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Question

Martin, please respond to my question on User: Martin Hogbin/Monty Hall History#Nijdam. Nijdam (talk) 00:09, 21 February 2011 (UTC)

I am always happy to discuss the subject with you, I have moved the question here and will respond here shortly. Martin Hogbin (talk) 09:00, 21 February 2011 (UTC)

The same problem with the "combined doors solution".

The chosen door No. 1 has chance 1/3 on the car. Hence the doors No. 2 and No. 3 together have 2/3 chance on the car. As the opened door No. 3 shows a goat, the remaining door No. 2 has chance 2/3 on the car.

Explain, how i.e. door No. 2 can have chance 1/3 on the car, due to the random placement, and also chance 2/3 on the car, as stated in the reasoning. Nijdam (talk) 17:33, 30 December 2010 (UTC)

Nijdam, you continue to try to teach me what I already know. Let me start by giving you a brief moment of victory. Using modern probability theory and with the sample space that you prefer and seem to assert is the only possible one to use, what you ask cannot be done. You are quite right, on the basis that you prefer, the "combined doors solution" makes no sense.
However, there are other ways of tackling this problem, even within modern probability theory. Please explain to me why you select the sample space that you do. Martin Hogbin (talk) 09:20, 22 February 2011 (UTC)
If this is victory, so be it. But you did not explain anything. Sorry, Martin, most of our discussions end by you finally not responding. What sample space are you talking about? Be my guest and select your own sample space and derive the appropriate probabilities. Nijdam (talk) 09:50, 22 February 2011 (UTC)
We have done this before. My sample space consists of only two elements. The player originally picks a car having probability 1/3, and the player originally picks a goat - probability 2/3.
The combining doors explanation merely shows what we both well know, that if the player switches they get the complement of their original choice. Martin Hogbin (talk) 14:23, 22 February 2011 (UTC)
Well, your sample space is not appropriate for the MHP. For instance, how do you express that the host opens door 3, or how that door 3 hides a goat. Etc. See, that's why I say, you're still a layman on probability. I've tried to explain you a lot, but somehow you refuse to understand. I say on purpose "refuse", because I'm sure you're capable of understanding. I'll give you the tools: the variables C (car), X (choice) and H (host) may be used to describe the MHP. No one of these three can be left out. Other sample spaces are equivalent. As far as I recollect, we used these on your MHP analysis page. Now back to the question. Nijdam (talk) 20:33, 22 February 2011 (UTC)
You say of C, X, and H may not be left out but that is not so. It is quite obvious that door numbers are not relevant to this problem. As Richard Gill has said, there is a stage before you put the problem into mathematical form where you have to decide how to formulate the question in mathematical terms. For a start, you must decide what sample space is appropriate to the problem. You have to make a decision as to what events are independent of the event of interest before you start to put the problem into mathematical terms. You already do this, it seems without realising it. Please tell me why, for example, the event that the host says the word 'pick' is not included in your sample space in any way? Martin Hogbin (talk) 21:44, 22 February 2011 (UTC)
Please Martin, not again. To describe any situation in the MHP problem, we need as a minimum C, X and H. That's why I say no one of these can be left out. Of course you may enlarge your sample space, i.e. with an event taking account of the host saying "pick" or whatever. That is not the issue. The issue is you can not do with less than C, X and H (or equivalent). Focus on this, and then respond to the question, at last. Nijdam (talk)
I have already agreed that, with a sample space based on door numbers in the way you suggest, the 'combining doors' solution makes no sense. There is no question to respond to, you are correct.
My question to you is this. Given Whitaker's question, what is it that tells you that a sample space using C,X, and H to represent door numbers chosen by various people is the correct sample space? What exactly tells you that including the word 'pick' is not necessary? What tells you that my sample space of only two elements is deficient? Or to put it anther way, in explaining to one of you students how to set up your sample space based on a natural language problem statement, what advice would you give? Martin Hogbin (talk) 09:26, 24 February 2011 (UTC)
To try and clarify what I am getting at, you say above, 'how do you express that the host opens door 3' in my sample space. My response would be that it is not necessary to express that specific event, given that the problem is totally symmetrical with respect to door number. It is only necessary to specify the event that the player picks a goat or the player picks a car. No doubt, you would respond in a similar manner to my question about the word 'pick'. You would say that it is not important what the host says, the problem is symmetrical with respect to the word 'pick' therefore we need not include terms containing this event in our sample space.
Now, if you were to ask me which is the better way of approaching the problem, I would agree with you. If in doubt as to whether a particular event is relevant to calculating the desired probability, it is always better to include it. Specifically, if a particular event was given as a condition of a problem, we would be wise to include it in our sample space. So we do not disagree about much. Given reasonable assumptions about the meaning of the problem, it is wise to tackle it in the way proposed by Morgan to avoid missing what could be an important point, however, in the totally symmetrical case, this is not the only way to tackle the problem. Symmetry is a very powerful concept. Martin Hogbin (talk) 09:39, 24 February 2011 (UTC)
Makes more sense what you say here. You only forget that speaking about symmetry is only possible in the sample space like the one I gave you. I never denied the importance of the use of symmetry. More than a year ago I already showed how to derive the conditional probability by means of symmetry, other than with Bayes'. That's not the issue. The point is how can i speak about choosing a door, if that door is not in my sample space. What you are aiming at is the reduction of the original sample space, by the use of the symmetry. That reduction, you may already guess, means conditioning. You may argue that for the final answer, the reduction leads to an equivalent sample space, rich enough to get the desired answer, but! also then you have to show the reduction and the equivalence. It is of course, for a sound explanation, not sufficient to just say "I know this". I hope, that, when you come to understand this, you give up your resistance against the criticism of the simple solution (the one without (factually) mentioning the use and significance of the symmetry). Nijdam (talk) 12:34, 24 February 2011 (UTC)

Starting from the start

I still think you are missing my point. You have to get from this:

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 No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, "Do you want to pick door No. 2?" Is it to your advantage to switch your choice?

to a sample space before you do anything.

Suppose I say right at the start that it is obvious from a Bayesian perspective that the door numbers and even the doors themselves are not important. There are only two events in my sample space: I pick a car, I pick a goat. The door number that I pick and the door number opened by the host and the door number remaining are all irrelevant. What is wrong with this approach? Martin Hogbin (talk) 16:55, 24 February 2011 (UTC)

Corrections, make that four terms: I pick a car and swap, I pick a goat and swap, I pick a car and do not swap, I pick a goat and do not swap. Who cares about doors or door numbers? Martin Hogbin (talk) 17:38, 24 February 2011 (UTC)

Before I may get to this, I insist you explain the following. A: The car is with probability 1/3 behind each of the doors 1, 2 and 3. B: The car is also with probability 0 behind door 3, opened by the host. doesn't this strike you ass odd? Or do you have an explanation? Nijdam (talk) 23:05, 24 February 2011 (UTC)

If the question is taken to ask specifically for the probability of winning by switching given that the player initially chooses door 1 and that you must use as condition of the problem the fact that the host has opened door 3 then you are correct. The first set of probabilities that you quote are prior to the condition and the second is after. We all agree about that.

Indeed is the question posed to the player who has chosen a door, be it door 1 or door 2 or door 3, that does not matter for the way of arguing. Your second "if" is just something you come up with to avoid reasoning that you have to condition. Nijdam (talk) 09:27, 25 February 2011 (UTC)

But what if I do not care which door the car and goats are behind? All I care about is whether the player has initially chosen a car or a goat and whether he swaps or not. The fact that the host is stated to open door 3 is not a condition, it is an irrelevance. We know the host must open a door to reveal a goat and we know, from symmetry right from the start, before we set up our sample space, that the door number that he opens is unimportant. Thus we do not include door numbers in our sample space and we do not take the door opened by the host as a condition of the problem, even if the host is stated to open a specific door. Martin Hogbin (talk) 23:43, 24 February 2011 (UTC)

I know, but this is a different MHP, the so called unconditional formulation. At least accept that the full MHP has to be solved by the conditional solution, whereas the unconditional version is solved by the simple solution. And ... the simple solution does not solve the full MHP. This is what you till now refused to accept. If we agree on this, what's left, is what's left in the discussion with Richard, namely which version of the MHP should be considered more acceptable and presented first to the readers. Nijdam (talk) 09:27, 25 February 2011 (UTC)
Nijdam's  "correct MHP", his  "full MHP"  is the  "conditional MHP",  based and conditioned on the given existence of non-existent, but "assumed" records of log lists that allow obscure presumptions about "additional info" on the contents of the remaining two closed diaphanous doors. Nijdam's additional "condition" is the given existence of (non-existing, but "assumed") records of log lists that have to "proof" a very special (but forever unknown) peculiar kind of behavior of the host in giving additional info on the actual secret location of the car behind the two still closed but diaphanous doors, in each and every game. That's his "conditional MHP", his "full MHP". That unconditionally has to be shown first, before proper, famous paradox is allowed to be shown to the reader. Gerhardvalentin (talk) 10:50, 25 February 2011 (UTC)

I think that we can all agree, therefore, that Whitaker's statement is open to different interpretations, some of which do not require the Morgan solution.

K&W formulation

So let us move on to the K&W formulation. Here the door numbers are clearly stated, as is the order of events. The player has to choose after the host has opened a door.

Nijdam, I am sure that you would say that this problem must be solved using a sample space based on the door numbers X, H, and C. I agree that that might be the wisest way to approach the problem since it covers possibilities such as those raised by Gerhard above, that the host might not act evenly.

However, in the K&W formulation, we are specifically told that the host acts evenly, thus, right at the start we are free to observe that, although door numbers are clearly given, and the host has already opened a specific door, the door numbers can, by symmetry, make no difference to the probability of interest (that the player wins the car by switching). We are free to ignore door numbers and choose a sample space that does not depend on them. I do not mean that we start with a sample space based on door numbers, then condition it, I mean that we start with a sample space that ignores door numbers, even though they are clearly given on the question. Whether you wish to use the term 'conditional' or not to describe the problem and solution I do not care. Martin Hogbin (talk) 14:10, 25 February 2011 (UTC)

Let me first ask you this: is it your intention to show that the simple solution (you know the one without any conditioning or reference to the symmetry) may serve as a valid solution to the full MHP? Even knowing that also Richard Gill admits it is not? Or do you just want to know where the error in your argumentation lies? Nijdam (talk) 18:50, 25 February 2011 (UTC)

I think the simple solutions are satisfactory solutions to the K&W formulation. I would also be interested to know where you think my error lies. Martin Hogbin (talk) 23:52, 25 February 2011 (UTC)

To be sure we understand each other: You say: "satisfactory" solution, does this mean "correct" solution? And with "simple solution" you mean just the following statement: "the car is with probability 2/3 not behind the chosen door 1, hence when you switch you get the car with probability 2/3". Nijdam (talk) 22:56, 26 February 2011 (UTC)

I think your terminology is invalid. This is not just one 'correct' solution to any given mathematical problem, there can often be several valid ways of solving it. Mathematical solutions have varying degrees of rigour, ranging from the most rigourous solutions known (which are completely incomprehensible to all but specialists) to hand-waving arguments that demonstrate a degree of plausibility. I believe that the simple solutions, meaning "the car is with probability 2/3 not behind the chosen door 1, hence when you switch you get the car with probability 2/3", are as correct and rigourous as the conditional solutions given in the article.

The point that you consistently miss is the first stage, where you have to turn a natural language statement into a clearly defined mathematical question. There are no formulae or fixed methods for doing this, it can only be done by applying a degree of common sense and logic to the question. In particular, one should always try to find out what is is that the questioner actually wants to know. Failure to do this is a failure to answer the question at all.

So for the sake of this discussion, I do mean that the simple solution, as defined by you, is a correct answer to the K&W problem statement. Martin Hogbin (talk) 10:03, 27 February 2011 (UTC)

The decision asked for will be based on some probability ( if we consider the MHP to be a probability problem). Let us consider the player,knowing having chosen door 1 and seeing door 3 opened with a goat. The player will consider his probability to find the car behind door 1 (or equivalent behind door 2). So he considers his situation as a realisation of several possibilities. Well, several means hre only two possibilities: either the car is behind door 1 or it is behind door 2. The probability law governing this is the conditional probability given door 1 chosen and door 3 opened. The player may take his situation as equivalent to a Bernoulli trial with outcomes 1 and 2, being the number of the door with the car. Do you recognize the similarity with you urn problem, containing 9 white and 1 black ball, and you the third to draw a ball without replacement. Then you had no problem at all to understand the conditional nature. If it is more understandable for you, the player could also compare the probability on the situation (event) with door 1 chosen, door 3 opened and door 1 hiding the car, with the probability on the situation with door 1 chosen, door 3 opened and door 2 hiding the car. And then decides for the one with the larger probability. This is completely equivalent to the more natural description with conditional probabilities.
In your reasoning I do not understand this phrase: the door numbers can, by symmetry, make no difference to the probability of interest (that the player wins the car by switching), Because if there is only one probability of interest it cannot depend on the door numbers, with or without symmetry. So you clearly mean the different probabilities of interest, due to the symmetry, do not depend on the door numbers. And there you are right, but you doesn't seem to understand what these different probabilities are. And, it will not be a surprise to you, they are the conditional probabilities. What else could they be? Nijdam (talk) 21:30, 27 February 2011 (UTC)

You seem fixated on door numbers. The numbers on the doors are completely unimportant, as are the doors themselves. As have said before, my sample space, which does not have any relation to door numbers or doors, has only four elements (picks car and stays, picks car and swaps, picks goat and stays, picks goat and swaps). You have yet to tell me what is wrong with this way of tackling the problem.

Just because door numbers are given in the problem that does not mean that we have to use them in any way. They are unimportant, irrelevant and I choose to formalise the problem without reference to them. Martin Hogbin (talk) 22:31, 27 February 2011 (UTC)

Note
  1. It is you who said: the door numbers can, by symmetry, make no difference to the probability of interest (that the player wins the car by switching). What do you mean then??
  2. As the door numbers are given in the problem we must use them. Why else are they given? And the player sees the door he has chosen and the door opened.
  3. You change the problem into the version I called the unconditional problem. It is the version in which we the audience have to decide before anything has happened. And indeed, I've repeated that several times, Morgan says so, it is the version the simple solution applies to.
  4. You cannot consider the full MHP to be the problem of interest and then just concern your sample space to describe it.
Nijdam (talk) 09:09, 28 February 2011 (UTC)

Our disagreement

Nijdam, I think the points above show where we disagree. If the problem is formalised as a conditional probability problem based on a sample space that uses door numbers then it must, of course, be treated as a conditional probability problem based on a sample space that uses door numbers, so we do not disagree there, so let us now discuss the points above.

You formulate this a little odd. The problem may be formulated in the sense as I described several times, that the player is offered to switch, after the host has opened a door. This is what is called the conditional formulation, like the K&W version. Or the audience is asked whether the player should switch, before he makes his first choice. This is the unconditional formulation. The appropriate sample spaces follow from the formulation. Nijdam (talk) 15:53, 28 February 2011 (UTC)
Even when answering the K&W natural language problem statement there is a stage where you have to decide how to state the problem in mathematical terms. Please tell me, what are the rules by which you do this? Martin Hogbin (talk) 22:02, 28 February 2011 (UTC)
The K&W formulation ends with: After Monty Hall opens a door with a goat, he will ask you to decide whether you want to stay with your first choice or to switch to the last remaining door. Imagine that you chose Door 1 and the host opens Door 3, which has a goat. He then asks you "Do you want to switch to Door Number 2? Is it to your advantage to change your choice? Isn't this clear enough? The decision will be made after the player picked door 1 and the host opened door 3. Natural language.Nijdam (talk) 22:22, 28 February 2011 (UTC)

Door numbers are not important

By this I mean that, at the start of the game all the door numbers could be swapped round and this would make no difference to the probability of interest. The problem is symmetrical with respect to door number, meaning that changing the door numbers, or any other means of identifying the doors, will not affect the probability that the player will win by switching. Note that this is not the case if the host has a known door choice policy. For example if the host always preferred to open door 2 when legal, the problem would have a different answer if the player had initially chosen door 3 and the host had opened door 1.

You again speak of "the probability of interest", whereas I made it clear that either there is only one probability of interest, and hence it cannot depend on the door numbers, or there are several probabilities of interest, all with the same value, and hence independent of the numbers of the doors. Don't you understand this? Nijdam (talk) 15:53, 28 February 2011 (UTC)
No I am sorry but I do not. Imagine the K&W statement followed by the words 'What is the probability that the player wins by switching'. That is what I mean by 'the probability of interest'. I mean that natural language statement. Martin Hogbin (talk) 22:02, 28 February 2011 (UTC)
Then the probability of interest can only be the conditional probability that the car is behind door 2, given door 1 chosen and door 3 opened, What else could it be? But explain to me what you mean by independent of the door numbers.Nijdam (talk) 22:22, 28 February 2011 (UTC)
There is no obligation to use all the information given in the problem statement. We have to make a judgment as to whether any particular piece of information is important. We agree that we do not need to use the information given in the words used by the host because they contain no relevant information. Similarly, there is no relevant information given in the door numbers, thus, although they are clearly given in the natural language K&W problem statement, we do not need to use them in our solution. Thus the probability of interest is the probability that the car is behind the remaining door, given an originally chosen door and a different, goat-hiding door which has been opened. In other words the unconditional formulation. Martin Hogbin (talk) 09:25, 1 March 2011 (UTC)
The point you are making is that the unconditional formulation is equivalent to the full problem in the case of symmetry. And indeed that's the case. And what you do is arguing why this is the case. And that's just my intent: we have to argue (show) that the full problem is equivalent to the simple formulation. Without the arguments it is logically flawed. Either we show the equivalence of the problems and use the simple solution to the full problem, or we use the symmetry argument to simply derive the conditional solution. It's either way. We cannot do without reasoning. Nijdam (talk) 10:49, 1 March 2011 (UTC)
That is not my point. You do not seem to realise that you, and everyone else, has to use some form of reasoning at the start of the problem in order to turn a natural language question into a well-defined mathematical problem. Before this stage the problem is neither conditional nor unconditional because it is not yet properly defined.
As part of this process you dismiss the words that the host says as unimportant but you insist on treating the door number opened by the host as being significant. The reverse could in reality be true. You have never yet explained to me why you make this decision. Perhaps you do not even realise that you are doing so, but you are. Please explain to me the basis on which you do this. Martin Hogbin (talk) 11:57, 1 March 2011 (UTC)

Must we use door numbers in our formalisation

You ask why they are given. The actual reason, we know, is that vos Savant added them to to Whitaker's question to try to make it clearer. She now agrees that this was a great mistake. K&W kept the door numbers in their formulation but that still does not compel us to use them. Whether we to use them depends on our understanding of what the questioner really wants to know. I doubt that Whitaker was interested in door numbers.

Well, to most people the problem becomes tricky, when they actually see an open door with a goat and two still closed doors, between which they have to decide. I really do not see any charm in the unconditional formulation. Nijdam (talk) 15:53, 28 February 2011 (UTC)
Whether you see any charm in it does not matter. The fact is that many people get the answer wrong. ther is no way to tell whether they have in mind the conditional or the unconditional formulation. Probably they do not distinguish between the two cases. Martin Hogbin (talk) 22:02, 28 February 2011 (UTC)

We are also told that the host says the word 'pick' but you choose (quite reasonably) to not make use of that event (although is some circumstances it could be highly significant). We have to use our own judgment in formalising the problem.

???Nijdam (talk)
See my reply above. Martin Hogbin (talk) 09:26, 1 March 2011 (UTC)

I changed the problem into an unconditional one

No, based on a plain language statement, you formulate it as a conditional problem and I formulate it as an unconditional problem.

Okay, but be aware they are different problems, and your concept is not the K&W version. Nijdam (talk) 15:53, 28 February 2011 (UTC)
No, the K&W statement can be made into an unconditional problem. Martin Hogbin (talk)
What is "made into"? Nijdam (talk) 22:22, 28 February 2011 (UTC)
Mathematically formalised as. Although the K&W natural language statement practically invites us to treat the problem as one where the doors chosen by the player and host are taken as conditions of the problem and this would, no doubt, be the way you might expect a student to formalise the problem, it is possible to conclude right at the start that the door numbers are not important and that the problem can be formalised as an unconditional one. Martin Hogbin (talk) 14:24, 2 March 2011 (UTC)

I cannot consider the full MHP to be the problem of interest and then use my sample space to describe it

If by 'the full MHP' you mean the conditional probability problem using your sample space then no, of course not. If you mean a perfectly valid interpretation of either Whitaker's question or the K&W formulation then my sample space is fine. Martin Hogbin (talk) 13:29, 28 February 2011 (UTC)

As above, the K&W formulation is a conditional problem. Accept it. Nijdam (talk) 15:53, 28 February 2011 (UTC)
You are arguing by decree. You have yet to tell me why this must be so. Martin Hogbin (talk)

An alternative sample space

Nijdam, please tell me why I cannot use this reasoning and sample space to solve the K&W problem statement.

There are three objects of interest one car and two goats, let us call them A and B.

My sample space consists of the following elements, X is the object originally chosen by the player and H is the object revealed by the host. The doors are of no interest. The only possible outcomes (up to the point that the player decides whether to switch) are:

(X=C,H=A),(X=C,H=B),(X=A,H=B),(X=B,H=A)

This sample space allows us to include the possibility that the host may have a preference for one or other of the goats. In what way is it not satisfactory? Martin Hogbin (talk) 22:13, 28 February 2011 (UTC)

Convention in probability questions

Nijdam, there are many conventions and understandings in probability questions but these vary according to the context. To give a simple example, there is a convention in general statistical discussions that a ball drawn from an urn is deemed to be selected uniformly at random from all the balls within the urn. In reality, this might not be the case; the picker might be lazy and prefer balls at the top of those within the urn, for example. This convention is used to enable people to communicate without giving a lot of unnecessary detail. Let me now give three contexts where the conventions used might vary:

A undergraduate statistics examination

Here I suggest that when information, such as door numbers, is given there is a strong expectation that this information will be relevant to the problem. Certainly, the student would be wise to formulate their approach to the problem on the basis that all information given in the question might be important.

A simple probability puzzle

In these there is generally a stronger set of conventions. Selections with no obvious bias are generally taken to be made uniformly at random. In general, the convention is to make the puzzle as simple as possible. Martin Hogbin (talk) 09:43, 1 March 2011 (UTC)

The real world

Here conventions and 'everybody knows' understandings can be misleading and dangerous. If a statistician were approached by a client who asked the Whitaker question they would be obliged to ask more questions to find out, as Seymann put it, the intent of the questioner. To try to answer without finding out exactly what the client wanted to know would be a failure of their professional duty. Martin Hogbin (talk) 09:43, 1 March 2011 (UTC)

Even when the door numbers were not mentioned in the problem statement, you had to use them. It is not mentioning of the door numbers, but the moment the player is offered to switch that makes the problem conditional. And about the K&W version: the player is only then offered to switch, after the host has opened a door. You may try to proof the equivalence with the unconditional formulation, it's pkay, but then you have to show the proof (reasoning). This all has been said before. Nijdam (talk) 23:52, 8 March 2011 (UTC)
The problem may be conditional, as are all problems in Bayesian probability, the question is, 'What is the condition?'. Is the condition that the host has revealed a goat? Is it that the host has revealed Billy the goat (as opposed to Annie)? Is it that the host has said the work 'pick'? Please explain what the condition is and why. Martin Hogbin (talk) 00:20, 9 March 2011 (UTC)
There we go again. Every event that has occurred is a condition. At the stage when the player is offered to switch, the events "initial choice of door 1' and "host opens door 3" has happened. Nijdam (talk) 10:25, 9 March 2011 (UTC)
There's no requirement, Whitaker didn't ask, and vos Savant says she didn't mean to imply, that it must be "initial choice of door 1' and "host opens door 3". It could equally, or more likely be, "initial choice of a door" and "host opens another door". That recognizes the event that occurred. Your continued exclusive claim to The Truth is, and has been BS. Glkanter (talk) 12:11, 9 March 2011 (UTC)
Nijdam, you quite rightly say, 'Every event that has occurred is a condition'. But many events have occurred, a door has been opened, a goat has been revealed, the host has spoken several words, how do you decide which of these events to condition on? Martin Hogbin (talk) 17:46, 9 March 2011 (UTC)
I hope you do understand that the notion "event" has a specific meaning in probability theory. So, if you took all the 'events', you mentioned, as events in your sample space, than, yes, you have to condition on them all. Your choice. Nijdam (talk) 23:53, 9 March 2011 (UTC)
Right, so we are back to my original question, 'How do you decide on which events to include in your sample space?'. Martin Hogbin (talk) 00:26, 10 March 2011 (UTC)
You tell me what is needed to describe the problem. Then I tell you which events you need. Nijdam (talk) 20:26, 10 March 2011 (UTC)
This is exactly the point that I am making (and Gerhard too I believe) it is up the the person who is answering the question to decide which events are important and which events are not. This has to be done right at the start based on your understanding of the context, any relevant conventions, and what the questioner actually wants to know. Maybe the door number opened by the host is important, maybe not, maybe the words said by the host are important, maybe not, the point you juts do not seem to get is that when you set up your sample space you have to make some judgments as to what events to include, what events not include and why. There is no mathematical formula or algorithm that tells you how to do this, so perhaps you could tell me how you decide what events to include. Martin Hogbin (talk) 10:43, 11 March 2011 (UTC)

No, the problem description tells you what is relevant. Whether a specific aspect is important, and I guess you mean with important, makes a difference for the solution, only appears after the analysis. If you want to decide that some aspect is unimportant beforehand, you have to argue, So, either you introduce the position of the car, the choice of the player and the door opened by the host as relevant aspects, or you reason that for instance by symmetry you may reduce your sample space. But then you cannot do without this reasoning. And this reasoning is about the conditional probabilities being all the same and equal to the unconditional. But, as you notice, also then it is about the conditional probability. And the simple solution just does not give the needed arguments, is actually not set up for this reasoning.Nijdam (talk) 13:09, 11 March 2011 (UTC)

You say, 'If you want to decide that some aspect is unimportant beforehand, you have to argue', so what is your argument for not including each word spoken by the host in your sample space? The words are clearly given in the problem statement. Martin Hogbin (talk) 23:06, 11 March 2011 (UTC)
I rather liked you stay serious, and do not digress to such pointless questions. Anyway, the words do not form aspects of the problem, as nothing depends on it, and nowhere in the problem formulation is said that the host may vary his words. Nijdam (talk) 22:14, 12 March 2011 (UTC)
And nowhere in the problem formulation is said that the host could/would / can/will present a log-list showing records of hitherto results of game shows that never did happen. I doubt that you watched all of them? This "one hypothetical game show" we are talking about did never happen. Repeat: Just one "hypothetical" game show. Please show me your log-list. As I repeatedly said before: In 100 million games you never can be sure to "know" that your "detected host's bias" is real, and so your "closer" result will be just for the birds. Counterproductive. Worse than "just for the birds."  Please apprehend that "conditional probability assumptions" belong to the field of probability calculus. Without impact on the very "one hypothetical game-show" called Monty Hall paradox. Still squirming? Gerhardvalentin (talk) 22:56, 12 March 2011 (UTC)

Which events go in the sample set

I am being serious. Please tell me how you distinguish between these events, based on Whitaker's question: 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 No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, "Do you want to pick door No. 2?" Is it to your advantage to switch your choice?

  • The host opens door 3

This is stated to occur in the problem statement.
It is not stated that the host could open door 2, but we could assume that he might.
It happens after the player's initial choice and before his final choice.
It could be a relevant fact if (contrary to TV game show rules) the host gives additional information to the player by his choice.

  • The host says the word 'pick'

This is stated to occur in the problem statement.
It is not stated that the host could say a different word, but we could assume that he might.
It happens after the player's initial choice and before his final choice.
It could be a relevant fact if (contrary to TV game show rules) the host gives additional information to the player by his choice.

Please tell me why the first event should be incorporated into your sample set and the second not. Martin Hogbin (talk) 00:24, 13 March 2011 (UTC)

The problem states: ...and the host, who knows what's behind the doors, opens another door,..., and then continues: say No. 3, which has a goat. It is quite clear, and (almost) anyone interprets so, that the host does not in every game opens door 3. Nothing, on the other hand, indicates that the host sometimes does not say pick, in order to influence the game. On the other hand, if you like, take thee host saying pick as part of your probability space, please go ahead, it does not change a bit.
But let us stick to the point of interest, i.e. why you do not want to take the picked door etc. as events. Nijdam (talk) 23:07, 13 March 2011 (UTC)

The point of interest to me is the means by which you select events for your sample space. You say, 'if you like, take thee host saying pick as part of your probability space...it does not change a bit'. How do you know that it will not change the outcome?

My answer to you question will be exactly the same as yours to mine, 'if you like, take the host opening the specific door 3 (as opposed to 'the host opens any legal door to reveal a goat') as part of your probability space...it does not change a bit'. How do I know it will not change the result a bit? The obvious symmetry with respect to door number tells me. Martin Hogbin (talk) 23:23, 13 March 2011 (UTC)

The difference is, as I explained above, that nowhere in the problem formulation is spoken of the host saying anything different. There are however three different doors. So you may freely add "pick" to your events, but you cannot leave the door numbers out. Well, having said this again, I have the idea you do not want to understand it. Nijdam (talk) 23:20, 14 March 2011 (UTC)

Neither does it mention that the host might open door 2, this is an assumption on your part, a very reasonable one I admit, but still an assumption.

The point that I am trying to lead you to is that in turning any natural language statement into a well-defined mathematical problem you need to apply some logic to determine what events are important. Your argument is essentially this, 'We are given door numbers in the problem statement, this must be for the reason that we are expected to use them in solving the problem'. This is good logic for an exam question but in other circumstances it may not be so good. It may be that some information available to us is irrelevant, and indeed in this case that turns out to be true; the door numbers are completely inconsequential, the value of the probability of winning by switching would be exactly the same had the player initially chosen door 2 and the host opened door 1. Maybe a little thought before formulating the problem in mathematical terms would reveal that fact and save you the trouble of performing and unnecessary complicated calculation. Martin Hogbin (talk) 13:26, 15 March 2011 (UTC)

I know what you're aiming at, but your way of applying does not make sense. In the first place is in the problem statement spoken of the host opening another door. As we do not know which one we add the possibility for each door, Secondly: as you say, it turns out that the door numbers are not relevant. You also could give the answer: switching is better, without any further explanation, because you gave it a little thought before. You see, we do not give the answer, we try to explain. That's why we describe our thoughts. It is not up to us to decide what arguments may be left out, because, in our opinion, anyone will know. And I asked you not to come up every time with your alleged complicate calculation. I explained it is not about the WAY the calculation are done, but about WHAT is to be calculated. Nijdam (talk) 22:57, 15 March 2011 (UTC)

You say, 'It is not up to us to decide what arguments may be left out', but we must do that or the problem becomes impossibly complicated. You have decided to leave out that the host says the word 'pick' but you still cannot give a clear reason for this. The only reason is that you think it is not relevant.

Perhaps you could answer my question below. Martin Hogbin (talk) 23:06, 15 March 2011 (UTC)

Another question

Let me ask you this. Assuming we take it that the player might have chosen any door to start with and the host may have opened any unchosen goat-hiding door, why do you not insist that the starting sample space must include all the possible door combinations? Martin Hogbin (talk) 13:23, 15 March 2011 (UTC)

I do not understand your question. I DO insist that all the combinations are in the sample space. You have seen them in the past. What is your point?Nijdam (talk) 23:00, 15 March 2011 (UTC)
You support the solutions given in the article which show only the case where the player initially picks door 1. These solutions are incomplete. Martin Hogbin (talk)
What's the connection with our discussion about the appropriate sample space???? Nijdam (talk) 23:14, 16 March 2011 (UTC)
Surely the solutions in the article should show the whole sample space? This is then conditioned using the initial player and host door choices. Martin Hogbin (talk) 23:18, 16 March 2011 (UTC)
I'm sorry, but your opening sentence sounds like: the car definitely has to be filled with distress. What on earth do you mean? A sample space is a reflection of the problem, reducing it to the necessary mathematics. The needed sample space, do you remember, consists of the 27 combinations of car location, player's choice and opened door. Some of these outcomes have probability zero, and may be left out, but this is unimportant. Tell me what you want to say. Nijdam (talk) 23:48, 16 March 2011 (UTC)
What I am asking is why, in the decision tree in the article and the diagram immediately below it which you support, do we only show the results of the player initially choosing door 1? These diagrams should show the results if the player initially chooses any door. Martin Hogbin (talk) 15:41, 17 March 2011 (UTC)
If it was up to me the diagram only showed the player choosing door 1 and the host opening door 3. But in general you're right, either my choice, i.e. conditioned, or showing the total of possibilities. Nijdam (talk) 15:17, 22 March 2011 (UTC)
Well we agree then. So the difference between the simple solution given in the article and the one you have supported is fairly minor, neither shows the full sample space.
By the way, I cannot understand why you have been treated so harshly by arbcom, I have tried to say that but it seems very hard to get through to them. Martin Hogbin (talk) 16:06, 22 March 2011 (UTC)
Comment by Gerhard

Please pardon for intruding  –  I just feel this comment really amusing for the audience, but boring soon. You really don't know what is needed to describe the paradox?
Well,  that's a fine how d'ye do.  I tell you what: You need a contestant. A contestant who just has selected one of those three doors. And you need a host. A host, who cannot change the location of the car anymore. A host that is totally unable to influence the "overall Pws" in any way, but who exactly knows where the car actually is. And: his action of showing a goat is needed. And his voice in offering to switch is needed. Yes, his voice. Does he say those words with a laughter and quite aloud, or with a moderate voice in an insinuating mode? That makes a great difference, you know. Because you are free to assume that, in most cases if he has got two goats to show, then he will make his offer to switch in a rather seducing tone, yes, with a really seductive voice. Might be in about exactly 73 % of those cases, you are free to assume. And, if the door in the middle should actually hide the car, we all are free to assume that he will almost never use the word "pick" then, but some quite other wording, like  "wouldn't you opt for"  or  "select",  but almost never will use the word "pick",  in that case. And everyone else also is free to make similar presuppositions,  and all of those specific assumptions enable you, and me, and anyone else, to exactly calculate a much  "better"  result for the actually given situation, than only the average probability to win by switching of just 2/3.  A quite better result, that obviously will be of great advantage for an exact "probability". Although we do not know whether our beliefs will ever correspond to reality. But that does not matter anyway, because that game has indeed and in fact never been played, anyway.  Not one single time in exactly that "MHP-way".  Never. Not one single time. But you can assume whatever you want. Whatever you like. And you even can assume that you knew what you don't know but what you would like to "need to know" in order to "know better". Repeat: Whatever you like.
Yes, maths and "q" can be a quite enjoyable illusion, indeed. So imho you better should stick to reliable sources, that never use such very absurd nonsense for "solving" and for getting better and "much closer results". And imho you should also show conditional probability, easy to understand in odds form, by using the clear functions of the doors, as there were no "door numbers" written on them. For that show that never was reality. There were no "door numbers", just three doors. No, they never had numbers, in this only one single game we're talking about, that never was for real.  And those two still closed doors never were transparent at all, not even at exactly 19 %. You understand? You can formulate anything you assume to be of any importance. You can assume it in an exact manner. And you may suppose that your assumptions to be of eminent importance. But you never proved that this illusion helps in any way to find a better decision than always to switch. Once more: You really should show conditional probability in odds form, and even show "q", but you should admit that all of this is just an illusion, and just a way to help to understand what the lemma is about.  Regards, Gerhardvalentin (talk) 21:39, 10 March 2011 (UTC) A fine game.

Of course you are right Gerhard, what seems obvious to you is somehow being missed by Nijdam. Martin Hogbin (talk) 10:43, 11 March 2011 (UTC)

This is just your interpretation, nowhere does it say that the host may open door 2. Martin Hogbin (talk) 00:37, 15 March 2011 (UTC)

This is getting silly, but okay. The player is given the choice of three doors. So we have to account for these possibilities. The host then opens another door. We have to account for these possibilities too. See? Nijdam (talk) 09:20, 15 March 2011 (UTC)
I do not doubt the reasonableness of what you say but you must understand that you are interpreting the original statement, which does not actually say that the host could open door 2. Martin Hogbin (talk) 12:48, 15 March 2011 (UTC)
This has nothing to do with reasonableness. I'm not interpreting, but modeling. And indeed, it is not said that the host may open door 2, but neither is said he cannot open it. That why we have to account for this door. Nijdam (talk) 23:10, 16 March 2011 (UTC)
Neither is it said that the host might not have said 'choose' instead of 'pick'. There is nothing in the problem statement that tells us that the words spoken by the host are less important than the number of the door that he opens. Martin Hogbin (talk) 18:38, 18 March 2011 (UTC)
No big deal; if you want, do add the host saying "pick" to the sample space. This comes down to extend any outcome with the host saying "pick". It doesn't change any relevant issue. But, be my guest. And to end all further discussion of this sort, extend any outcome with all other non-relevant info. The sample space you will end with, is equivalent to mine. Nijdam (talk) 11:37, 24 March 2011 (UTC)

The flawed full solution vs. any correct solution

You are through, Martin, with the so called "conditional frequentists", getting better knowledge by telling door 2 apart from door 3 and distinguishing carefully for students of cond.prob.?
Yes, he's here again, our and everyone's good old friend, and everyone calls him the "Ol' Catch 22". If he accompanied us to the casino, we were sure to win. No one doubts?
If s.o. assumes to have "additional frequentist's information", or even that "he could have any", regarding that one special game the contestant is in, and the famous question is about, and he "assumes his assumption to be right", and even given he "assumes to know his assumption to be right" regarding that one special game, then – with or without using maths – then he for sure "could" give a much closer answer indeed for this very game, than just only the honest:

Pws is within the range of "at least 1/2" (but never less) to "1", and on average it is 2/3, and that's all we know and will ever know.

Yes, then  –  without any question  –  this frequentist "could"  assign a much closer value to Pws indeed, for this one special game the contestant is in.  More than that, he could assign "really a correct one". But that will just be based on the famous flawed assumption that "if he knew" what he doesn't know indeed, and never will know, "then he could and would know much better, indeed".

Because all of those flawed assumption never can nor will be "given to be right" regarding that one special game the contestant actually is in, and it just remains the "Ol' Catch 22":

"He could know much better if he just knew better, or vice versa "if he just knew better, then he could know better".

So all of that reported "correctness" offered by those frequentist's conditional probability solutions proves to be just a flawed "if you knew better, then you could know better" -joke, indeed. Yes, and: If the doors were assumed to be made of glass, then the contestant could know a much closer probability to win by switching, than she actually knows.

That's why serious reliable sources emphasize that, although mathematically absolutely correct, it's useless to mention this

only correct but absurd "Ol' Catch 22 – The cat bites her tail circle". Because it's just suitable to train students of probability theory, only.

Though mathematically absolutely correct, but of no avail whatsoever for the decision to be made. Because the "range of Pws" (it never can be of disadvantage to switch) is sufficiently known in advance, anyway. Just by the humble acceptance "what if he always uses ..." and "what if he never uses ..." The only "advantage" of conditional probability is that it can show this insight in a very clear manner. But not more. Because that's all of its marginal utility for the MHP.

Other formalists with narrow prospect firmly believe in that "if you just knew, then you really could know much better" circle and they are quite happy with it. Amusement for the audience, but boring soon. Just suitable for students to train stubborn conditional probability calculus methods, with no need to question the underlying "never-to-be-given" -basics.

Though mathematically absolutely correct, its only merit is that it can show the exact range of Probability to win by switching of   "at least 1/2, but never less"   to   "1".
Repeat: That is all of its marginal utility for the MHP.

Though mathematically absolutely correct, it's no "solution", it's just only very well suited for practicing a method of probability calculus for students. And, written in odds-form, it can help to understand the MHP.  But it is no "solution".  And so for good reasons this is not perpetually repeated in most reliable sources. And yes, for a very good reason.  Gerhardvalentin (talk) 21:57, 27 February 2011 (UTC)

  • (1) The first thing I noticed about all the "simple is flawed" arguments from editors, and the "here's where the simple solutions can fail" sources is that they immediately start with different premises to the problem. Well, that approach does nothing to demonstrate any flaws in any problem statement that does not include these new or changed premises.
  • (2) It's a lot of hot air receiving way too much attention in the Wikipedia article (UNDUE WEIGHT).
  • The argument I just presented (1) is not OR, or my opinion, it is a logic/philosophy fact. That the ownership editors will not acknowledge this is the NPOV violation. And the emphasis on this fallacy/canard is what ruins the article so early. Glkanter (talk) 11:55, 11 March 2011 (UTC)

Timeline for evidence in Monty Hall case

Please see Wikipedia talk:Arbitration/Requests/Case/Monty Hall problem/Evidence#Timeline for Evidence, Proposed Decision. On behalf of the Arbitration Committee, Dougweller (talk) 16:42, 21 February 2011 (UTC)

The goats

I know that this has been discussed before by various editors, but can anybody give me a reason why the problem is normally formulated in terms of the door numbers (1,2,3) and not the objects behind the doors (the car, goat 1, and goat 2). Is this just because the door are given numbers in the problem statement but the goats are not given names? Martin Hogbin (talk) 10:07, 27 February 2011 (UTC)

I can answer that. It's because the premise of your question is invalid.
  • It's because the goats are of no interest. Selvin had car keys & 2 empty boxes. You gonna name them 'emptiness 1' and 'emptiness 2'? Go for it!
  • Countless sources give car/goat solutions. It's only the Wikipedia MHP editors who don't acknowledge their existence. We call these 'simple' on these pages, unfortunately. Nijdam ignores them because he knows they are 'wrong', and therefor not reliable. See how that works?
  • Glkanter has tried, with no success whatsoever, to rename these as 'simple conditional', as distinct from the simple, unconditional tables of outcomes from Selvin & vos Savant
  • Richard has insisted on telling me that my terminology differs from all the other editors, and refuses to acknowledge that there are 3 solutions put forth by the reliable sources. He posted 'The Truth' as Evidence on the arbitration page, completely ignoring the solution you are now asking about. I am trying to discuss this on Richards talk page, with little success.
  • Glkanter has turned those solutions into a conditional decision tree. You have found problems with it, something about the 100% condition being of no value, I think. Richard's only criticism was that the column headings should not have door #s. Still, he does not acknowledge these solution in his 'The Truth' section in his evidence.
  • The editors who dominate the article are aided and abetted by this imprecise terminology, and it's corresponding confusion/dismissal, so have no interest in bettering it.
  • Nijdam's point about [paraphrasing] 'the contestant must be faced with exactly two doors' is satisfied by these solutions (the 100% condition is the host opens another door revealing a goat). The Combining Doors solution does, too. Now, on Richard's talk page, Nijdam has *actually engaged me* on this very topic! ps whatever happened to "1/3 <> 1/3"? Oh, right, that decision tree proved that wrong, too.
  • Glkanter is about to be blocked from his own arbitration for making this very point, both in his evidence and on the talk pages. The sources overwhelmingly provide this solution, and the article's POV is contrary to this. That is, the article's POV is based on OR, not the sources. But I can't get anybody to pay attention to this simple fact.
Glkanter (talk) 10:36, 27 February 2011 (UTC)

Tree shaping

Can you point to the examples of spamming, because I don't see them. SilkTork *YES! 13:09, 7 March 2011 (UTC)

Thanks for contacting me. For a start, pretty well all of the section 'Chronology of notable practitioners' seems to be a series of advertisements for non-notable small businesses. We do not find this in articles on other subjects. An IP thought it looked like spam and I agree. Martin Hogbin (talk) 15:39, 7 March 2011 (UTC)
The section you mention contains sourced information about people who developed Tree shaping. When reliable sources write about something then that something becomes notable according to our guidelines, which includes small businesses. Apart from that section, what other reason do you have to feel there is spam in the article? SilkTork *YES! 18:50, 7 March 2011 (UTC)
I think we need some outside opinion on this. To me and to at least one other it looks like blatant commercialism. Martin Hogbin (talk) 22:30, 7 March 2011 (UTC)

Can you point to the blatant commercialism and explain it? At the moment you are asserting your opinion without giving me much evidence. I've looked at the section, and I see information culled from various books and journals on the people who are most notable in the field of tree shaping. I do not see direct links to commercial sites, and while the language is not top class, and does fly close to promotional in nature in places, I do not see it as obvious advertising. It has to be borne in mind that primary sources are allowed, and information about practitioners and artists, such as the works they have done, books they have written, etc, is part of what we deliver. If you have specific concerns about any of the links or any of the wording, this is a good opportunity for you to point to it, and discuss it. If you are unable to do that, then it may be that you have got the impression that the material was promotional when it wasn't. These things happen. SilkTork *YES! 02:52, 8 March 2011 (UTC)

SilkTork, if you cannot see what is plainly there in front of you there is no point in my trying to convince you of anything. Have a look at the articles on topiary and bonsai for example, we do not see a small business advertisement there. As I said, we need to get outside opinion on this. Martin Hogbin (talk) 09:46, 8 March 2011 (UTC)

Other people have looked - you are aware that the article is under the scrutiny of various people who do look into such matters - you have yourself commented on this thread on the COI noticeboard where people have said that they don't see a problem in the article, rather, just a problem with the ongoing dispute between the two main contributors. I'm going to remove anything from that section that is near to the line, and then remove the tag. If you feel that there is any promotional material left, then please either directly remove it yourself, or let me know what the material is. Putting the tag back would be unhelpful and somewhat provocative, as you are unable to indicate any specific problems. See WP:Tagging. SilkTork *YES! 12:43, 8 March 2011 (UTC)

OK. I will have a go at making the section more encyclopedic and less promotional. No doubt ther will be some resistance from at least one editor with a commercial interest. Martin Hogbin (talk) 14:59, 8 March 2011 (UTC)

Archiving your talkpage

It's up to you - there's no specific guideline or rule. Your talkpage is quite large which makes it difficult for others to navigate and use your talkpage, so it would be helpful to archive it. Information is given in: Help:Archiving a talk page. SilkTork *YES! 18:56, 7 March 2011 (UTC)

ANI notification

Please see Wikipedia:Administrators' noticeboard/Incidents#Proposed Topic Ban for Blackash and Slowart on Tree shaping related articles where I have mentioned your name. Johnuniq (talk) 07:36, 9 March 2011 (UTC)

Whatever Happened to "1/3 <> 1/3" ?

I'll tell you what happened.

The simple conditional decision tree based on Monty Halls's and Carlton's, and Morgan's F5 (and countless others') simple solutions show that the 1/3 likelihood that the contestant selects the car is *still* 1/3 after a door has been opened revealing a goat. Because that condition is 100%, and a number multiplied by 1 doesn't change. That the 2/3 *did* change from 1/3 + 1/3 to 2/3 + 0 is of no importance. Because of the law of total probability.

Nijdam uses that 1/3 <> 1/3 argument (without any sources) to say that all simple solutions are wrong.

Morgan clearly shows that 1/3 * 1 = 1/3:

  • "Solution F5. The probability that a player is shown a goat is 1. So conditioning on this event cannot change the probability of 1/3 that door 1 is a winner before a goat is shown; that is, the probability of winning by not switching is 1/3, and by switching is 2/3."

Nijdam (without any sources) argues that all simple solutions are unconditional, and don't address the 'deciding between 2 doors' nature of the problem. The same simple conditional decision tree demonstrates clearly that the contestant is choosing between exactly two doors.

Morgan clearly states it's a conditional solution:

  • "Solution F5. The probability that a player is shown a goat is 1. So conditioning on this event cannot change the probability of 1/3 that door 1 is a winner before a goat is shown; that is, the probability of winning by not switching is 1/3, and by switching is 2/3."

Nijdam's only remaining argument is that the problem must be solved specifically for door 3 being opened. Well, that's not derived from the sources or any science. He doesn't have a leg to stand on. Glkanter (talk) 12:46, 11 March 2011 (UTC)

Mediation

Martin, I'm asking you to agree to mediation. I give some more details on Tree shaping talk page. Blackash have a chat 05:36, 12 March 2011 (UTC)

I am happy to participate in any dispute resolution process. Martin Hogbin (talk) 10:00, 12 March 2011 (UTC)
Martin going by your comment on ANI noticeboard you seem unsure. I'm ready to list. Are you still willing to go ahead with formal meditation. Blackash have a chat 12:10, 17 March 2011 (UTC)
Done listed [[1]] Blackash have a chat 14:33, 18 March 2011 (UTC)

Sex and psychology

Thanks for joining the discussion. I've replied at Talk:Sex and psychology#Sex and psychology. Kaldari (talk) 03:28, 13 March 2011 (UTC)

It looks like there is a consensus for a ban. Martin Hogbin (talk) 19:09, 17 March 2011 (UTC)

It would be appropriate for an uninvolved admin to close the discussion. The discussion has, unfortunately, somewhat wandered so the consensus is not clear, and there is a fair bit of reading to be done. When discussions get complicated, it takes longer for them to be closed. SilkTork *YES! 07:15, 18 March 2011 (UTC)
I have asked AGK to look at the case. Martin Hogbin (talk) 18:39, 18 March 2011 (UTC)

Glkanter

You seem to be a friend of his. He has been blocked for his behaviour in the past few days, not because of the evidence presented by anyone at the Arbcom case. Can you persuade him that edits like this aren't helping his case. Three admins have already reviewed his unblock request on the grounds that his behaviour was sufficient to warrant the block, and far from making any attempt to address it, he is denying that he has done anything wrong, and saying that he'd do it all again. Arbcom hasn't yet decided that banning him is an appropriate step, but the more he carries on like this, the likelier it becomes. --Elen of the Roads (talk) 15:40, 18 March 2011 (UTC)

Thanks for your response. I should first point out that my comment on the ban was not prompted by friendship but by a sense of fair play. The ban does seem disproportionate to the offence. However, I will do what I can to help the situation. Martin Hogbin (talk) 18:34, 18 March 2011 (UTC)

Formal mediation has been requested

Formal mediation of the dispute relating to Arborsculpture 3 has been requested. As an editor concerned in this dispute, you are invited to participate in the mediation. The process of mediation is voluntary and focuses exclusively on the content issues over which there is disagreement. For an explanation of what formal mediation is, see Wikipedia:Mediation Committee/Policy. Please now review the request page and the guide to formal mediation, and then, in the "party agreement" section, indicate whether you agree to participate. Discussion relating to the mediation request is welcome at the case talk page.

Message delivered by MediationBot (talk) on behalf of the Mediation Committee. 18:42, 18 March 2011 (UTC)

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