaster does, and that this is the best one can hope for. It's amusing that the quizmaster's minimax strategy is actually the symmetric stategy, which makes the conditional probabilities equal to the unconditional ones. Gill110951 (talk) 21:35, 17 January 2010 (UTC)

If only it were that simple. There's still the issue of Morgan saying 'All simple solutions are false', then 'proving' it by contriving a host bias, which leads to the conditional non-symmetrical non-solution which is clamoring for equal time as well. Glkanter (talk) 21:46, 17 January 2010 (UTC)

Now also Gill is presenting his game theory in this section. We should really bring more structure in our discussions. Let's separate possible article restructuring (?) from improving the current structure, which will also be very helpfull in case of restructuring. If you state there cannot be such improvement without agreement on restructuring, then you're actually saying that you don't want to participate, which is really not necessary to mention. So I understand Rick is working out a proposal, which is quite welcome to me. Heptalogos (talk) 22:44, 17 January 2010 (UTC)

I'm not sure what proposal you're talking about. I suggested a unified solution section above. I thought progress was being made, but it was definitely derailed and is somewhat moribund at this point. I think what's actually going to happen is the mediation committee will decide fairly soon whether to accept the mediation request. Although I think it makes sense to wait on structural changes until after we know their decision, there's certainly no harm in making improvements we can all live with in the interim. -- Rick Block (talk) 04:17, 18 January 2010 (UTC)

No structural changes indeed, but (y)our suggestion to revise the section. I don't think that 'the unconditionalists' would mind too much about changes in the conditional section anyway. There are obvious defects that may be repaired relatively easy. Heptalogos (talk) 08:23, 18 January 2010 (UTC)

I now see that you already did change, thanks for that. Heptalogos (talk) 08:47, 18 January 2010 (UTC)

"Suppose you're on a game show..."

"You're" is a contraction for "you are." This means YOU. The reader. Do you know of any host bias? Can you assign anything but a uniform distribution to the host's 2 goat door choice? Glkanter (talk) 18:26, 17 January 2010 (UTC)

If you're not talking about what sources say, this thread belongs on the /Arguments page. Please move it there (or simply delete it since we've talked about this ad nauseam already). Thank you. -- Rick Block (talk) 18:40, 17 January 2010 (UTC)

No, Rick, the arguments page is for this:

"Please place discussions on the underlying mathematical issues on the Arguments page."

I'm not discussing the underlying mathematical issues. I'm discussing how much weight Morgan's paper should receive in the article. That's an article editor's responsibility. Which is the purpose of this talk page.

And we have NOT discussed this before. We have discussed that the MHP needs to be solved from the contestant's SoK. We have certainly not discussed that I, or you, or anyone, as the contestant, have no knowledge of any host bias. Glkanter (talk) 18:55, 17 January 2010 (UTC)

That's really nonsense Glkanter. You are not at all correctly weighing any viewpoint by personally judging the content of a source. Then you found a gap in the reference to the arguments page, misusing that. So we should change the reference from an including to an excluding one: "please post any underlying discussion not directly adressing changes in the article to the arguments page." I suggest that these new sections, including the one from Gill110951, all get removed directly by the admin. Heptalogos (talk) 19:52, 17 January 2010 (UTC)

Hepatlogos: you want to move the new section I wrote to the arguments page. Fine by me, but I put it here because it leads to proposals of how the article could be organised: it can be much shorter and needs much less maths, now we have a short integrated solution to the two main variants which people like to formulate. Gill110951 (talk) 21:45, 17 January 2010 (UTC)

Your arguments cannot lead to acceptable proposals because they are fully POV if there's no reliable source telling us what the MHP is(, but you). Heptalogos (talk) 21:55, 17 January 2010 (UTC)

Glkanter, you are saying that if the player doesn't know anything about the host behaviour, then the player *has* to assign a uniform distribution. I disagree on this. I think that the player has to take account of all possible host behaviours. Gill110951 (talk) 21:45, 17 January 2010 (UTC)

I didn't see this argument coming. Other than, 'Here I am on this game show, heck, I don't know where they put the car', what else is there for me to account for? Glkanter (talk) 21:52, 17 January 2010 (UTC)

Though Laplace promoted it, the argument that ignorance should be represented with uniform probabilities is not much believed these days. Especially when it is not difficult to account for the fact that you don't know the strategy of the quiz-team and quizmaster. It's called game theory. More or less invented by von Neuman, one of the greatest scientists of the 20th century. Nowadays *everyone" knows about it, and it is used and abused all over science and economics and politics. I know of a lot of disasters in applications of statistics where people plugged in uniform probabilities when they didn't know what to plug in, not realizing that this choice can actually produce a very biased/unrealistic answer. EG the legal case of the suspected Dutch serial killer nurse, Lucia de Berk. Gill110951 (talk) 18:23, 18 January 2010 (UTC)

I'm not so good with 'subtle'. And you're raising an issue, 'can we assume a uniform distribution?' that I thought had long been settled. So, if you will, please offer your comments of the Huckleberry section. Glkanter (talk) 18:40, 18 January 2010 (UTC)

Despite the very long discussion we have had, so far all have managed to remain civil, which is to our credit. Demands to move discussions and threats to call admins do nothing to cool tempers here. The only way to move forward is to all try to understand the other side's point of view. That may require still more discussion. That may be tiresome for those that believe the article is right as it is but better to discuss that edit war. I suggested earlier that we all made the effort to use the two discussion pages effectively but said that should be done gently. As the original point was essentially about an underlying philosophical issue I would ask the original poster to consider moving this to the discussions page. Martin Hogbin (talk) 20:35, 17 January 2010 (UTC)

I don't agree that we should account tempers and practice gentleness, or whatever emotions that give the discussion other dimensions than plain reasoning. We'd better also not explicitly imagine such emotions. Heptalogos (talk) 22:15, 17 January 2010 (UTC)

We should always be civil here and it seemed to me that the above conversation was heading in a direction where it could have become uncivil. Martin Hogbin (talk) 11:14, 18 January 2010 (UTC)

Revised version of probabilistic solution

I've edited the content of the Probabilistic section, attempting to make it more NPOV (similar to the proposal above). If anyone violently objects to this feel free to revert, although I hope it is viewed as an improvement. -- Rick Block (talk) 05:41, 18 January 2010 (UTC)

Good change. This is also better explaining how the conditional approach adresses the very specific, although it might not seem to matter in this case. Heptalogos (talk) 08:52, 18 January 2010 (UTC)

Nijdam has reverted this change saying "it was no improvement". More specific comments would be helpful. Another idea is to incrementally edit, rather than revert wholesale. Here's what I changed it to. It was intended to address at least most of JeffJor's comments as well, on the version now archived at /Archive_13#Proposed unified solution section. -- Rick Block (talk) 03:16, 19 January 2010 (UTC)

---

Tree showing the probability of every possible outcome if the player initially picks Door 1

Another way to analyze the problem is to determine the conditional probability in a specific case such as that of a player who has picked Door 1 and has then seen the host open Door 3, as opposed to the approach above which addresses the average probability across all possible combinations of initial player choice and door the host opens (Morgan et al. 1991). This difference can also be expressed as whether the player must decide to switch before the host opens a door or is allowed to decide after seeing which door the host opens (Gillman 1992).

The probabilities in all cases where the player has initially picked Door 1 can be determined by referring to the figure below (note the case where the car is behind Door 1 is the middle column) or to an equivalent decision tree as shown to the right (Chun 1991; Grinstead and Snell 2006:137-138 presents an expanded tree showing all initial player picks). Given the player has picked Door 1, the player has a 1/3 chance of having selected the car. Referring to either the figure or the tree, if the host then opens Door 3, switching wins with probability 1/3 if the car is behind Door 2 but loses only with probability 1/6 if the car is behind Door 1. The sum of these probabilities is 1/2, meaning the host opens Door 3 only 1/2 of the time. The conditional probability of winning by switching for players who pick Door 1 and see the host open Door 3 is computed by dividing the total probability (1/3) by the probability of the case of interest (host opens Door 3), therefore this probability is (1/3)/(1/2)=2/3. Although this is the same as the average probability of winning by switching for the unambiguous problem statement as presented above, in some variations of the problem the conditional probability may differ from the overall probability and either or both may not be able to be determined (Gill 2009b), see Variants below.

Car hidden behind Door 3	Car hidden behind Door 1		Car hidden behind Door 2
Player initially picks Door 1
Host must open Door 2	Host randomly opens either goat door		Host must open Door 3
Probability 1/3	Probability 1/6	Probability 1/6	Probability 1/3
Switching wins	Switching loses	Switching loses	Switching wins
If the host has opened Door 2, switching wins twice as often as staying		If the host has opened Door 3, switching wins twice as often as staying

---

The MHP - relations between sources

Selvin described a problem which he called the MHP. Savant Vos described another problem. Several sources reacted to Savant Vos (Morgan, Gillman, Grinstead) but did not mention Selvin. Who connected Selvin to Vos Savant? Or even more interesting (at least to me): can we create a graphical presentation of the links between all sources?

The reason why this could be interesting to all, is IMO that the question "what is the MHP" can only be answered by such a graphic. Where is the centre of gravity and how are sources connected? If any sources are outside (not connected), they should not me mentioded as the MHP. Heptalogos (talk) 12:46, 18 January 2010 (UTC)

Similar problems.

Can we judge other problems to be similar, if not related by sources? Heptalogos (talk) 12:08, 18 January 2010 (UTC)

Prominence.

I don't think 'weighing sources' is a formal Wiki-term. Only viewpoints in proportion to the prominence of each in the sources is mentioned. What is prominence? Apart from the position of a viewpoint within a source, how about the amount of sources in which a viewpoint exists? How about the amount of readers of a source (and thus the viewpoint)?

If many secondary sources write about a primary source, should the viewpoints of all secondary sources together be more prominent in the article than the viewpoints of the primary source? Would that be strange? Heptalogos (talk) 12:37, 18 January 2010 (UTC)

Any 'source' which attributes to the contestant some knowledge of how the host opens doors is not describing a story problem which begins, 'Suppose you're on a game show...' Which, as I understand it, is how most (all?) popular versions of the MHP begin. Glkanter (talk) 14:24, 18 January 2010 (UTC)

That's your opinion, and you're welcome to it. But since there are not just one or two, but many sources that don't agree with you we have to go with what the sources say. We can't exclude them because of something you or anyone else thinks about them. If it helps you understand their viewpoint any better, just imagine (for yourself) they're saying "Suppose you're on a game show and you knew ...". Furthermore, we can't even say (in the article) anything like "these sources violate the premise that you're on a game show" unless there's some published source we can attribute this to. The bottom line is what you or anyone else thinks about what reliable sources have to say is irrelevant. If they've made egregious errors, there would presumably be other reliable sources that call them on it. -- Rick Block (talk) 15:13, 18 January 2010 (UTC)

No Rick, my paragraph above is not an opinion. It is a logical conclusion. Glkanter (talk) 15:43, 18 January 2010 (UTC)

Rick, you wrote this, above:

"just imagine (for yourself) they're saying "Suppose you're on a game show and you knew ...". "

That contradicts the very essence of a game show. And the problem begins, "Suppose you're on a game show..."

And it's not in an any problem statement. That the host will always reveal a goat, and always offer the switch, have over time become 'accepted' premises. The contestant either colluding or mind reading with the host has not. Glkanter (talk) 16:04, 18 January 2010 (UTC)

@Heptalogos: the notion of prominence (it is also called weight) is primarily discussed in non-scientific articles, e.g. biographies. One example - during the recent US presidential election there was a continuous debate at talk:Barack Obama over how much prominence (if any) to give to Obama's relationships with William Ayers and Tony Rezko. These were stories that Fox News was broadcasting constantly, but mostly ignored by the mainstream media. The point is that accurately reflecting the prominence of a viewpoint within the complete set of reliable sources is an integral part of being NPOV. The readership of a viewpoint is not the issue, but rather the prominence of a viewpoint within reliable sources. One of the goals of this policy is to prevent Wikipedia from being used to promote "fringe" theories or partisan causes (this is policy as well, see WP:NOT#Wikipedia is not a soapbox or means of promotion). Prominence within secondary sources, not primary sources, is exactly what is meant. -- Rick Block (talk) 15:13, 18 January 2010 (UTC)

I have to wonder how prominent a source should be when it is accompanied by a commentary such as Seymann's. Is that common in peer-reviewed professional journals? Glkanter (talk) 15:43, 18 January 2010 (UTC)

@Glkanter, The American Statistician is a peer-reviewed journal for professional statisticians and professional teachers of statistics but not what within professional statistics would be called a research journal. It contains discussion and gossip and a teacher's corner and the like... I am not being disparaging, I am just trying to say that from a professional research-oriented statistician's point of view the journal does not carry a lot of weight and that particular article certainly doesn't contain much work. People who do important novel work publish it in big journals and maybe later do some advertising in The American Statistician. The Morgan et al paper exists and makes an important point which people like to refer to (distinguish conditional from unconditional) so it became a standard reference. At some point no-one reads the references anymore, people just refer to the standard references. The folklore as to "what is" the Monty Hall problem evolves. Science is a cultural, a social phenomenon, as much as anything else. I did not know about te Seymann commentary till I read about it here. He expresses my own gut feelings, I'm glad that that has been written down before. Long live Wikipedia, long live amateur science! You guys are doing the work which the so-called "professionals" (like me) don't have time to do anymore, since we need to spend all our time writing grant applications and grant reports and going to department meetings and doing politics just in order to survive. Gill110951 (talk) 18:16, 18 January 2010 (UTC)

My understanding is that Selvin first brought up the conditional formula a few months after his original letter to the journal. Other than contriving the 'host bias', but not a 'car placer bias', thereby creating an entirely new and different puzzle which is not about a game show, what did Morgan contribute? Glkanter (talk) 18:45, 18 January 2010 (UTC)

The MHP in economics and game theory

Here is what some say is the first solution of Monty Hall by Game Theory:

Barry Nalebuff (1987) Puzzles: Choose a Curtain, Duel-ity, Two Point Conversions, and More. Economic Perspectives vol. 1 nr. 1 pp. 157--163

http://www.jstor.org/pss/1942987

"Puzzle 1" is our very own Monty Hall. I'll try to collect more literature references (and find out what the contents are). But if doesn't belong on the talk page but somewhere else, please move it. Gill110951 (talk) 20:00, 18 January 2010 (UTC)

This is the same Nalebuff reference that's in the article (referred to in the History section). If you want more literature references you might look up the Barbeau references that are in the article. Many of the folks commenting here don't seem to realize this, but it really is quite a good article. Wikipedia's featured article standards are quite high - at least aspirationally equivalent to Brittanica. The sources are generally the original sources for the points that are made, and are the sources that other sources refer to. For example, if you read Rosenhouse's recent book you'll find its references look mighty similar to the references in the article. -- Rick Block (talk) 21:07, 18 January 2010 (UTC)

Rick, what about the issue described above on linking sources? Shouldn't all sources be linked to be addressing the same thing? Would such a presentation be able to show some prominence? Please react above, if you wish. Heptalogos (talk) 21:20, 18 January 2010 (UTC)

The History section of the article contains most of what I have been able to find about, well, the history of the problem. Barbeau's survey (the 1993 one in particular) is quite detailed, but contains nothing in the gap between Selvin's publication in 1975 and Nalebuff's paper in 1987 (which Barbeau does not mention). I haven't been able to find anything that was published in this interval although Nalebuff says "This puzzle is one of those famous probability problems, in which, even after hearing the answer, many people still do not believe it is true" - clearly implying it was famous (at least within academia) by that point. Nalebuff doesn't say where he got it from. There was a mention of it in Mathematical Notes from Washington State University newsletter shortly before vos Savant's first column (I don't have this source). I don't know where Whitaker heard of it. It would be interesting to compare Whitaker's version to the one in Mathematical Notes from WSU. Following the publication in Parade the problem was extremely widely known, both in popular sources and academia. Others on this page have claimed it was an example problem in probability classes at MIT - this is informally supported by a scene in 21, the movie about the MIT Blackjack Team - although I don't know how to pin down exact dates for this. -- Rick Block (talk) 02:38, 19 January 2010 (UTC)

"The basis to my solution is that Monty Hall knows which box contains the keys and when he can open either of two boxes without exposing the keys, he chooses between them at random." - Steve Selvin

The American Statistician, August 1975, Vol. 29, No. 3

http://montyhallproblem.com/as.html

Glkanter (talk) 22:47, 18 January 2010 (UTC)

And vos Savant completely overlooked the "when he can open either" part of this. Do you have a point you're trying to make? -- Rick Block (talk) 01:38, 19 January 2010 (UTC)

vos Savant published a reader's letter in a general interest magazine. As authors/critics in a peer-reviewed scientific journal, Morgan, et al (and/or the peers) have the responsibility of understanding the existing literature on the subject, which certainly includes Selvin's letters. Selvin's letters were in the same journal Morgan published their critique in. They shouldn't have been hard to find. Selvin completely puts the kibosh any any contrived 'host bias'. Without 'host bias', Morgan's statement that all simple solutions are 'false' has no legs to stand on. So, one more time, what is noteworthy about the Morgan paper? How did it advance the understanding of the MHP? Glkanter (talk) 12:59, 19 January 2010 (UTC)

Here's more from the same letter:

"Monty Hall wrote..."Oh and incedentally, after one [box] is seen to be empty, his chances are no longer 50/50 but remain what they were in the first place, one out of three. It just seems to the contestant that one box having been eliminated, he stands a better chance. Not so." I could not have said it better myself." - Steve Selvin

So Monty doesn't mention door numbers at all, talks about 50/50, (the probabilities) remain what they were, and 1/3. Steve Selvin says "I could not have said it better myself."

But Morgan and Rick know what the paradox 'really' is, and they claim this isn't it. 16 years and 35 years after Selvin himself already told us it is.

So, let's talk about how much weight to give to various sources. And I don't mean sources in the 'publication' sense. I mean 'sources' as in which author is (most) reliable.

Did the paradox change due to Morgan's paper? For Rick's interpretation to be right, it must have. It didn't. I covered this topic in more detail here. Glkanter (talk) 02:59, 19 January 2010 (UTC)

Are you suggesting some change to the article? If so, please say what it is. Thank you. -- Rick Block (talk) 03:20, 19 January 2010 (UTC)

Well, my contribution to the discussion would be along the lines of, "Selvin directly contradicts Morgan's contrivance of a 'host bias', and also directly contradicts Rick Block's interpretation of what the MHP paradox is. In this light, along with all the other errors and fallacies in the Morgan paper, and presumably those that rely on it, I recommend that Morgan's emphasis in the article be reduced to no more than a footnote in an appendix. Near the end of the article." But that's just my opinion, based on the reliable sources. What would you suggest, Rick? Glkanter (talk) 04:20, 19 January 2010 (UTC)

I would suggest that Morgan et al. is unarguably a WP:reliable source and that since its viewpoint (that the MHP is fundamentally a conditional probability problem) is consistent with a large number of other reliable sources and is a standard (if not the dominant) academic viewpoint, that this viewpoint should be prominently mentioned in the article. -- Rick Block (talk) 05:20, 19 January 2010 (UTC)

These last 2 paragraphs are instructive. I based my recommendation on how to edit the article on the words of the sources. You base your recommendation on your personal, unsupported opinion of the 'academic viewpoint' and a non-comparative use of the phrase 'large number of other reliable sources'. However many there may be, if they're based on Morgan, clearly they're ill-advised. This reliance on your personal interpretations, rather than the sources is consistent with the pro-Morgan POV of the article, and in the veto power you and Nijdam continue to yield over the editing of the article. Glkanter (talk) 13:10, 19 January 2010 (UTC)

You have this exactly backwards. I base my recommendation on what the predominant sources say. If you'd like me to list them again I'd be happy to. You base yours on your own OR and that of a few others commenting on this page who have concluded (on their own, not from ANY published sources) that Morgan et al. contains "errors and fallacies" and your argument that what this paper says contradicts what Selvin says (??!!). Even if this latter point were true (it's not), that would make the POV of this paper simply another POV that by the fundamental Wikipedia content policy of WP:NPOV SHOULD be included, "in rough proportion to [its] prevalence within the source material." Rather than try to assess this prevalence you say "However many there may be, if they're based on Morgan, clearly they're ill-advised." What you're saying is that you don't want the POV of these sources, no matter how many there are (!), fairly represented in the article. You are the one here relying on your personal interpretation, rather than the sources. -- Rick Block (talk) 14:27, 19 January 2010 (UTC)

Yes, I'm familiar with this aggregation technique you subscribe to. I learned about it here.

Of course Morgan's paper is full of errors and fallacies. They mis-quote vos Savant, they have a math error discovered by Martin and Nijdam, they contradict Selvin by creating a 'host bias'. There's plenty more. Glkanter (talk) 14:01, 20 January 2010 (UTC)

Morgan includes a very brief history of the problem, referring only to two sources of the "prisoner's dilemma" from the 1960s. No mention of Selvin. I just did a search of the Morgan article. No mention of Selvin. Not so good for a piece titled, "Let's Make A Deal: The Player's Dilemma" that criticizes the work of others, twice accusing vos Savant of 'false' deeds in the introductory paragraph. Glkanter (talk) 20:59, 19 January 2010 (UTC)

This is not relevant to their point. They're not criticizing Selvin. They're criticizing vos Savant (who never mentioned Selvin either). -- Rick Block (talk) 22:22, 19 January 2010 (UTC)

Yeah, just why did these 4 uninformed hooligans pick on that nice general interest magazine lady in their prestigious peer-reviewed professional journal? Glkanter (talk) 22:30, 19 January 2010 (UTC)

Well, what do the sources say? Ah yes, right at the end of the intro of Morgan et al. they say that although, under certain circumstances, her answer is correct, her methods of proof are not. This is their POV. You apparently don't agree. But you're not a reliable source. Gillman is. He says (presumably untainted by Morgan et al. since he published essentially simultaneously) "Marilyn's solution goes like this ... This is an elegant proof, but it does not address the problem posed.". Grinstead and Snell is. They say (in their textbook, 14 years later, plenty long enough for Morgan's and Gillman's egregious errors to have been discovered) "This very simple analysis [the outcome of a predetermined "stay" strategy compared a predetermined "switch" strategy], though correct, does not quite solve the question that Craig posed." (not quite as direct as Morgan et al. or Gillman, but it means the same thing).

How many sources would you like me to produce before you're willing to call this a mainstream POV? -- Rick Block (talk) 01:33, 20 January 2010 (UTC)

There are reliable sources that criticise Morgan, Seymann, of course, who was published in the same journal and Rosenhouse, in his book devoted entirely to the MHP. He refers to the paper as 'their bellicose and condescending essay', in which they 'presumed to lay down the law regarding vos Savant’s treatment of the problem'. Of Morgan's criticism of vos Savant, Rosenhouse says, 'Rather strongly worded, wouldn’t you say? And largely unfair,...'. Martin Hogbin (talk) 10:14, 20 January 2010 (UTC)

And, how many sources would you like me to produce before you're willing to call this a mainstream POV? Even if some sources criticize Morgan et al., given that there are other reliable sources supporting the POV that vos Savant doesn't quite address the question this is a perfectly valid POV. -- Rick Block (talk) 13:09, 20 January 2010 (UTC)

That depends, Rick. Is the Wikipedia article about the Monty Hall problem, or a critique of vos Savant's column? Glkanter (talk) 13:20, 20 January 2010 (UTC)

I'll be more specific. The POV is that unconditional solutions (such as those used by vos Savant and most popular sources) don't quite address the Monty Hall problem. -- Rick Block (talk) 13:37, 20 January 2010 (UTC)

No, Rick. Morgan criticizes vos Savant and doesn't mention Selvin. Gillman criticizes 'Marilyn', and Grinstead and Snell refer to 'Craig'. This is all from your diff earlier in this section.

Rick, are those sources criticizing vos Savant, or the simple solutions to the Monty Hall problem? In their words, please, not your interpretation of what they might have meant. Glkanter (talk) 14:08, 20 January 2010 (UTC)

Do they rely on a 'host bias' to make their point? How does the 'Combining Doors' solution fail to address the Monty Hall problem? Glkanter (talk) 13:44, 20 January 2010 (UTC)

No, Morgan et al. generically criticize all unconditional solutions. Their "false" solutions F1, F2 (one of vos Savant's), F3 (vos Savant's experiment), and F5 are specific unconditional solutions, but it's clear they are criticizing all unconditional solutions:

• "Thus is the player having been given additional information, faced with a conditional probability problem."
• "The distinction between the conditional and unconditional situations here seems to confound many"
• "The correct simulation for the conditional problem is of course to examine only those trials where door 3 is opened by the host. The modeling of conditional probabilities through repeated experimentation can be a difficult concept for the novice, for whom the careful thinking through of this situation can be of considerable benefit."
• "In general, we [meaning anyone] cannot answer the question 'What is the probability of winning if I switch, given that I have been shown a goat behind door 3?' unless we either know the host's strategy or are Bayesians with a specified prior."

Gillman criticizes Marilyn directly, but the reason he states for his criticism is that Marilyn's solution does not address the conditional probability: "Game I [what he considers to be the MHP] is more complicated [than Game II in which "you have to announce before a door has been opened whether you plan to switch" - italics in the original]: What is the probability P that you win if you switch, given that the host has opened door #3? This is a conditional probability, which takes account of this extra condition." (italics in the original). His POV is clearly that the MHP is a conditional probability problem, and that this is not addressed with an unconditional solution.

What Grinstead and Snell say (from above) is clear as well. They're not directly criticizing Marilyn, but saying that the problem Craig posed (that vos Savant addressed unconditionally) is a conditional probability problem.

Do they rely on host bias to make their point? What difference does it make?

How does "Combining Doors" fail to address the Monty Hall problem? It is an unconditional solution (are you arguing that it isn't?). -- Rick Block (talk) 16:09, 20 January 2010 (UTC)

Selvin rules out any 'host bias' in the Monty Hall problem. The 'Combining Doors' solution shows a goat revealed by the host. Then the contestant decides whether or not to switch. I don't even call it 'probability', let alone 'unconditional'. I call it 'simple'.

Do any of these sources mention Selvin? Glkanter (talk) 16:52, 20 January 2010 (UTC)

What sort of obligation did Morgan, et al have as writers in a peer-reviewed professional journal?

The title of their paper is "Let's Make A Deal: The Player's Dilemma".

Where they expected to know the history of the Monty Hall problem? In 1991, they mention the "prisoner's dilemma" from the 1960s, but not Selvin's letters of 1975 to the very same journal Morgan was published in. Glkanter (talk) 14:15, 20 January 2010 (UTC)

Do you have some point related to editing the article? It would be helpful if you make whatever point you're trying to make in your initial post without making someone ask what your point is. -- Rick Block (talk) 16:19, 20 January 2010 (UTC)

Rick, surely you're familiar with the 'Socratic Method'? I could call them 'lazy' or 'uninformed' or 'unprofessional', but that would be my personal opinion. This way, qualified people will hopefully answer my question, and that these guys were 'lazy' or 'uninformed' or 'unprofessional' and wrote a paper that is not a reliable source for the Monty Hall problem article (other than a footnote, perhaps) will become self-evident. Just maybe not to everyone. Glkanter (talk) 16:59, 20 January 2010 (UTC)

So, you're saying because they don't mention Selvin they should not be considered a reliable source? Please read Wikipedia:Reliable sources. What makes a source reliable has nothing to do with your (or anyone else's) judgment of the content. What you're effectively arguing is that we should ignore sources that don't match your POV. This is contrary to the fundamental content policies of Wikipedia (specifically WP:V and WP:NPOV). It is NOT our job to "fact check", or "ensure the logical consistency", or apply any value judgment at all pertaining to what reliable sources say. We need to understand what they say, and fairly represent it in the article. That's all. -- Rick Block (talk) 17:47, 20 January 2010 (UTC)

I'm saying by asking a question, the answer becomes self-evident. Each editor who takes part in the consensus editing will make his own judgment based on his understanding of the source materials and Wikipedia's policies and guidelines. It's The Monty Hall problem article, not the 'Marilyn vos Savant's Parade Magazine Column Is Not Fit For Use As A University Text Book On Probability' article. Glkanter (talk) 18:16, 20 January 2010 (UTC)

This Archiving Is So Stupid...

I would rather we just wrote in the archives, and then someone told us when to start a new one. It would make more sense than what's going on now. Glkanter (talk) 17:11, 20 January 2010 (UTC)

This page is very big — still over 350k. It seems to me that it's easier to let the bot prune the deadwood discussions than to do it manually, but you can change it if you wish.

—WWoods (talk) 07:59, 21 January 2010 (UTC)

Thanks for you prompt response. You indirectly pointed out a pet peeve of mine. The talk pages and archives are maintained for the benefit of the users. The way the archiving is taking place does not maintain the chronology of the sections. In fact, there may be older sections in archive 13 than in archive 12. So in order to use this bot, the users are not nearly as well served as they are with some other methods. Glkanter (talk) 10:02, 21 January 2010 (UTC)

Proposed Edits To The Probabilistic solution

"The basis to my solution is that Monty Hall knows which box contains the keys and when he can open either of two boxes without exposing the keys, he chooses between them at random." - Steve Selvin, The American Statistician, August 1975, Vol. 29, No. 3

Given that the originator of the Monty Hall problem clearly states that the host chooses doors (boxes) randomly when he has two goats (empty boxes) to choose from, any 'host bias' scenarios should be treated the same as the other 'variants' included in the 'Variants - Slightly Modified Problems' section.

Accordingly, I propose removing the following from the Probabilistic solution section:

From paragraph 1: These solutions correctly show that the probability of winning for all players who switch is 2/3, but without certain assumptions this does not necessarily mean the probability of winning by switching is 2/3 given which door the player has chosen and which door the host opens.

From paragraph 1: The difference is whether the analysis is of the average probability over all possible combinations of initial player choice and door the host opens, or of only one specific case—for example the case where the player picks Door 1 and the host opens Door 3. Another way to express the difference is whether the player must decide to switch before the host opens a door or is allowed to decide after seeing which door the host opens (Gillman 1992). Although these two probabilities are both 2/3 for the unambiguous problem statement presented above, the conditional probability may differ from the overall probability and either or both may not be able to be determined depending on the exact formulation of the problem (Gill 2009b).

From paragraph 2: This analysis depends on the constraint in the explicit problem statement that the host chooses randomly which door to open after the player has initially selected the car.

Eliminate the second image. It's just the first image rotated 90 degrees.

I noticed that the only solutions offered in this section are the 2 detailed images of every possible outcome once a door has been selected. From the 'Probabilistic' images the reader can determine that the likelihood of his choice being the car is 1/3 by adding the 1/6 + 1/6 from the 'Total probability' column, or he can do the (probably unknown to him) calculation of the remaining door '(1/3)/(1/3 + 1/6), which is 2/3'.

Or he can use logic and derive the 1/3 for his selection hasn't changed, much like in Selvin's second letter to The American Statistician, "Monty Hall wrote..."Oh and incidentally, after one [box] is seen to be empty, his chances are no longer 50/50 but remain what they were in the first place, one out of three. It just seems to the contestant that one box having been eliminated, he stands a better chance. Not so." I could not have said it better myself." - Steve Selvin Glkanter (talk) 12:53, 21 January 2010 (UTC)

Rather than delete, there's another suggestion for revisions above, see #Revised version of probabilistic solution. Specific comments on these suggestions:

• My suggestion from above also deletes the "without certain assumptions" bit from the first paragraph. Is this what you're actually objecting to, and if so does the suggestion above address this concern? I think introducing this solution as "another way to analyze the problem" is about as flatly NPOV as possible.
• I think it's important to explain what the difference is between the two approaches (average probability vs. probability in the specific case). Does the version I suggest above address the concern here as well (which I'm thinking is actually the sentence starting "Although these two probabilities..."). In what I suggest above this is moved, and rephrased with the intent of making it clear that the average probability and probability in the specific case differ only in variations of the problem statement.
• The figure is rotated (showing all possible car locations against a constant initial player choice and door the host opens rather than all possible player choices against one arrangement of goats and car). I'd be fine with one image, but I strongly prefer this one rather than the other one. My reasons for this are
  1. This image matches the example case given in the problem description where the player has picked door 1 and the host has opened door 3.
  2. This image shows the symmetry between the host opening door 2 and the host opening door 3 (the image itself is symmetrical)
  3. This image does not have the cartoonish graphic.
  4. The column widths in this image match the probabilities. This creates a visual interpretation consistent with the text.
  5. With this image, it's easy to see the result where the host opens either door.

-- Rick Block (talk) 15:16, 21 January 2010 (UTC)

Thanks for the prompt response, Rick. I think just having a symmetrical condition solution section is instructive enough. And if both solutions rely on the same chart, pointing this out may be enough for the reader. The less ornate image is much easier to discern both the (1/3)/(1/3 + 1/6) and the 1/6 + 1/6 from.

Your description of how to do a conditional formula would be instructive. So, we could add:

Referring to either the figure or the tree, if the host then opens Door 3, switching wins with probability 1/3 if the car is behind Door 2 but loses only with probability 1/6 if the car is behind Door 1. The sum of these probabilities is 1/2, as the host will open Door 3 only 1/2 of the time. The conditional probability of winning by switching for players who pick Door 1 and see the host open Door 3 is computed by dividing the total probability (1/3) by the probability of the case of interest (host opens Door 3), therefore this probability is (1/3)/(1/2)=2/3.

I changed a couple of words. Glkanter (talk) 15:44, 21 January 2010 (UTC)

Again, not arguing, just trying to understand what you're saying. Is the "less ornate" image you're referring to the tree diagram as opposed to the table with the pictures at the bottom of the "Probabilistic solution" section? Which figure are you referring to in your conditional solution, and where are you suggesting adding this?

To clarify my comment to you, I'm saying I prefer the table-with-pictures image in the Probabilistic solution section to the similar one in the Popular solution section (for the reasons provided above). -- Rick Block (talk) 01:25, 22 January 2010 (UTC)

The tree/table that you added to this discussion is the one I want to keep. For both sections. For the reasons I gave above. There are currently 3 unique solutions in the Popular section. The first one would be replaced by my proposal, including the tree/table.

[moments later] I just got your point. You want to remove the image with the heads. The tree/table could be used for both the revised first solution and the 'you get the opposite' solution. Chun's chart shows both, as I mentioned to Martin. And I still want to delete the 2nd image from the probabilistic solution. Glkanter (talk) 01:49, 22 January 2010 (UTC)

... and keep the image with the heads in the Popular solution section? I'll note that there's no correspondence between Chun's diagram and the "heads image" (Chun's diagram is "rotated" in the same way as the "no heads image" in the Probabilistic solution section). -- Rick Block (talk) 04:56, 22 January 2010 (UTC)

No, the heads image gets removed. Chun works with Popular's revised '1/3 2/3' and 'opposite'. And Probabilistic. Glkanter (talk) 05:40, 22 January 2010 (UTC)

Proposed Edit To The Popular solution

I'd like to make this the first solution offered. Attributed to Selvin's 2nd letter; Chun 1991; Grinstead and Snell 2006:137-138),

Your initial chance of selecting the car is 1/3. This is unchanged by the host revealing a goat. Therefore, when offered, switching doubles your chance of winning the car from 1/3 to 2/3. Glkanter (talk) 13:14, 21 January 2010 (UTC)

I think the concept is good but the reason why the unchanged chance of having originally chosen the car mean that the chances of winning by switching are 2/3 is afar from obvious to most people. The solution needs further explanation, maybe along the lines of you always get the opposite of your original choice if you swap. Martin Hogbin (talk) 14:31, 21 January 2010 (UTC)

Actually, my proposal is just a re-write of what's already in there. But, let's flesh out your idea while sticking with reliable sources. There's already 3 sources for the current more-complicated statement in the article. Selvin agrees with Monty Hall that it remains at 1/3 in his 2nd letter to The American Statistician. In his 1st letter, he has a table of all 9 possible outcomes, 3 locations for the car * 3 contestant choices. He lumps each of the the two-goats choice as 1 line item. This chart, which shows all possible outcomes, could accurately be summarized as 'you get the opposite'. (Chun's and Grinstead & Snell's table also shows this 'opposite' result by switching.) Chun and Grinstead & Snell demonstrate the 1/3 in their chart in the Probabilistic section. I guess we could add the chart to the Popular solution. I think it would demonstrate the equivalency of the differing approaches if they both used the same sources. All they do in the chart is divide the original 1/3 contestant door by 2. Then all the contestant does is add the 1/6 & 1/6 back together. And, there are 2 other solutions already provided in the section. Glkanter (talk) 15:11, 21 January 2010 (UTC)

"This is unchanged by the host revealing a goat." is not what Grinstead and Snell say. I can't find my copy of the Chun reference, but I highly doubt this is what he says either (do you have a copy of this reference, or are you interpreting this from the tree diagram?). What Grinstead and Snell actually say is: "Using the “stay” strategy [deciding beforehand to stay with the initial choice whatever the host does], a contestant will win the car with probability 1/3, since 1/3 of the time the door he picks will have the car behind it. On the other hand, if a contestant plays the “switch” strategy, then he will win whenever the door he originally picked does not have the car behind it, which happens 2/3 of the time." Selvin doesn't say this either - he's quoting Monty Hall. If you want to include the full quote that's fine, but from a sourcing perspective it would be much better to have a secondary source for this.

And, you're completely missing the point of the table and the tree. The host only opens one door, not both. Before the host opens a door the player's chance is 1/3 (in the tree this is the 1/3 for Door 1 on the left). After the host opens either, but only one, of the doors the player's chance is 1/6 and the other door's chance is 1/3. Viewed as a conditional probability this means the player's chance, in this case, is 1/3 and the other door's chance is 2/3. You don't add the 1/6 and 1/6 to get "the player's chance". You divide 1/6 by the probability of being in this case (which is 1/2). -- Rick Block (talk) 15:45, 21 January 2010 (UTC)

Yes, I am using them as a source based on the diagram showing the Total Probability is 1/6 + 1/6 = 1/3.

Selvin says of Monty Hall's quote, 'I could not have said it better myself'. That means he agrees.

I can use that table any way that is mathematically sound. The column heading is 'Total Probability'. It's really nothing more than Selvin's original table from his first letter reduced to just 1 of 3 random contestant picks, plus the 2-goat options are split out. That I choose to add 1/6 + 1/6 rather than do the unfamiliar division is certainly a valid use of the figures. Just not what the authors expected. Glkanter (talk) 15:56, 21 January 2010 (UTC)

If you are interpreting the table the words should reflect that. As stated it sounds like you're saying these sources state this in words. To make it clear you're interpreting the table (which is a valid thing to do) I'd suggest you say what it is in the table that you're referring to.

My point about adding 1/6 plus 1/6 is that by doing this you're determining the player's chance of initially selecting the car (before the host has opened a door). This is the exact point we've been talking about for over year. It is NOT mathematically sound to add these together and call it the chance of the player's door hiding the car after the host has opened a door. This is not what the table shows. It's the chance of initially selecting the car. It is also the chance of winning the car if you ignore what the host does and stick with your original choice. But this 1/3 (=1/6+1/6) is not the chance in effect after the host has opened a door (say Door 3) where the opened door's chance is now 0. If you're saying the player's door's chance is 1/3 because it's 1/6+1/6, the chance of either of the other doors (by the same logic) is 0+1/3. The opened door's chance is 0 only conditionally, i.e. 0 divided by 1/2. Its total probability (considering all cases) is STILL 1/3! Look at the table. The other door's chance is 2/3 only conditionally, i.e. 1/3 divided by 1/2 - but its total probability is also still 1/3. Similarly, the original door's chance after the host has opened a door is also only the conditional chance, i.e. 1/6 divided by 1/2. The numeric answer is 1/3 which is the same number as its total probability considering all cases, but where this number comes from (according to the table) is not 1/6+1/6 "unchanged" by the host opening a door. It's the original 1/3, divided into two pieces (reflecting the cases where the host opens door 2 and door 3), and then divided by the probability of these cases (which is 1/2). The result is the numeric probability doesn't change, but the reason for this, as shown by the table or the tree, is that it splits it into 1/6 and 1/6 and then becomes 1/3 only as a conditional probability (i.e. by dividing by 1/2). -- Rick Block (talk) 18:03, 21 January 2010 (UTC)

The tables in the Probabilist solution section are derived from Selvin's first letter. He lists 9 cases and determines 3 lose when switching, for 1/3. The Probabilistic section's table shows only 1 of the 3 random contestant choices (door #1) and splits out the 1/3 for 2 goats by dividing by 2 for 1/6 and 1/6. This gives 2 cases at 1/3 each and 2 cases at 1/6 each in the Total Probability column of Chun's and Grinstead and Snell's table.

1. It looks like you can't solve the conditional problem without also solving the unconditional problem. That's what the 1/6 + 1/6 gives us. From the Total Probability column of the same table they use to solve the conditional problem. I have now solved the problem unconditionally.

2. To get to 1/6, they divided Selvin's 1/3 by 2. To solve this conditionally, you're telling me I need to divide by 1/2. OK. To determine my door's probability of having a car, I will divide by 1/2. Which is the same as multiplying by 2. So, (1/3)/2 = 1/6. 1/6 * 2 = 1/3 probability I have chosen a car. I have now solved the problem conditionally.

3. Boris suggested "The coexistence of the conditional and the unconditional can be more peaceful." What could be more peaceful than both solution sections referencing the same table of outcomes? Glkanter (talk) 18:48, 21 January 2010 (UTC)

I'm not sure I'm understanding what you're saying - I'm not arguing here but would like to echo back what I think you're saying.

Tree showing the probability of every possible outcome if the player initially picks Door 1

By the tables in the Probabilistic solution you mean this tree diagram (which is Chun's, not Grinstead and Snell's) and the large table with the images at the end of the section. The diagram and table show only one of the 3 possible initial player picks (i.e. using player picks door 1 as an example). [just a note - these don't derive from Selvin's table. Chun published the tree diagram, and the large table is simply another view of Chun's diagram. Grinstead and Snell's diagram is larger and shows all possibilities, not just the ones involving the player picking door 1]

1. The diagram and the table shows the probability across all cases, so you can solve either the conditional or unconditional problem. Unconditionally, if you don't switch you win the car with probability 1/6+1/6 (top two lines of the diagram - middle column in the table) and if you do switch with probability 1/3+1/3 (bottom two lines of the diagram, outer two columns in the table).

2. Where the 1/6 comes from is the original 1/3 (the chance of a player who has picked door 1 selecting the car before the host opens a door) divided by 2 (because the host can open either door). To make this the conditional probability you divide by the probability of the case of interest (e.g. host opens door 3) which is 1/2 (from the diagram this is one of the 1/6 lines plus one of the 1/3 lines, from the table it's either the right half or the left half). [just a note - perhaps a little more intuitively, what this is saying is the door you've picked has a 1/6 out of 1/2 chance of hiding the car in the case the host opens door 3] This is the conditional solution.

3. Boris suggested peaceful coexistence of the conditional and unconditional - what could be more peaceful than showing both in the same diagram and table?

You don't explicitly say it, but it sounds like you're suggesting you're OK with using these two figures (Chun's diagram and the table) in both the "Popular" and "Probabilistic" solution sections. Do I have this right? -- Rick Block (talk) 19:33, 21 January 2010 (UTC)

As a component of all the edits I suggested, yes, the 1 table (I already suggested removing the 2nd one) could be added to the Popular solution section. While the 2 1/6 lines are more detailed than necessary, I think we would be OK. Once the reader got to the symmetrical Probabilistic section and saw the same table, he might just grasp the coexistence we're trying to show.

I don't know what you mean by 'outer column'. All the values I referenced come from the 'Total probability' column.

I'm using the conditional method to derive the probability of my door being the car (1/6)/(1/2) which is the same as 1/6 *2. It's a much less complicated formula than door 3's. And it's a more consistent approach to always solve for my door.

I'd like to see some changes in the FAQs, too. Glkanter (talk)

I'm losing track of all the proposals. And already some time ago I made aa suggestion on this page: Talk:Monty Hall problem/Construction. There you find my proposal for the beginning of the article. Nijdam (talk) 22:16, 22 January 2010 (UTC)

Nijdam, do you intend to unconditionally revert any edits that I make? Do you agree with the reasoning I'm using to propose these changes? Glkanter (talk) 22:50, 21 January 2010 (UTC)

Let's carry on

As I read this discussion between Rick and the guy from the Mediation Committee, we shouldn't do anything different as we wait for the formal mediation.

Accordingly, I will continue proposing, and when appropriate, making changes to the article. Glkanter (talk) 17:07, 22 January 2010 (UTC)

What happens now?

I've shown that Morgan overlooked Selvins' 'the host acts randomly when faced with 2 goats (boxes)'.

Nijdam has been uncommunicative about his intentions and reasons.

I edited the article and Nijdam reverted me. I reverted him back. What's next? Glkanter (talk) 12:33, 23 January 2010 (UTC)

I've undone it. Your change to the popular solution is not good, because you make an unexplained jump, which is clearly explained in the original. Your changes to the probabilistic solution cannot be done by the argument that you proved Morgan wrong, or similar, which is POV. Morgan did not criticize Selvin anyway. It might me easier for you to make several logical subchanges, with less chance to be undone all. Heptalogos (talk) 13:18, 23 January 2010 (UTC)

Yes, had Morgan, et al even the vaguest knowledge of the puzzle's history, a simple letter to vos Savant referencing Selvin's 2nd letter would have allowed her, as Selvin also found it necessary, to clarify that the host chose randomly when faced with 2 goats. Glkanter (talk) 14:12, 23 January 2010 (UTC)

She did not even need to clarify, because it's perfectly reasonable to assume no host bias. But this discussion doesn't make any sense in discussing an encyclopedian article. Heptalogos (talk) 14:19, 23 January 2010 (UTC)

I think it is best to leave any editing until we get an input from the mediator. So long as this happens within a reasonable time. Martin Hogbin (talk) 13:28, 23 January 2010 (UTC)

You changed Sources of confusion into 3 parts: 50/50 paradox, assumptions, and (un)conditional. But the last one is hardly explaining the discussions concerning the number of the door. Also, the second one starts with "selvin", out of the sky. Heptalogos (talk) 13:55, 23 January 2010 (UTC)

'Increasing the number of doors' and 'N doors'

'Increasing the number of doors' is in the 'Aids to Understanding' section. 'N doors' is in the variants.

It seems confusing to me that the same idea would be appropriate for both sections. Glkanter (talk) 13:16, 23 January 2010 (UTC)

Sources of confusion

Most of the article's content is about confusion. I see three sources:

1. Incomplete information: we assume worlds outside and/or within the stated problem.

How is the setup? What is the behavior? What is the knowledge?

2. Surplus information: we decide which information to use and which not.

Game show, door numbers, host knowledge, talking host.

3. Paradox: the presentation of the information leads to wrong assumptions and decisions.

A door is not just randomly opened out of three or two, which is the missing key for many.

Source 3 is the basic reason for the problem.
Source 1 is the basic reason for the paradox.
Source 2 is the basic reason for the afterparty disagreements.

The article uses the same order: paradox first, then the assumptions explained, and then the discussion about the details included in or exluded from the conditions. I propose to setup the article using these headers, or similar:

• Problem statement: the usual and the correct answers
• Paradox: simply explained
• Assumptions: reasonableness and explicitness
• Conditions: possibilities and variations
• History: (conflicting) perspectives
• Bayesian analysis
• etc. Heptalogos (talk) 20:13, 23 January 2010 (UTC)

Your section 'Paradox:simply explained' needs to convince people of the right solution. I may not normally be the purpose of an encyclopedia to convince people but, unless readers believe the solution, the rest of the article is wasted. As most people get the answer wrong and many do not believe the answer even when explained to them, this point is of primary importance.

Split the article into 2 articles: The MHP Problem and Solution, and The MHP's Conflicting Perspectives. Because nobody, other than you guys, gives a shit. Glkanter (talk) 16:58, 24 January 2010 (UTC)

Where will you put the conditional solution? Martin Hogbin (talk) 16:08, 24 January 2010 (UTC)

I think the article should indeed not be basically explanatory, but that's already done now in the current article, e.g. in the popular solution section. This may be in the Paradox section. We need to end it with the explicit assumptions needed for this simple explanation(s) to be correct, which is then an inroduction to the next chapter. Is it an option to link to this, which is about the best primary source available? This will also provide an opportunity for people to understand it better. Marilyn offers some examples, like the sea shells. If people still don't understand, they should maybe visit an internet forum to discuss.

The assumptions section will be the introduction to the Conditions section. This seems to be the best section for those sources that go into detail, like Morgan. But Morgan may already be mentioned as a source in the assumptions section, or even in the last part of the Paradox section where the necessary assumptions are given. We'll need a source for that statement anyway. This setup might also be in line with the combined solutions idea of Rick. Heptalogos (talk) 18:48, 24 January 2010 (UTC)

I'm not seeing a significant difference between what you're suggesting and the current structure. You're missing the WP:LEAD (which needs to summarize the entire article - or is this what you mean by "Problem statement"?), but other than that it seems extremely similar. I think it would be helpful if you mapped out where the existing content (by section) would go in this structure and if you're suggesting deleting anything explicitly mentioning that. Without this, it's a little difficult to understand what you're really talking about. For example, where would the content currently in "Aids to understanding" go? -- Rick Block (talk) 20:32, 24 January 2010 (UTC)

Roger. I think I need to shuffle this into a new article on my personal page. Nothing needs to be deleted principly. Heptalogos (talk) 20:46, 24 January 2010 (UTC)

For those who don't give a s...

Glkanter: How about near the beginning of the article we state, For a simpler and less comprehensive summary see this version or some such? hydnjo (talk) 20:40, 24 January 2010 (UTC)

Interesting link from that page. A reliable online source that treats the problem simply. Monty Hall Problem Martin Hogbin (talk) 20:51, 24 January 2010 (UTC)

Is Selvin's Unconditional Solution 'False'

Morgan, without any acknowledgment of Selvin, including his 'equal goat door constraint', calls all unconditional solutions 'false'.

Selvin used a 9 row table (3 car locations * 3 contestant choices) to solve the puzzle he created. Glkanter (talk) 15:02, 25 January 2010 (UTC)

And, in his initial solution, he didn't make all his assumptions explicit. In his second letter, he said "The basis to my solution is that Monty Hall knows which box contains the keys and when he can open either of two boxes without exposing the keys, he chooses between them at random." [emphasis added] With these qualifications, his initial solution is fine. Without them, not so much. Let's review. Selvin poses the problem and solves it unconditionally. When questioned, he says what the critical assumptions are behind his solution. 16 years later, vos Savant publishes the problem. When questioned, she omits one of the critical assumptions. Morgan et al. (and others) follow through the consequences of omitting this assumption, concluding the probability of winning by switching (without this assumption) is not 2/3 but 1/(1+p) and, if we take p to be 1/2 (which is what the omitted assumption does) the answer is 2/3. If not, we don't exactly know the probability of winning by switching but since it's in the range of 1/2 to 1 it makes sense to switch anyway. The analysis that leads to the 2/3 solution does so regardless of what we assume p is. What Morgan et al. (and others) consider the "proper analysis" doesn't. Does that roughly match your understanding? -- Rick Block (talk) 02:54, 26 January 2010 (UTC)

You seem to be accepting that in the symmetrical case, a solution that does not distinguish between legal doors opened by the host is acceptable. I agree.

I also agree that vos Savant failed to make the assumption of symmetry explicit in her explanation, but as I have demonstrated, however you treat the problem the only logical and consistent assumption is that the host chooses a legal door randomly. Martin Hogbin (talk) 09:39, 26 January 2010 (UTC)

Let's review, Rick.

Selvin introduces his puzzle in The American Statistician

He solves it unconditionally, with the 9 line table of all possible outcomes

A few months later he clarifies that Monty Hall knows where the car is, and that Monty Hall chooses randomly when faced with 2 goats

15 years later vos Savant answers a reader letter and leaves some of Selvin's premises unstated

1 year after vos Savant, while never mentioning Selvin, Morgan claims all unconditional solutions are false. This is also published in The American Statistician, in a piece called 'Let's Make A Deal: The Player's Dilemma', not 'A Critique Of vos Savant's Parade Column'

Selvin's puzzle and solution leave no ambiguities as to the premises, or insistence that it 'must be conditional' or room for 'without certain assumption'. Glkanter (talk) 11:46, 26 January 2010 (UTC)

I never noticed this. I will add it to my Morgan criticism page. The 'certain assumptions' had already been answered, and in the same journal as the Morgan paper! It makes Morgan's attack on vos Savant even less justified. Unless you assume that Whitaker was asking about one of the many other game shows with one car and two goats ;-) Martin Hogbin (talk) 12:49, 26 January 2010 (UTC)

Selvin corresponded with Monty Hall himself. Morgan calls their paper, 'Let's Make A Deal: The Player's Dilemma'. There's only 1 game show that these two parties can be talking about. Although Morgan was apparently oblivious to Selvin's letters, and it shows. Glkanter (talk) 14:16, 26 January 2010 (UTC)

Yes, I was joking. Obviously Morgan are talking about the same show as Selvin. Odd that they did not spot his letters, but that would have spoiled their fun. Martin Hogbin (talk) 17:03, 26 January 2010 (UTC)

A few months later he clarifies that Monty Hall knows where the car is, and that Monty Hall chooses randomly when faced with 2 goats

He solves it as a conditional probability that does not depend in any way on specific door numbers and/or box letters. No mention is made of the possibility that the host might prefer one door/box over another, or that placement might be similarly biased. So it did not address "the conditional problem" as Morgan poses it, and would be lumped in with their "false solutions." JeffJor (talk) 17:39, 26 January 2010 (UTC)

15 years later vos Savant answers a reader letter and leaves some of Selvin's premises unstated

It states the same premises as Selvin's original letter did, and her answer was intentionally worded so as to imply the same premises Selvin clarified. Whether or not you agree she succeeded, she has stated that was her intention.

1 year after vos Savant, while never mentioning Selvin, Morgan claims all unconditional solutions are false. This is also published in The American Statistician, in a piece called 'Let's Make A Deal: The Player's Dilemma', not 'A Critique Of vos Savant's Parade Column'

And conspicuously omitted a dependency that is more important to their solution technique than q, the bias toward opening a specific door. Allowing for placement bias is just as necessary. So they did not address the full "conditional problem," and their solution is just as "false" as those they criticize. We can't use that, I know; but we can acknowledge it in how we use their work.

Later, the assertion that the MHP is "a conditional problem" that depends on door numbers is reiterated in three other works: Gillman, Grinstead & Snell, and Krauss & Wang. Interstingly, the first two do not justify this assertion, whcih clearly is interpreted by others differently. And the third says it is not true but, that people do use door numbers in the same way that Selvin did, which is not the "conditional problem" Morgan raised.

The problem continues to appear in popular literature, most publically in the NY Times, and most recently in Leonard Mlodinow's book A Drunkard's Walk: How Randomness Rules Our Lives. None of these treat it as "the conditional problem" as Morgan did; and in fact, their solutions are among what Morgan calls "false." And even when sources acknowledge Morgan's assertion (i.e., Rosenhaus), no discussion of why the problem is important or controversial mentions "the conditional problem" at all. Rosenhaus even says Morgan's issue "was hardly the point at issue between vos Savant and her angry letter-writers," and that "what vos Savant discussed was surely what was intended," thus allowing Morgan's assertion to be discounted, officially, in Wikipedia. JeffJor (talk) 17:39, 26 January 2010 (UTC)

It is not clear at all that Whitiker's letter - which uses doors, cars, goats, a proffered switch - derived from Selvin - which uses boxes with keys, empty boxes, and an offer to buy the box back for cash (the contestant raises the possibility of a switch). Selvin's game, despite his mispelling "Monte Hall," is true to the game show he mentions, while Whitaker's is not. Vos Savant has even disavowed any connection to it. (It's possible she edited that out.) Morgan treats it the same way, except in their title. Which may be as much a reference to the vernacular usage that led to naming the show "Let's Make A Deal", as to the game show itself. JeffJor (talk) 18:00, 26 January 2010 (UTC)

That seems a remarkable coincidence to me. Are you seriously suggesting that there is no connection between the two problems?Martin Hogbin (talk) 18:27, 26 January 2010 (UTC)

That's what I also raised in "relations between sources". Who thought it to be the same problem? The same question applies to the game theory source mentioned, which is about curtains. I think we only have Vos Savant and all sources explicitly linked to that. All other problems are related, similar, variants, whatever, including three prisoners. Heptalogos (talk) 20:35, 26 January 2010 (UTC)

Which means that it should be called the "Game Show Problem", which is indeed better. In fact, MHP is not correct at all. Heptalogos (talk) 20:44, 26 January 2010 (UTC)

Should I put a "citation needed" to "A well-known statement of the problem was published in Parade magazine"? Where's the Monty Hall connection? This seems to have been editor's consensus in the past. In the Dutch article it is even named after a Dutch show host! I don't even care so much about the name, but the quoted phrase above is not in line with "puzzle based on the American television game show". Wiki-rules-Rick, what's your reaction? Heptalogos (talk) 21:54, 28 January 2010 (UTC)

My statements:

• It's unknown whether the puzzle is based on a specific show.
• There are many puzzles which may be similar to many persons, but for the article we should let the sources decide which are similar and should therefore be mentioned.
• The main source that most sources use is Parade, after which the problem should be named. (Game Show Problem)

Heptalogos (talk) 22:32, 28 January 2010 (UTC)

Very interesting this all (See also Keller.), especially for the historic part. What nowadays is called the MHP, is mainly the K&W version, a well defined probability puzzle. And of course one studies weaker versions, like Morgan did. Nijdam (talk) 01:20, 29 January 2010 (UTC)

That's from a maths perspective, which is quite narrow. Heptalogos (talk) 08:44, 29 January 2010 (UTC)

There is a long tradition in mathematical and logical puzzles that they should be framed in a way that makes the solution simple and as intended by the originator. Even if there are minor loopholes on the puzzle statement it is usual to overlook these. Martin Hogbin (talk) 10:14, 29 January 2010 (UTC)

The history section of the article mentions Nalebuff's version, which appeared three years before the initial Parade column. Here's his version (reference is in the article):

The TV game show "Let's Make a Deal" provides Bayesian viewers with a chance to test their ability to form posteriors. Host Monty Hall asks contestants to choose the prize behind one of three curtains. Behind one curtain lies the grand prize; the other two curtains conceal only small gifts. Once the costumed contestant has made a choice, Monty Hall reveals what is behind one of the two curtains that was not chosen. Now, Monty must know what lies behind all three curtains, because never in the history of the show has he ever opened up an unchosen curtain to reveal the grand prize. Having been shown one of the lesser prizes, the contestant is offered a chance to switch curtains. If you were on stage, would you accept that offer and change your original choice?

As far as I know, no one has claimed that this is where Whitaker's version came from or that this version is a restatement of Selvin's, although the similarities in both directions are striking. Dozens of sources refer to the Parade version as the "Monty Hall problem". Since these earlier sources also mention Monty Hall and the problems are obviously isomorphic, saying these are different problems seems like a fairly absurd stance. -- Rick Block (talk) 15:17, 29 January 2010 (UTC)

What seems absurd to me is that you kept saying that it doesn't matter a bit what we all think is very obvious, because only reliable sources matter. And now you're talking about 'striking similarities' and 'obvious isomorphic problems'. These dozens of sources are very welcome to provide the missing link here, that's all I'm saying. Heptalogos (talk) 21:45, 29 January 2010 (UTC)

Wait a minute. What I've said all along is that what we all think about whether the problem must be addressed conditionally doesn't matter a bit because only reliable sources matter. What I'm saying here is that reliable sources call "vos Savant's problem" the Monty Hall problem which is the same thing Selvin calls his problem, and that Nalebuff uses the same host (and same problem set up). If this is not enough, I'm perfectly willing to provide more sources. How about Barbeau's literature survey (referenced in the article): "The problem, known variously as Marilyn's Problem, The Monty Hall Problem, and The Car-and-Goats Problem reads as follows ..." BTW, if you're interested in Barbeau's statement of the problem it's this:

A contestant in a game show is given a choice of three doors. Behind one is a car; ehind each of the other two, a goat. She selects Door A. However, before the door is opened, the host opens Door C and reveals a goat. He then asks the contestant: "Do you want to switch your choice to Door B?" Is it to the advantage of the contestant (who wants the car) to switch?

And, Barbeau lists as references for this problem Selvin's two letters, vos Savant's Parade columns, Morgan et al., Gillman, Falk, ... (about 40 altogether). -- Rick Block (talk) 02:34, 30 January 2010 (UTC)

I don't need more sources, I need any source! You did not yet mention one that connects all, but now you mentioned Barbeau. A few others would be welcome indeed, thank you. I am willing to draw the picture, to see how everything is connected. I think this should be part of the article in any way, because otherwise it's not clear what is the scope of the article anyway, and what the scope is based on. Heptalogos (talk) 15:28, 30 January 2010 (UTC)

Question: Will Rick answer the question directly asked by the section header: Is Selvin's Unconditional Solution 'False'? Glkanter (talk) 03:37, 30 January 2010 (UTC)

Would Morgan et al. consider this solution a "false" solution? I believe the answer is yes.

Does Rick believe this solution is "false"? We could talk about this on the/Arguments page if you'd like, however just like I believe for the purposes of this page it does not matter in the least what you think about this, I believe for the purposes of this page it doesn't matter in the least what I think about this. What editors believe (as opposed to what reliable sources say) is completely irrelevant as far as editing is concerned. Will you ever understand this? -- Rick Block (talk) 05:32, 30 January 2010 (UTC)

What editors believe is important, Rick. It says so right here

"Likewise, exceptional claims in Wikipedia require high-quality reliable sources, and, with clear editorial consensus, unreliable sources for exceptional claims may be rejected due to a lack of quality (see WP:REDFLAG)." Glkanter (talk) 13:31, 30 January 2010 (UTC)

OK, fine. I'll amend my statement. If something is said by multiple high-quality reliable sources, whether editors agree with it or not is irrelevant. Also see below. -- Rick Block (talk) 02:41, 31 January 2010 (UTC)