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The following is an archived discussion of a featured article review. Please do not modify it. Further comments should be made on the article's talk page or at Wikipedia talk:Featured article review). No further edits should be made to this page.

The article was kept 20:43, 18 May 2008.

Monty Hall problem

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Review commentary

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Previous FAR

Notified Wikipedia:WikiProject Mathematics, User:Rick Block, User:Antaeus Feldspar, User:Glopk, User:Father Goose

Concerns:

1(c), factual accuracy/verifiability. Huge sections of unsourced content, including lengthy mathematical proofs. Without being cited to a reliable source, it's difficult to think that they're anything but OR.
2(c), inline citations. See also above. If these proofs are not original research, they should be directly sourced with inline citations, rather than requiring the user to hunt through the lengthy external links section to find the relevant proofs. Furthermore, the number of references in this article seems disproportionately low, given its length.
4, length. The article is extremely long, preferring apparently to offer every possible explanation of the correctness of the solution rather than picking one or two choice ones. (The objective of Wikipedia is to present verifiable facts, not to convince people of the truth where the truth may be counterintuitive.)

- Chardish (talk) 06:09, 28 March 2008 (UTC)[reply]

Judging by the previous FAR, it's probably worth spending the effort up front to present a more detailed list of the problems alluded to as 1(c) and 2(c), as many sections have already had inline citations added, and the remaining spots will be more actionable if identified as such. For example, the "Decision tree" section is currently unreferenced, but this could be fixed almost trivially. Melchoir (talk) 06:52, 28 March 2008 (UTC)[reply]
...or even better. Melchoir (talk) 06:54, 28 March 2008 (UTC)[reply]
Yes a detailed list would be good. Note that Harvard referencing is used. -- Rick Block (talk) 13:26, 28 March 2008 (UTC)[reply]
Per the above, sections that appear to lack sources:
These sections comprise 12.5 kB of text, or approximately 2,280 words. (This isn't terribly pertinent, but personally I'm not much of a fan of Harvard referencing, especially on Wikipedia, since footnotes are quickly becoming the de facto standard here, if they haven't already.) - Chardish (talk) 15:04, 28 March 2008 (UTC)[reply]
"Unsourced content including mathematical proofs", creating a "verifiability" problem?? Mathematical proofs can be verified by reading them and checking them. Sources won't help with verifying them. That's just not how proofs work. Michael Hardy (talk) 15:52, 28 March 2008 (UTC)[reply]
On the contrary; please read the policy on original research. Who is to verify that the proofs contained in the article are correct, free of errors, etc? This is why all information - including mathematical proofs - must be attributed to reliable secondary sources. Wikipedia is not a mathematical journal and must not publish original proofs. - Chardish (talk) 17:01, 28 March 2008 (UTC)[reply]
On the contrary, these statements, which are too trivial to be publishable in a mathematical journal, are as self-verifying as a plot summary (for which see WP:WHEN. We are permitted to do our own arithmetic; this is the same thing. Septentrionalis PMAnderson 19:13, 30 March 2008 (UTC)[reply]
I'm sorry, you are incorrect. While the information may be too trivial to be published by a journal of advanced mathematics, certainly there are books, lesser journals, magazines, etc. with the same information. Wikipedia is not a place to publish information that is not already published elsewhere, plain and simple. That is what no original research means in a nutshell. You will also note on the talk page of the essay you linked to a significant amount of disagreement with the claims made by the essay. Cheers. - Chardish (talk) 18:44, 31 March 2008 (UTC)[reply]
But it is exactly correct. I recommend that this disruptive abuse of WP:OR be ignored, and this review speedy closed, as nominated in bad faith, and in disregard of Wikipedia policy. Septentrionalis PMAnderson 19:01, 31 March 2008 (UTC)[reply]
I'm sorry, how is this a bad faith nomination? Simply because we disagree does not mean that one of us must have sinister motives. - Chardish (talk) 21:24, 31 March 2008 (UTC)[reply]
When Infinite monkey theorem went on FAR, I found and fixed an incorrect proof that had been allowed to lie for some time. I detected the error because I was looking for sources. Monty Hall problem is a somewhat different beast, since it is already undergoing active revision on its talk page. What that implies for the FAR I can't say. But I can say that sources do help verify proofs. Melchoir (talk) 17:17, 28 March 2008 (UTC)[reply]
No, close reading verifies proofs, here and elsewhere. Close reading should be encouraged, and should not be distracted by superscript numbers, or we will wind up citing the significant number of invalid proofs in the published literature. Septentrionalis PMAnderson 19:13, 30 March 2008 (UTC)[reply]
Close reading should be encouraged as well. It would be naive to think that an article can be maintained at a high quality merely by enforcing a certain density of citations. But it would also be naive to think that readers can be trusted to maintain quality on their own, without citations.
There is a theoretical danger that providing citations for proofs will result in some incorrect proofs gaining a veneer of acceptability. But there is a proven danger that writing proofs without citations results in some incorrect proofs never getting fixed, since they are equally well-cited as their neighbors. Infinite monkey theorem had a proof that started out correct but was complex and little-understood. It wasn't cited. An editor attempted to simplify it and broke it in the process. No one noticed. Untold numbers of people read this proof inside a Featured article and did not correct it. One editor commented on the talk page that the proof smelled, and the talk page regulars actually insisted that it was correct.
The above failure points out several intrinsic challenges for mathematical proofs on Wikipedia, which I won't get into here. The point is that citations could have prevented the problem, and citations fixed it. Melchoir (talk) 21:24, 30 March 2008 (UTC)[reply]
The lesson I draw from that is "use citations, where possible". If a given piece of information improves an article and is verifiable one way or another, I am prepared to not excise it. I've seen a lot of people on the talk page of the article independently derive "combining doors"-type solutions, so it must have use as a way of explaining the problem, and I consider it an alternative way of describing the basic (unconditional) solution.--Father Goose (talk) 02:45, 31 March 2008 (UTC)[reply]
See, in that case, the "combining doors" solution could simply be a popular fallacy that happens to reach the correct answer by accident. It is not obvious to me how the solution can avoid being used for different host behaviors with different probabilities -- where it is wrong. The article does say "if and only if the game host is required..." but at what point is this assumption applied?
On the talk page, Rick Block indicates that there may be sources that describe the theory behind such a solution. I for one am curious about what they have to say! Melchoir (talk) 06:20, 31 March 2008 (UTC)[reply]
I'm given to believe (as I stated above) that it's merely a way of visualizing the basic, unconditional solution, so it is neither a popular fallacy or an accident. As for your question about "at what point is this assumption applied", is there more than one point at which it could meaningfully be applied?--Father Goose (talk) 06:50, 31 March 2008 (UTC)[reply]
I'm saying that I don't see any place where it is applied. Here's the same section with the host behavior changed in bold:
Instead of one door being opened and shown to be a losing door, an equivalent action is to combine the two unchosen doors into one since the player cannot, and will not, choose the opened door. The player therefore has the choice of either sticking with the original choice of door with a 1/3 chance of winning the car, or choosing the sum of the contents of the two other doors with a 2/3 chance. The game assumptions play a role here — switching is equivalent to taking the combined contents if and only if the game host is required to open a door with a goat and chooses between two losing doors randomly with equal probabilities. Assume that the game host is required to open the rightmost unchosen door with a goat.

In this case, what should be ignored is the opening of the door. The player actually chooses between the originally picked door and the other two — opening one is simply a distraction. There is only one car and it does not move. The original choice divides the possible locations of the car between the one door the player picks with a 1/3 chance and the other two with a 2/3 chance. It is already known that at least one of the two unpicked doors contains a goat. Revealing the goat therefore gives the player no additional information about the originally chosen door; it does not change the 2/3 probability that the car is still in the block of two doors.

This time the conclusion is wrong. But what has changed about the argument that makes it more wrong than the version in the article?
Personally I suspect that there is a symmetry principle at work that salvages the argument and explains when it can and cannot be used. The problem is that this principle is not in evidence. The following section titled "Bayes' theorem" goes step-by-step through the derivation that P(C_1|H_13) = 1/3, and this 1/3 appears to depend on every input to the problem. It is far from obvious that P(C_1) has simply been conserved, and if so, why. Melchoir (talk) 07:49, 31 March 2008 (UTC)[reply]
Ah. That change you made to the text changes the problem from unconditional to conditional (and very specific conditions, to boot), so that indeed the "combining doors" or even the basic explanation given in the "Solution" section can no longer be used. How to address the differences between unconditional and conditional solutions has been the subject of many weary months of discussion on the article's talk page.
You could also change the statement of the problem in the section by changing the game to the "host doesn't know" variation. Not surprisingly, the "combining doors" explanation would be invalid for that as well.--Father Goose (talk) 08:19, 31 March 2008 (UTC)[reply]
"Unconditional"? I don't know what that word means in this context. Melchoir (talk) 08:26, 31 March 2008 (UTC)[reply]
This is the topic of a long discussion on the talk page. As generally presented the problem asks about a situation given that the host has opened a door (conditional), not an overall average. Note that the argument above is still correct if the question is "what is the overall chance of winning by switching" (as opposed to "after the host has opened a door, what is the player's chance of winning"). The overall chance of winning by switching is 2/3 regardless of how the host selects between two goat doors, but if the host selects unevenly between goat doors the chances are not split evenly based on which door the host opens. I'd suggest not continuing this thread here. -- Rick Block (talk) 13:51, 31 March 2008 (UTC)[reply]
Thanks for the explanation. I think I understand the relationship between the two versions, and I can see how it's a tough editorial call on how to present them. Back to Combining doors, then: it's currently worded to suggest the conditional problem, i.e. "...opening one is simply a distraction. There is only one car and it does not move. ...Revealing the goat therefore gives the player no additional information...". This is all post-door-opening, and why the player hasn't gained additional information about the chosen door isn't explained. Do any of the sources help? Melchoir (talk) 17:22, 31 March 2008 (UTC)[reply]
I haven't found anything yet that is entirely satisfactory. Until recently, the entire article other than the Bayes' theorem section has presented an unconditional analysis which comes up with 2/3 as the answer (which is the same numerical answer as the conditional answer given the "equal goat" constraint on the host). Whether there's even a need to distinguish between the unconditional 2/3 and the conditional 2/3 and, if so, how has been a topic of heated discussion on the talk page. -- Rick Block (talk) 18:35, 31 March 2008 (UTC)[reply]

FARC commentary

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Suggested FA criteria concerns are referencing (1c) and focus (4). Marskell (talk) 03:25, 21 April 2008 (UTC)[reply]
  • Comment I've strengthened the referencing and made the article at least somewhat shorter (meant to be responsive to the identified concerns). If folks could take a look at the current state of the article and make specific suggestions for what else may need improving that would be helpful. -- Rick Block (talk) 23:42, 1 May 2008 (UTC)[reply]
  • Comment: I made some edits, mostly to avoid repetition, but they were reverted, without discussion, and I'm not entirely sure why. The lead doesn't require inline references. And it seems important to separate out a simple statement of the problem with an account of its history (which has its own section). It's true that that history section should probably be moved up; but that's better than duplicating it. Or perhaps those elements should go in the lead, so (again) the lead complies better with WP:LEAD. --05:15, 10 May 2008 (UTC)
    The problem statement in the lead is a quote, and as such must be referenced (per WP:MOSQUOTE and WP:CITE#When quoting someone), as mentioned in the summary for this edit. Do you seriously have a problem with including three sentences about the origin of the problem and its relationship to an earlier (mathematically equivalent) problem in the "Problem" section? The problem statement that you have now duplicated in both the lead and this section (which are contiguous!) is as long. We can certainly discuss this on the talk page if you'd like. -- Rick Block (talk) 05:37, 10 May 2008 (UTC)[reply]
    It's not a question of length, but of logic and structure, and I think I've explained it clearly enough: there is already a section on the history of the problem; it's probably misplaced, but so be it. The section on "The problem" should best be kept for outlining the problem. Previously, it didn't even do that very gracefully, as it referred readers back to the lead. See, again, problems as per WP:LEAD. --jbmurray (talk • contribs) 05:42, 10 May 2008 (UTC)[reply]
    The lead was indeed rewritten a few months back to serve as an overview of the problem, to better conform to WP:LEAD. What do you feel is missing from the lead, or erroneously included in it?--Father Goose (talk) 22:05, 10 May 2008 (UTC)[reply]
    The lead is to be an overview of the article, not of the problem, right? As such, for instance, I'd have thought there should be at least some reference to the "History of the problem" section and the Bayesian analysis (though to be fair this latter may be too technical). Also something on the reasons why the solution is counter-intuitive, as per the discussion in the section on "Sources of confusion." --jbmurray (talk • contribs) 22:11, 10 May 2008 (UTC)[reply]
    The last paragraph of the lead is a reference to the "History" section. The Bayesian analysis is too technical to summarize in the lead, but is implicitly referred to in the last sentence ("formal mathematical proofs"). The sentence starting with "Because ..." in the paragraph immediately below the problem statement is meant to be a concise version of the "Sources of confusion" section (and the recent change from "nearly all" to "most" in this sentence considerably weakens the point - in most studies the number is 90% or more). -- Rick Block (talk) 16:38, 11 May 2008 (UTC)[reply]

Closing: The article, if anything, is improved since the last FAR. Rick has worked to deal with the comments on the review. We don't have explicit comments, so this is a default keep. Marskell (talk) 20:25, 18 May 2008 (UTC)[reply]

The above discussion is preserved as an archive. Please do not modify it. No further edits should be made to this page.
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