Talk:Monty Hall problem

Dispute resolution

Guy and others, I understood we were going to use some form of dispute resolution. So far we have had only two suggestions as to how to frame the dispute any there is no sign of anyone writing another. I therefore we suggest we go with both the questions below: Martin Hogbin (talk) 09:58, 2 August 2011 (UTC)

Rick's question

The dispute is whether the article should primarily satisfy

1) Wikipedia:Make technical articles understandable, with an initial, extended section focusing exclusively on "simple solutions" that makes no mention of any other solution approaches, in particular the approach using conditional probability. All other approaches will be relegated to later sections of the article intended for experts only. This structural outline (but not the content aspects) are shown in this version of the article.

or

2) Wikipedia:Neutral point of view, with initial sections of the article addressing the most common interpretation of the problem using various approaches specifically including both simple and conditional solutions. The version of the article following the May 2008 FAR (this version) was more or less along these lines, although the "Solution" section in this version of the article arguably expresses a bias in favor of the conditional approach.

Martin's question

Should this article treat the MHP principally as an undergraduate exercise in conditional probability or should it treat it as a simple, well-known, probability puzzle that most people get wrong but which was correctly and simply solved by vos Savant and many other sources and also include a full discussion of all other aspects of the problem for the more specialist reader? — Preceding unsigned comment added by Martin Hogbin (talk • contribs) 09:58, 2 August 2011 (CEST) (UTC)

Discussion

Martin asked: Should this article

a) treat the MHP principally as an undergraduate exercise in conditional probability or

b) should it treat it as a simple, well-known, probability puzzle that most people get wrong but which was correctly and simply solved by vos Savant and many other sources and also include a full discussion of all other aspects of the problem for the more specialist reader?

Gerhard says: b) Gerhardvalentin (talk) 10:23, 2 August 2011 (UTC)

Gerhard thanks for your comment. The purpose of this section was to propose a question that we could use as a basis for a dispute resolution process. I imagine we will have an RfC or the like Martin Hogbin (talk) 10:48, 2 August 2011 (UTC)

RocksAndStones says: I stay for Rick's 1), although I do not see what can make up "extended" section. The two "simple" arguments presented now are almost identical. Simulation is not an argument at all, and increasing the number of doors adds a little too. What is important, is the explanation which questions the "simple" solution answers, and why intuition fails. Regarding Martin's itemisation, I stay for c), explain simple solution first then move to strategism and conditionalism, not missing to say which questions these approaching answer, and how they are connected to "simple solution". Then move to symmetrism, variations, etc. Sample articles whose structure could be helpful: Prisoner's dilemma, Poincare conjecture.RocksAndStones (talk) 12:56, 2 August 2011 (UTC)

You chaps do not seem to have understood what this is all about. We are going to engage in some form of dispute resolution but in order to do this we have to tell other people what the dispute is all about. We cannot even agree on how to do that so here are two ways of asking what is essentially the same question. Rick's 1 is essentially the same as what Gerhard has called my b) which is my proposal of simple first without health warnings followed by discussion of more complex solutions. Rick's 2 is the same as my a) which is Rick's suggestion to have some mention of the conditional solutions right from the start.

We hope to get some other people to help us decide which way to go, although those already here will obviously still have a say.

It looks as though we may have to explain to those who come to help resolve the dispute that these are just two ways of asking the same question. Martin Hogbin (talk) 13:28, 2 August 2011 (UTC)

Before we go anywhere with this, I think we should have actual content to show people so they aren't misled by intentionally pejorative descriptions (i.e. no one is arguing the article should "treat the MHP principally as an undergraduate exercise in conditional probability"). I've created two copies of the current article content, Talk:Monty Hall problem/draft1 and Talk:Monty Hall problem/draft2. I don't care who edits which copy, let's say I and anyone else interested in the approach I'm talking about (I welcome anyone) edit draft1 while Martin and anyone else interested in his approach edit draft2. Since they have identical starting points (the current article), we'll be able to diff these against each other as well as the current article. -- Rick Block (talk) 15:45, 2 August 2011 (UTC)

No problem. My only interest is in keeping the simple solutions simple with no health warnings. The rest can then be discussed later. I will edit draft 1 if you like. Martin Hogbin (talk) 16:42, 2 August 2011 (UTC)

Martin - I suggested above I edit draft1 and you edit draft2. Is your suggestion you edit draft 1 simply a typo? -- Rick Block (talk) 19:28, 2 August 2011 (UTC)

Not exactly a typo but I did not read properly. I will edit draft 2 to how the article was after my major editing. Martin Hogbin (talk) 21:34, 2 August 2011 (UTC)

Excellent! Thanks to both Martin and Rick. I want the best possible arguments to be made for each position, and this goes a long way towards accomplishing that. Of course there will also be ample opportunity to simply argue your case.

Anyone interested should take a look at Wikipedia:Requests for comment/Maths, science, and technology to see how other content disputes have turned out and Wikipedia:Requests_for_comment for a more general description of the process. I will also be posting invitations to participate at Wikipedia talk:WikiProject Statistics, Wikipedia talk:WikiProject Mathematics and Wikipedia talk:WikiProject Probability. --Guy Macon (talk) 17:18, 2 August 2011 (UTC)

I have now changed draft 2 to show my compromise proposal. I should stress that it is not the detail that I want to show but the basic structure, where the simple solutions are shown and discussed first, with no health warnings. Everything else, much as it is now, can come later. Martin Hogbin (talk) 21:47, 2 August 2011 (UTC)

Martin - you say this draft does not show your preferred content yet, but it does include various content changes [1] (I'm guessing you overwrote the draft I created with something from some time ago). Are the changes relative to the current text part of your proposal or not? Please edit the text to your liking (without this I think it is not clear what you're suggesting). If you'd like, I could make a stab at what I think you're after (which you could revert if you don't agree). I've edited /draft1 through the "Solution" section (diff here) and have left the remainder of the article essentially untouched (although parts of it definitely need work). -- Rick Block (talk) 15:32, 3 August 2011 (UTC)

I have a couple observations on the current drafts:

• The current revision of Draft1,[2] in characterizing the first solution (vos Savant) as "an intuitive explanation," could be taken to indicate that this involves lies-to-children, i.e., heuristic aids to understanding that should not be taken as valid demonstrations. In the interest of taking a neutral point of view, I think we should avoid language that could be interpreted as a disclaimer.
• The current revision of Draft2,[3] (which includes only the initial sections, with a placeholder for the rest) is confusing in the sentence beginning "Although not explicitly stated in this version..." because most of this is stated in the antecedent version (K&W). All that is missing is that "random" is taken to be a uniform distribution. This is very redundant with the previous paragraph: did you mean to refer to the previous version (Whitaker)?

In both versions I heartily endorse moving simulation from "Solution(s)" to "Aids to understanding." It is neither a solution nor an explanation. (I know that some people find this persuasive but, personally, I think that using stochastic modeling for a discrete problem space that can be fully enumerated on a 3x5 card is a bit ridiculous.)

Ok, that was three observations, not a couple. I will have more at a later time. ~ Ningauble (talk) 16:43, 3 August 2011 (UTC)

The "intuitive explanation" wording in draft 1 is directly from the source (Carlton) - it pertains to that one sentence, not vos Savant's solution, and was the result of an extended discussion during mediation. Perhaps this should be made more clear (I'll make a stab at this). Per Martin's comments below he has made no attempt to make the content of draft 2 reflect his intent (other than the outline). I've made some edits that I think reflect Martin's intent. -- Rick Block (talk) 04:59, 4 August 2011 (UTC)

Better, thanks. I confess to quibbling, but since the validity of solutions has been the subject of heated dispute I am inclined to strive for the utmost neutrality. ~ Ningauble (talk) 15:23, 4 August 2011 (UTC)

I withdraw my support for Draft 2

I am not trying to be awkward and I was willing to give Rick's suggestion a try but it seems that even the regulars here are misunderstanding the purpose of the two drafts and quibbling about the details. Newcomers are even more likely to do that.

All I am trying to get across is that we should first concentrate on the simple puzzle by Whitaker/vos Savant in Parade magazine, the simple solutions, why the answer is not 1/2, and the media furore. Everything else is an academic extension. I therefore feel I can only withdraw my support for Draft 2 and stick with my dispute statement ant the start of this section. Martin Hogbin (talk) 19:11, 3 August 2011 (UTC)

Martin, I think your attempt has limited success because there is too much excitement by the furore. Instead of taking clear academic viewpoint people start telling a story about silly PhD's who got it wrong. It is obvious to me that many disagreed with vos Savant's "solution" because the framework of what later became "standard problem" was not firm at the moment, or people confused designs. It was perhaps not clear if host by chance did not reveal prize or it was the rule of the game. The simple argument tells that always 50:50 is impossible. But it is equally impossible for untrained mind to see that under circumstances it could be sometimes this, sometimes that, and in fact under some mode of Host's behavior 50:50 *can* be possible. All what needs and must be said about the simple approach is just that: picking 1 then always staying wins if prize behind D1; picking 1 then always switching wins if prize behind 2 or 3. Same for picking x in some way. If under all cicumstances the conditional odds were 50:50 then it'd make no difference, contradicting to what was just said. There is really nothing more to say about the simple solution. If somebody tosses a fair coin to solve the dilemma, then odds are 50:50, in this sense there is a way to "create" 50:50. Another fundamental question is the following: in Selvin's letter of 1975 the talk is about probability, with the solution based on symmetric assumptions. In vos Savant's column I do not see the word *probability* at all, look:

"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?"

Maybe the word "advantage" means "probability"? Or maybe the advantage is 2000 buks vs 1000? In my view, one can do no mistake by saying "we assume that..., then we obtain that...". Explainin three sentences why there is one case vs two cases and explain that discarding history is a source of confusion, then move on to deeper issues.RocksAndStones (talk) 20:48, 3 August 2011 (UTC)

Martin - I've made some content changes in /draft2. I believe this is more or less in the direction you want the article to go. Why I'm fairly insistent on showing approximate content rather than just an outline with headings is because without specific content different people will imagine the sections to contain what they would like rather than what I think you're actually suggesting (and I believe these may be considerably different). Regarding sticking with your dispute statement, as both Guy and I have mentioned, your description of the conflict comes across as pejorative. For example, are you seriously claiming the content of /draft1 through the initial "Solution" section (the part I've edited to reflect what I'm actually suggesting) treats the MHP "principally as an undergraduate exercise in conditional probability"? -- Rick Block (talk) 04:51, 4 August 2011 (UTC)

My point

I do not want to or claim to be able to write this article by myself, I like the concept of cooperative editing. My point is one of principle not of detailed content. The MHP may be addressed at three basic levels:

The popular level

This is undoubtedly the level at which this puzzle was aimed, it was published in a popular, general interest, magazine. At this level, the solutions of vos Savant and the other simple solutions are perfectly adequate.

The fact that most people get such a simple puzzle wrong is what the MHP is all about.

The undergraduate level

With a little licence (in allowing the show host to exhibit a personal preference on a TV game show) this puzzle can be turned into an interesting and instructive exercise in conditional probability. This is pretty well what Morgan say in presenting their solution.

Apart from students of conditional probability, this solution will be of little interest to our readers.

The professional level

At this level, as alluded to by Seymann, you cannot even start to answer the problem without a clear understanding of the exact circumstances, the exact question that the questioner would like answered and the basis on which they would like that answer. As Richard will confirm, to attempt to answer questions of this nature on the undergraduate level, without properly attending to the other issues can lead to serious real-life consequences.

My objection, in common with a the vast majority of other editors, is that you want to give undue prominence to the undergraduate level approach to this problem. Specifically that you insist on complicating one of the world's hardest simple puzzles by mentioning in the solution one specific, irrelevant, alternative method of solution that is somewhat narrow in its interest and applicability. Martin Hogbin (talk) 09:57, 4 August 2011 (UTC)

Martin, I think this is very nicely said, and I like your three levels picture. One might even categorize editors according to which of the three levels is where they can best operate. I am not implying any kind of superiority as one goes "up" levels. Someone with skills and knowledge at level 3 could well be a hopeless Wikipedia editor when trying to work at level 1. I think of myself, in this regard. Now readers will also belong primarily in one of the three levels. All have a right to find what they need when they come to Wikipedia MHP; all of us editors working on the article are doing so, because we think that a) our level is not done justice too; b) the other levels could well use a bit of our level's insight. We are a random sample of readers. Richard Gill (talk) 11:59, 12 August 2011 (UTC)

"Random sample of readers"? Was there a lottery or other randomized technique used for selection purposes? 76.190.251.93 (talk) 09:39, 13 August 2011 (UTC)

You forget the zero level, on which it is explained that the odds are equal. And also the divine level, stating any solution is right as we are all mortal in the end.77.248.232.44 (talk) 14:28, 12 August 2011 (UTC)

I like the general idea of this structure, even though I think some of the spin and rationale veer into a non neutral point of view. I fully endorse the proposition that the article should progress from simple, relatively easy treatments of the problem to more advanced, sophisticated, and general analyses for two reasons: (1) This is a direct application of the WP:TECHNICAL style guideline. (2) This is not counter to the WP:NPOV policy: it does not, in the words of that policy, "create an apparent hierarchy of fact" where the initial treatments appear more "true"' and later treatments are deemed "controversial" but, on the contrary, readers will typically understand this arrangement as leading to "deeper" analysis of the subject.

If some readers look on the more sophisticated treatments as mere sophistry, all we can do is write them as clearly as possible and bear in mind that some readers will regard the whole article as an elaborate hoax, believing that there is no advantage to switching at all. ~ Ningauble (talk) 13:36, 13 August 2011 (UTC)

I was not really proposing a structure for the article, I was just trying to show how the 'health warning' that some editors insist on represents a rather narrow approach to the problem, essentially that of undergraduate probability. Martin Hogbin (talk) 17:13, 13 August 2011 (UTC)

If you think I'm insisting on a "health warning", please tell me exactly what words through the "Solution" section of /draft1 constitutes this "health warning". IMO, the prominence given to the conditional approach in /draft1 being more or less equal to the prominence given "simple approaches" proportionately reflects the prominence of these approaches among reliable sources. The fact is both of these approaches are extremely common among reliable sources. Presenting the conditional approach as a minority view because there are (say) 800 sources presenting simple solutions but only 400 presenting conditional solutions is absurd - particularly since the 800 includes a very large number of popular sources more or less parroting vos Savant's view while the 400 includes a very large number of independently published academic sources. -- Rick Block (talk) 18:36, 13 August 2011 (UTC)

Prominence given to the conditional approach among reliable sources and "importance"

Actual academic sources concerning the MHP and even concerning the total solution of the MHP show that, for solving the MHP and for making the right decision, a conditional solution using door numbers is an irrelevant aspect , not helpful to make "a better decision". Not addressing the MHP, but using the MHP to show conditional probability theorems. Not indispensable to give the only correct answer and to making the only correct decision to switch in that one very game the question is about.

A very large number of independently published academic sources showing conditional probability theory just use the MHP as an example to show conditional probability theory. They are sources showing the correct use of conditional probability theory. They do not belong to the MHP, they belong to maths. Quite unnecessary to making the only correct decision asked for in the MHP, in that very one game the question is about. Regarding weight and importance, that must be considered mandatory. Gerhardvalentin (talk) 08:22, 14 August 2011 (UTC)

Rick, in your /draft1 you do worse that have a health warning, you have a diagram that is unnecessarily and arbitrarily over-complicated in that it shows, as two distinct cases, the doors that the host might have opened, despite the fact that we know that it makes no difference, and the fact we know the host did, in fact, open door 3. For some unexplained reason the diagram does not show cases where the player initially chose a different door, even though they might have done so under the game rules.

This diagram is not exactly wrong but it is in the wrong place. It belongs to the more complicated case,described by Morgan, where we consider that the player initially chooses uniformly, the car is initially placed uniformly but the host does not choose a goat-hiding door uniformly. When addressing the simple, fully symmetrical, case the diagram is unnecessarily complicated and confusing. It should come later in the article when we discuss academic extensions to the problem. Martin Hogbin (talk) 09:01, 14 August 2011 (UTC)

Martin – I am sorry that I misunderstood your characterization of levels of analysis as a proposal to structure the article with the most understandable parts of the article up front. I evidently do not understand what it is that you are proposing, so please disregard my earlier response in this thread. ~ Ningauble (talk) 17:30, 14 August 2011 (UTC)

The Third Draft

May I just start drafting a new version, through which Guy Macon will lead us on the line-by-line basis.

MHP site is falling down, falling down, falling down?

MHP site is falling down? My fair lady...

Build it up with stone so strong, stone so strong, stone so strong.

Build it up with stone so strong, my fair lady.

Stone so strong will last so long, last so long, last so long,

Stone so strong will last so long, my fair lady!

RocksAndStones (talk) 21:09, 7 August 2011 (UTC)

A third draft would be welcome, if neither of the current drafts suits you. And it's OK if someone else writes a fourth. It's also OK for someone to decide they like another version better. If it ends up that nobody prefers a particular version, we will delete it.

Here is what I am looking for in these drafts, and what I am asking everyone to do:

• Show us what you believe is the best MHP article you can create. No need to be concerned about making someone else happy on this one.

• Try to help others to improve their version in areas where you don't disagree.

• Whenever you can, copy the wording of another version exactly. I don't want a bunch of trivial differences. I want the differences to be a true reflection of the places where editors have an intractable good-faith disagreement about content.

Thanks, everyone, for working so hard on this. Guy Macon (talk) 05:12, 8 August 2011 (UTC)

Note: I have been sick for the last few days, so there will be a short delay until I feel better. Guy Macon (talk) 04:27, 9 August 2011 (UTC)

I thought that was the third draft. ~ Ningauble (talk) 16:06, 14 August 2011 (UTC)

Ningauble, that indeed was a sketch of the third draft. Patience! To be continued.RocksAndStones (talk) 19:59, 14 August 2011 (UTC)

Deal Or No Deal

I realise that you're in the middle of a dispute about the page but I was wondering what people's thought were regarding including info about Deal Or No Deal. I know that it's not the same but I've seen it brought up quite often when the Monty Hall problem is mentioned. Maybe some sort of comparison as to why the situations are different and how much the knowledge of the host affects the problem. Sorry if this has been brought up before, I'm still new and not sure how everything works. AlbionBT (talk) 19:17, 11 August 2011 (UTC)

Never mind, I've just noticed this has already been mentioned in the archives. Just ignore me. AlbionBT (talk) 19:19, 11 August 2011 (UTC)

I think it is an interesting point which should be mentioned in the article. As you say the difference is that in Deal or No Deal nobody knows which prize is where, but in the Monty Hall problem the host does know. The fact that this makes a difference surprises many people. Martin Hogbin (talk) 20:10, 11 August 2011 (UTC)

This goes to the point I remarked earlier about the host providing selective evidence. I don't like the idea of bringing Deal or No Deal into the article because there are too many differences between the problems (not least being the issue of a bird in the hand vs. two in the bush); but it would be very good to find sources to cite in the "Sources of confusion" section that explicitly discuss the issue of selective evidence in MHP because I rather suspect this is the aspect of the problem most overlooked by PhDs and other knowledgeable people who famously got it wrong. ~ Ningauble (talk) 12:07, 13 August 2011 (UTC)

Your point is one of the most important points in the MHP. Many people find it surprising that the host's knowledge makes a difference. A more convincing way of putting it might be to say that the host can never open the door hiding the car. After that point has been made, Deal or No Deal might be mentioned as an example where the host does not know where the prizes are, although I agree that that game is significantly different from the MHP. Martin Hogbin (talk) 13:21, 13 August 2011 (UTC)

Academic extensions

Following on from a thread above, I wonder how many here agree with this analysis of the situation here. I am sure all of you will agree with some of the points above but I am interested to know where the disagreement starts.

1. The most well known version of the problem was published in a column in a popular, general interest, magazine.
2. In the 'standard' MHP the producer initially places the car uniformly, the player chooses uniformly, and the host chooses a goat-hiding door uniformly. Many other very natural simplifying assumptions, appropriate to a simple mathematical puzzle, such as that the host does not try to give a clue to where the car is by the language he uses, are also made.
3. The above formulation is completely symmetrical with respect to door number. That is to say, the door numbers make no difference whatever to the outcomes.
4. As the door numbers are not important we can simplify the problem and the solutions by not considering every door number that the player might initially choose, because we know it can make do difference to the outcome.
5. As the door numbers are not important we can simplify the problem and the solutions by not considering every door that the host can legally open, because we know it can make do difference to the outcome.
6. Everything else is essentially an academic extension to the problem. Interesting to many, but not necessary to solve the simple mathematical brain teaser.

Who agrees with all 6 steps and where do the others disagree? Martin Hogbin (talk) 09:20, 14 August 2011 (UTC)

• Agree 1-6, and what about that simple but clear table based on door #1 (or alternatively door "A") chosen, showing all possible variants of actual car location, and the respective outcome, no matter which door the host has opened, like there on citizendium.org? You can call the doors "door A, door B and door C, if you like). Most important imho is your item 6. Gerhardvalentin (talk) 11:19, 14 August 2011 (UTC)

• Comment

In #2 there is a standard assumption about the placement of the car, but no such assumption about the player's choice - and you're missing a very important 2.5:

2.5. In the standard MHP the player's decision to switch or stay is made after seeing which door the host has opened. Moreover, the reader is explicitly encouraged to think about the specific case where the player has picked door #1 and the host has opened door #3 in which situation the probability the car is behind door #3 is obviously 0 and the car is clearly behind one of only two doors.

Your point #3 is a true statement, but it is shown only by a conditional analysis that you are so desperately trying to cast as an "academic extension". Your points 4 and 5 describe what some, but certainly not all, sources do. Your point 6 is simply a statement of your POV - it is specifically not a published POV widely held by reliable sources.

Starting with #3, sticking with a source-based list of points, we could say

3. Many sources choose to ignore the specific case (player picks door 1 and host opens door 3) described in the problem statement showing instead that a strategy of always switching wins 2/3 of the time while a strategy of always staying wins 1/3 of the time. Many other sources show the probabilities in the specific case mentioned in the problem description are 1/3:2/3:0 using elementary conditional probability.

4. Some sources analyze variations of the problem using assumptions other than the standard ones in #2 - typically using conditional probability or game theory.

My point is that this list is simply yet another attempt to justify your bias. Your opinion is that using conditional probability to address the fully symmetric case is an "academic extension" or "unnecessarily and arbitrarily over-complicated" - but this is your opinion, not a statement reflected by a preponderance of reliable sources. -- Rick Block (talk) 17:35, 14 August 2011 (UTC)

Rick, I disagree with your assertion that point #3 (door numbers make no difference) "is a true statement, but it is shown only by a conditional analysis." Conditional analysis is not strictly necessary for the particular variety of standard problem formulations that use an "equal goat" or equivalent stipulation. Consider Morgan's rejoinder to Seymann's comment on Morgan's paper (American Statistician 45 NB: all three were published together with an apparent editorial interest in neutrality.) "Certainly the condition p = q = 1/2 should have been put on [...] It could also have been mentioned that this means that which of the unchosen doors is shown is irrelevant, which is the basis for solving the unconditional problem as a response to the conditional one." [emphasis added] Perhaps Morgan is not the most reliable source but, although I am aware of multiple sources demonstrating that simple unconditional analysis is inadequate when p != q, I am not aware of any sources that convincingly demonstrate conditional analysis is essential when there is an a priori stipulation that p = q. What are the preponderant sources that show this? ~ Ningauble (talk) 19:39, 14 August 2011 (UTC)

What I mean is that the fundamental meaning of Martin's sentence "The above formulation is completely symmetrical with respect to door number." is that the conditional answers are all the same, and that showing this requires (in some form) talking about the conditional cases. Morgan et al. assert that stipulating p=q=1/2 provides a basis for solving the unconditional problem as a response to the conditional one, i.e. that this forces all conditional answers to be the same as each other as well as the same as the unconditional answer (which is indeed what it means for the problem to be symmetrical). I'm not claiming (and /draft1 certainly doesn't say) that a conditional analysis is essential when there is an a priori stipulation that p = q. What I am saying is that many, many sources present a conditional analysis even in this case and that considering such an analysis to be an "academic extension" of the basic problem is merely Martin's POV - not the POV expressed by a preponderance of sources. I am not (as Martin seems to think) saying simple solutions are wrong, or that only a conditional solution is correct. I'm saying both are commonly presented, so the article should not favor one over the other but rather should present both as equally valid alternatives. -- Rick Block (talk)

Gentlemen, you are in the devil's circle, repeating five yrs long the same simple facts. Under the assumption that it makes sense, the conditional solution implies the simple. The simple solution plus a small additional argument about its optimality implies the conditional.

The simple solution is mathematically stronger as it does not require host tossing (perhaps, biased) coin. The conditional solution quantifies the conditional risk, an aspect which the simple solution ignores. What else can be conceptually added to that? I do not see.RocksAndStones (talk) 21:35, 14 August 2011 (UTC)

Me neither. The same simple facts are repeated for five years, some other simple facts remain ignored. The simple facts which remain ignored are the ones which allow for the different approaches to be unified and simplified. Why is this possibility ignored by wikipedia editors? It's a fact that people who resolve a paradox are thereafter extremely fond of their own resolution and critical of all others. After experiencing one paradigm shift we cannot accept another. Wikipedia editors have to be aware of this in their own work.

In a history section one can give due weight (and due criticism) to the vast literature. Not only were there influential papers by Selvin and by Morgan et al., there were also a large discussion and many responses and criticisms. Standard textbooks duplicated a particular approach suitable in the context of teaching Bayes theorem in Probability 101 courses, for making various didactic points to the students. That approach can be reported in an appropriate section. Richard Gill (talk) 13:54, 16 August 2011 (UTC)

My statement, "The above formulation is completely symmetrical with respect to door number" does not require any analysis. It is self evident from the fact that all distributions relating to door number are uniform. This point is confirmed by Falk and several mathematicians here. Martin Hogbin (talk) 21:47, 14 August 2011 (UTC)

Rick, also if there is not an obvious symmetry with respect to door number then what is your justification for not having a diagram showing all the doors which the player might have chosen. The door initially chosen by the player is as much a condition of the problem as the door chosen by the host. Martin Hogbin (talk) 21:51, 14 August 2011 (UTC)

My justification is that it is what many, many sources do. What is your justification for treating the many, many sources that present this argument as if they hold a minority viewpoint? I want the article to be NEUTRAL and to represent what the many, many, many reliable sources say "fairly, proportionately, and as far as possible without bias". Since you're arguing so hard about it, I can only conclude that you do not. -- Rick Block (talk) 02:03, 15 August 2011 (UTC)

Rick, so it is still your opinion that it is indispensable and necessary to confuse the readers just at the start of the article in forever repeating meanwhile disproved outdated sayings, disproved by reliable academic sources. Read the latest authoritative tertiary literature. And you can show all of that outdated sayings, together with the colorful historical conflicts, in a subsequent section "History of the problem". And there you can also show that an extremely biased host, the more the better, will reinforce the decision to always switch, especially in this one special game called MHP. And that no conditional approach can ever give better advice than to switch here and now.

To get the question correctly, to capture the full extent of the issue and to make the only correct decision the reader should be "defused", and it is better not to confuse the reader just in the beginning. That would never be a "neutral point of view". All of unnecessary burden can be shown in the section "History of the problem". Gerhardvalentin (talk) 22:36, 14 August 2011 (UTC)

What is "indispensable and necessary" is that the article follow WP:NPOV. This specifically means NOT picking one approach as most correct, but instead presenting all published approaches "fairly, proportionately, and as far as possible without bias". -- Rick Block (talk) 02:03, 15 August 2011 (UTC)

The vast majority of sources concentrate on trying to give simple solutions that show why the player doubles their chances by switching. We must report what these sources 'without adding our own opinion or the opinion of other sources. Our evaluation of the correctness of sources should be based on what reliable secondary/tertiary sources say about them. Martin Hogbin (talk) 08:49, 15 August 2011 (UTC)

Rick, the prior odds on the car being behind each door are 1:1:1, and the charm of the MHP is that most people believe that, after a goat has been shown behind one of the two host's doors, the odds on the car being behind the two still closed doors still are 1:1. To convince the readers, I am in favor of also showing the (conditional) chances, short in odds form, just at the beginning of the article to be 1:2:0 then. Starting simple, and later showing that no reasonable (unnecessary) assumption can proof that switching can nor will ever hurt. But please stop confusing the reader with unnecessary assumptions just at the beginning of the article. Gerhardvalentin (talk) 07:54, 15 August 2011 (UTC)

Rick, the quotation from Morgan et al. does not say that "this forces all conditional answers to be the same;" they say this means that which of the unchosen doors is shown is irrelevant. The former refers to invariance among solution results, but it is the latter which is "what it means for the problem to be symmetrical." [emphasis added] There is no basis for saying that "showing this requires (in some form) talking about the conditional cases," and attempting to do so in the midst of presenting analyses that treat the choice of goat as irrelevant only confuses the issue.

I completely agree that it is imperative to treat different approaches fairly, proportionately, and without bias, and not favor one over the other. To wit:

• Treating them without bias means not disparaging any of the approaches as merely academic diversions, whether expressly or by implication, as, e.g., in the manner of Martin's characterization of conditional solutions during discussion.
• Treating them without bias also means not commending any of the approaches as more meritorious than others, as, e.g., where Draft1[4] singles out conditional analysis as "Mathematical formulation" with the unsubtle implication that other formulations are not.
• Treating them fairly means presenting each in an equally clear and coherent manner without unnecessary digressions, as, e.g. where Draft1[5] interjects conditional analysis betwixt a symmetric combinatorial answer and answers that apply symmetry to the unchosen doors. (IMO these are all of a piece.)

I completely agree that the conditional approach merits substantial coverage, but there is more to NPOV than proportionate weight. ~ Ningauble (talk) 15:17, 15 August 2011 (UTC)

Ninguable I actually used the term 'academic extensions'. There is nothing pejorative or biased about this. The original problem was a puzzle in a popular magazine, which was answered quite correctly as such by vos Savant. The whole media furore was about vos Savant's solution and why the answer was 2/3 not 1/2. Some months later a bunch of academics, Morgan et al, decided to extend the problem to a particular case where the producer hid the car uniformly but the host did not choose a goat-hiding door uniformly. This is a different, more complex, problem that requires conditional probability to solve. Since then many academics have added different assumptions and used different methods to solve various extensions and modifications of the problem. None of these are relevant to the original puzzle. Martin Hogbin (talk) 15:55, 15 August 2011 (UTC)

I apologize for the hyperbole, and confess that it was intentional. It was an exaggeration to say your discussion regarding what is of primary and secondary importance in the article was disparaging of the latter, and I am not aware that you have ever proposed including disparaging language in the article. ~ Ningauble (talk) 18:40, 16 August 2011 (UTC)

1) Conditional probability is not needed to solve the biased host problem. Since you can't beat 2/3 probability of winning by switching, the conditional probability must also favour switching. No need to calculate it.

2) Some academics have solved the original problem by using symmetry (of the problem description) explicitly in advance to discard the "information" given by the numbers on the doors, e.g. Georgii in a standard textbook, also Richard-Gill-the-real-person in an online peer-reviewed statistics encyclopedia. Richard Gill (talk) 13:41, 16 August 2011 (UTC)

• Agree 1-3.. Agree w/reservations 4-5. Disagree 6. I'm disappointed that Martin asks a clear question, someone makes a clear reponse, and then the section explodes with text. IIRC, VoS said her description could be better, but the complainants were not misled by the description; they just got it wrong. Another source said that VoS conveyed the quantification in her description ("say, <number>"), that quantification was understood by the contestant, but then the thought processes of the contestant got hung up by the specific door numbers. Too much information. By modifying the description, the hang ups can be reduced. I agree that indistinguishable doors simplify the problem. I'm not sure that means they can be completely jettisoned. Door numbers are needed to explain confusion in VoS. Parts of so-called academic extension are needed to explain MHP. Glrx (talk) 16:30, 15 August 2011 (UTC)

Responding to Girx: In my opinion MHP is a mathematical joke. A brainteaser. VoS's specific formulation is brilliant because it reinforces the deception, by focussing the person who is being teased (the reader) on what he sees in front of him at a late stage of the proceedings. (a) it brings in irrelevant information, (b) it destroys the memory of the process which led to that situation. Now if you want ordinary folk to get the joke, you have to let them make the shift of perspective which makes the natural wrong answer stupid, and the right answer obvious. That's what most of the wikipedia page should be about since that is what most readers are after, that's why the problem is so famous (because it is such a good joke), etc.

The Morgan et al. conditional approach is about how to get the right answer by plodding calculations without changing the initial point of view. It destroys the joke, and converts it into an exercise in Bayes probability calculations. Very valuable in the right context but not at the heart of a famous brain-teaser about a popular game-show!

I would prefer, but I fear we'll have to wait for ten more years of both popular and academic publications, not to present the brainteaser joke and the conditional probability calculation as opposed approaches. I would rather work as follows.

1. On the assumption only that your initial door has probability 1/3 of hiding the car, switching gives the car with probability 2/3.
2. Observing that *however* you choose a door and subsequently decide to stay or switch, there is always a door such that you'll never get a car hidden there, we see that if all doors are equally likely to hide the car initially, you cannot do better than get the car with probability 2/3.
3. For Bayes theorem fans, it follows (from the law of total probability) that if all doors are initially equally likely to hide the car, then the conditional probability that the car is behind door 2 given you chose 1 and the host opened door 3 is at least 1/2, i.e. favours switching, as do all the other five conditional probabilities you might like to think of.

I think the article could be about 10 times shorter than the present one if it were inspired by this line of argument. Richard Gill (talk) 13:14, 16 August 2011 (UTC)

I too would much prefer not to present these as being in opposition, but I fear you are being overly optimistic about resolving it in ten years. It may never happen because it is inherent in the Wikipedia process that once a controversy arises, as happened when Morgan et al. uncollegially accused vos Savant of ignorance, the application of NPOV almost inevitably results in including "balancing" points of view and giving UNDUE weight to the controversy itself, describing everything remotely connected to it in terms of opposites, never in terms of complementary or tangential information. I hope I am wrong. ~ Ningauble (talk) 18:40, 16 August 2011 (UTC)

Wikipedia is like Democracy. It is fundamentally flawed. But unfortunately there is nothing better. Richard Gill (talk) 11:48, 18 August 2011 (UTC)

• Agree 1-6 w/reservations. Reservations: because there is not need of any opposition between popular and academic if we move a bit with the times. Or do we want to stay quarreling here for ten years till the academic and popular literature has again exponentially grown, and the pre-2010 literature on MHP is an insignificant, historical amusement (or embarrassment)? MHP is a joke. VoS asks for a decision. All experts will tell you that phrasing a real world question as "I want to know the probability that..." is a recipe for disaster. Ordinary folk just don't have available in their minds the needed concepts, let alone the calculus or the theorems, to understand what they are asking, and anyway, a whole load more outside information would be needed before some operationalism of the question could be answered. My 1) to 3) above seems to me to be a summary of the all mathematical truth about MHP which needs to be in the article. Richard Gill (talk) 13:30, 16 August 2011 (UTC)
• Agree. 71.166.38.174 (talk) 20:21, 20 August 2011 (UTC) — 71.166.38.174 (talk • contribs) has made few or no other edits outside this topic.

So let us solve the MHP problem problem

The MHP is a famous paradox, based on human psychology. Unquestioned the Monty Hall Paradox, in incredible ways, is surprising the average citizen, strikingly contradicting our vehement "clear judgment and discernment", and contradicting our perception.  Seeing two closed doors, and knowing for sure that one of them hides the desired prize, while the other one must be hiding the second goat, our knee-jerk answer – without any pause for reflection – is  "it makes no difference whether to stay or to switch".  To comprehend that the chances are not 1:1 but 1:2 is easy to grasp when the basics are didactic elucidated and expounded. To give the only correct answer: "switch" here and now, in that actual game. That's the whole secret.

Necessarily (or unnecessarily) far-fetched and boldly supposing that there "could" be some (or even maximal) additional information on the actual location of the prize, anyone can easily grasp also that the chances of staying vs. switching will be 1/3:2/3 on average, but at least 1/2:1/2 for sure, and never less, in two out of three, but will be full 0:1 in one out of three (!), that means always to be around 1/3:2/3, and honestly no-one can in fairness say that he "knows" better. Because there definitely is no additional information, you just can imagine to have "supposed" additional information on the actual location of the car. A very weak and purely hypothetical moot point, to be taken with a pinch of salt, but blaming any ignoring of that ludicrous point for the decision to be made. On the other hand just reinforcing the decision to

"switch here and now".

However very suitable for teaching probability theory maths, as umpteen times proven in reality, but forever being without the least effect on the decision to be made. Never able to be helpful or insightful, but very interesting as a mathematical problem in conditional probability theory.

So the article could be short and clear, closing with a revealing section on the colorful history in literature, including pedestrian disputes and numerous textbooks just for teaching purpose.

Let's start.  Gerhardvalentin (talk) 21:58, 16 August 2011 (UTC)

Gerhardvalentin, OK, let us solve. Discard probs for a while. Connie can guest correctly 2 out of 3 cases A,B,C. Why can't she do better? Suppose Monte has a known to Connie signal system: shows either ticket L in his left hand or ticket R in the right hand. Connie gets one bit of information, but needs to distinguish among 3 cases A,B,C, hence there is no way to always communicate the location of prize by sending one bit. This may be seen as an instance of pigeonhole/Dirichlet principle: having 3 coins in 2 pockets, in one of the pockets there are at least 2 coins.

Put another way, consider transmitting letter from the alphabet {A,B,C} through a noisy channel whose output is L or R. Which way of transmission has minimal distortion? For example A->L,B->L, C->R. When Connie picks, say A, there is Left door (door B) and Right door (door C). A switch offered to B means encoding B->L (Monte shows L ticket), and similarly for C->R (Monte shows R ticket). Indeed, when Connie picks A, and the prize is behind B, then switch is offered to B, which is equivalent to encoding B->L. Similarly for C->R. We see that no strategy wins all three cases. Hence strategy S="pick D1 always-switch" is optimal combinatorially. Assigning equal probabilities to A,B,C, we see that S is average-case optimal as well.RocksAndStones (talk) 14:18, 18 August 2011 (UTC)

Exactly:  to suppose that some message could be given from host to Connie in a "restricted" or say "legal" form, then he is unable to communicate, even in the most extreme case, much more than either "switch and win" or "stay or switch, it will be the same". – He impossibly can give any closer info. Knowing that, and knowing that staying never can be any better than to switch, because switching will never hurt, shows that Connie will be wise to switch in any case, completely regardless of all those signals. The host is never able to signal other recommendation, and so Connie knows already before that hypothetical imaginary game show that she will switch in any case, and – after the host has given all his available signals – she knows just as well, maybe even better than before, that to switch is and forever will be the only correct decision. Btw, did you see Richards remark below on Gnedin's solution, trashing "probability"?  Regards, Gerhardvalentin (talk) 15:16, 18 August 2011 (UTC)

Gerhardvalentin, if the host could in some way signal, "don't switch", then the contestant has received useful information that takes her beyond the 2/3 winning %. But this has nothing to do with the MHP of Selvin, vos Savant, Whitaker, Morgan, or any other reliable source. 76.190.236.207 (talk) 16:45, 18 August 2011 (UTC)

Answer: You are correct. Under the given rules of the standard MHP (no illegal "sayings")  the host can only signal a "minimum level" to win by switching of  "1/2",  but never ever less, what means equivalent full  "1"  likewise, and purportless any possible grade between  "1/2 to 1"  as per fictive assumptions. He forever is out of position to signal "don't switch".

Chances of   "door selected : door offered to switch to : door opened"   originally were "1/3 : 1/3 : 1/3".  And after a door has been opened showing a goat, all we forever will "really know" is that they are  "1/3 : 2/3 : 0"  now. We never can nor will have better "knowledge".  But we are free to "assume" just what we like (though observing some "rules"), as I said on the "Arguments" page:

The host could be "assumed" to be (extremely) biased to open only the door with the brightest color e.g., whenever he can, i.e. if a goat is behind his preferred bright door. He can open his preferred door in two out of three cases:

• if in 1/3 he has got two goats to show and switching will LOOSE the car     ("1 : 0 : 0")  and
• if in 1/3 he has got the car and one goat, and the goat being behind his preferred bright door, and switching will WIN the car     ("0 : 1 : 0").

So, whenever he opens his preferred door in 2 out of 3 cases, you know that the chance to win by switching is 1/2 (and never ever less):  "1/2 : 1/2 : 0".

• but if, in the last 1/3, he has got one goat and the car, but the car being behind his preferred bright door, he has to open his avoided door of darker color e.g., and in this 1 out of 3 -case switching is very likely to win for sure:  "0 : 1 : 0".

So we definitely know, just from the start, that in any case the posterior chances definitely must be within the fixed range of  "1/2 : 1/2 : 0"  to  "0 : 1 : 0",  and all we really "can know" is that they are  "1/3 : 2/3 : 0"  now.  And it's finally clear: the more biased the host, the better. And the only correct answer, the only correct solution must be to "switch here and now", whereas to stay forever is out of the question. Without travail of effectless conditional probability theory-training.

But advisable to show all of that effectlessness in the History-section of the article.  Gerhardvalentin (talk) 17:52, 18 August 2011 (UTC)

Well, my command of German is not perfect. Ziege must be goat, and gehfaul perhaps lazy to walk, so reading will take some time. I wish to add to the above that with four doors the situation is as you just described, provided two useless doors are revealed at once. Then the signal is the door-to-switch. However, if two doors are revealed in sequence, it is easy to design signaling scheme which communicates the location of prize with certainty. I wonder how this informational aspect of the problem could be quantified under biased allocation of the prize.RocksAndStones (talk) 15:41, 18 August 2011 (UTC)

RocksAndStones, try to read it there. Gerhardvalentin (talk) 21:46, 18 August 2011 (UTC)

Thanks for the translation. The article makes a clear point, which one can put in a slightly different way. Every strategy is evaluated by a win-loss vector whose components are labeled by the pure counter-strategies. The set of Pareto-optimal strategies consists of three always-switching strategies. All other strategies are irrelevant.RocksAndStones (talk) 00:19, 21 August 2011 (UTC)

Yes, that's the point. Any kinds of irrelevant pretended "solutions", never being solutions but just unnecessary theorems using "conditional" probability theory, pretending to be indispensable for making the only correct decision "in a given game" – with "fixed door numbers as the base footing for decision making", based on doubtful and highly questionable fictive assumptions that never ever may be given nor will ever be able to influence the correct decision, not in the slightest, should clearly be shown in the article as what they forever have been and as what they really are: Just only welcome examples to teach and to learn conditional probability theory, without any relevance to the famous paradox, and completely irrelevant for the decision asked for. So 15 - 20 more years to go? Gerhardvalentin (talk) 10:18, 21 August 2011 (UTC)

Ignorant Monty

What is the difference between the “Ignorant Monty” and the standard problem? It sounds like the same, Monty is choosing a random goat. --Chricho ∀ (talk) 12:19, 21 August 2011 (UTC)

"Ignorant Monty" in 1 out of 3 will show the car (i.e. out of 3 eliminating a full 1/3-chance to "win"), and only in the subset of 2 out of 3 will show a goat, what means that the probability to win by switching is reduced from 2/3 to 1/2. Chances no more "1/3 : 2:3 : 0", but within the subset of the actual case now "1/2 : 1/2 : 0". Gerhardvalentin (talk) 12:38, 21 August 2011 (UTC)

And if he shows the car the guest can only lose? --Chricho ∀ (talk) 20:26, 21 August 2011 (UTC)

Yes, correctly, the guest has lost. In the hypothetic "Ignorant Monty"  the host, in presenting the car behind an unchosen door, has shown that the guest's choice was wrong, and game over. Regards, Gerhardvalentin (talk) 21:24, 21 August 2011 (UTC)

Unless of course, he finds one goat to be especially attractive... :) -Guy Macon (talk) 00:12, 22 August 2011 (UTC)

Actually, the usual "ignorant Monty" variant considers only the case in which the host fortuitously happens to reveal a goat (leaving it completely unspecified what would happen if Monty were to reveal the car, because the car was not revealed), and asks the question "in this case (in which Monty HAS revealed a goat) what is the chance of winning by switching". This question is easier to visualize in the context of a specific example, i.e. assume the player has picked door 1 and Monty has (without knowing what's behind it) opened door 3 revealing a goat. This creates the same apparent condition as the usual problem (player initially picked door 1, host opened door 3 showing a goat, and the player is now standing in front of a closed door 1 and closed door 2 looking at a goat behind the now open door 3)- but the probabilities are different. In the ignorant Monty case the probabilities the car is behind each door are 1/2:1/2:0, while in the usual problem the probabilities are 1/3:2/3:0. IMO, it is very difficult to discuss the difference between these two problems without talking about conditional probability. In particular, if you assume the player loses if the host reveals the car and "simplify" this variant in the same way the usual problem is often simplified by talking about the overall chances of winning by switching or staying (as opposed to the conditional probabilities in a specific case where you're now looking at an open door showing a goat), you find the somewhat disturbing result that you win 1/3 of the time and lose 2/3 of the time whether you switch or not. -- Rick Block (talk) 04:50, 22 August 2011 (UTC)

Breaking News

Gnedin's "dominance" approach is featured in today's "Die Zeit", Science section. Those who can read German will enjoy it. Here are screen-shots from my ZEIT ONLINE iPad app: [6]. And here an English translation. [7]. Richard Gill (talk) 14:04, 18 August 2011 (UTC)

With the entry http://de.wikipedia.org/wiki/Ziegenproblem#Strategische_L.C3.B6sung_mit_Dominanz the German Wiki goes ahead.LoveMe2XBaby (talk) 18:20, 23 August 2011 (UTC)

Rough Draft of RfC: Please Comment

I have a rough draft of the RfC here: Talk:Monty Hall problem/RfC

Please help me to improve it before I submit it.

Comments placed in the RfC may be edited. Comments placed here will not. --Guy Macon (talk) 11:04, 20 August 2011 (UTC)

There are no links to the two versions. Which are they and where can I find them? Martin Hogbin (talk) 11:08, 20 August 2011 (UTC)

In the first sentence, which reads...

Which approach to the Monty Hall problem should we choose; VERSION ONE or VERSION TWO?

...does clicking on "VERSION ONE" and "VERSION TWO" lead you to the two versions? Guy Macon (talk) 12:15, 20 August 2011 (UTC)

I am sorry Guy, but I do not think the RfC is posing the right question. To choose "which approach", the RfC needs to present some clear statements of the of the approaches these drafts purport to represent. Presenting this as a choice between drafts of article content (even if one of the drafts had not already been repudiated by its drafter!) is not going to settle the question because article content is going to continue changing and there will be future disagreement as to what aspects or characteristics of the drafts have been decided upon.

Maybe it's just me, but I am also uncomfortable with the either/or framework in the present formulation of the RfC.[8] It feels like a loaded question because I am not "neutral" about these two drafts and I do not "support" either draft. (This is only partly due to the problems inherent in trying to define approaches by example.)

In the words of Neutral point of view/FAQ, part of what is needed is to "step back and ask ourselves, 'How can this dispute be fairly characterized?' This has to be asked repeatedly as each new controversial point is stated." This can be very difficult for disputants to do for themselves. It ain't easy to mediate the question of what the question is, but I think it needs more clarity before the question is put to the larger community. ~ Ningauble (talk) 13:47, 20 August 2011 (UTC)

No need to be sorry. Asking whether this is the right question is exactly the right thing to ask, and I have no problem with asking a better question - and that's why it is still a rough draft. In fact, I have repeatedly asked for a brief description of the dispute suitable for formulating the question. Alas, none has been forthcoming so far. Perhaps someone will come up with a better question now that there is a rough draft RfC to examine.

What I am not willing to do is to put up an RfC without offering the reader a clear-cut choice. I have no problem if we end up listing five alternatives, but we already have a bunch of "that's not the real issue, this is the real issue" comments that only the person making the comment completely supports. There are thousands of words on this very talk page exploring every aspect of this issue, all without resolving the underlying content dispute. If you or someone else can formulate a better question that most people here like, great. If not, I will move forward with the best I have so far. Guy Macon (talk) 19:33, 20 August 2011 (UTC)

I agree with Ningauble that neither the substance of the dispute or the proposed resolution is clear from anything in the current draft RFC. I have tried several times in the past to describe the dispute in neutral terms, e.g. [9] [10]. Martin will (of course) argue that these are highly biased descriptions, although I'll note that his own description, [11], completely mischaracterizes one of the positions. If we view the dispute as between polar opposites, where on the one side the article endorses the view that the simple solutions are all that's necessary and on the other side the article endorses the view that conditional solutions are the only correct approach, IMO Martin is arguing one side of this but no one is arguing the other side. In particular, I'm arguing for a balanced NPOV approach which endorses neither of these views but instead presents both approaches as equally valid. -- Rick Block (talk) 19:37, 20 August 2011 (UTC)

I also agree that neither the substance of the dispute or the proposed resolution is clear from anything in the current draft RFC - and I wrote it! I am completely open to suggestions, but I am not willing to spend another year or two stalled because nobody can state the issue in a way that the other side finds acceptable. To all: Give me a better description of the issue or accept the fact that I had to go forward with the best description of the issue I could come up with without help. Guy Macon (talk) 19:53, 20 August 2011 (UTC)

Alternatively, one might consider the reason for the never ending dispute arises from a breach in policies. Rather than issue a flawed RfC for no real benefit, perhaps it should be considered whether one of the editors continues to exert ownership of the article, or whether, maybe, another editor has claimed ownership by bogging down these discussions 184.81.169.186 (talk) 20:25, 20 August 2011 (UTC). — 184.81.169.186 (talk • contribs) has made few or no other edits outside this topic.

I agree with Ninguable that this is not the way to approach an RfC. Presenting two different versions will only cause newcomers to argue about irrelevant details. You asked for a description of the dispute and got two, one from Rick and one from me. We might both argue that the other one's version presents a biased view, but that is why we have to versions of the question. We should simply present them both to the RfC. Martin Hogbin (talk) 22:46, 20 August 2011 (UTC)

I have no problem with that. I can simply note on each description that other editorss disagree about whether it is a valid description of the conflict. Does anyone have any objections? Do you wish me to use the exact words you posted before or would you like to rephrase before the RfC is submitted? You might want to consider whether calling your position "simple" and "correct" while describing the other position as "wanting to treat the MHP principally as an undergraduate exercise in conditional probability" might possibly strike some folks as being biased. Your choice, of course, but I want each side to put forth the best arguments they can. Guy Macon (talk) 00:35, 21 August 2011 (UTC)

Just a thought, but how about I have a go at rewording Rick's statement and he has a go at rewording mine? Martin Hogbin (talk) 08:43, 21 August 2011 (UTC)

I'm fine with trying that. -- Rick Block (talk) 15:43, 21 August 2011 (UTC)

Looking at "Martin's modified version of Rick's question" (the only part done at the time I am writing this) it has IMO the advantage of focusing on what the dispute is rather than why one side or the other is preferred. That's important information, but IMO things like what policies apply to one side or the other are best put in the arguments section, simply because someone else is sure to disagree about whether those policies apply. On the other hand, "which will be of greater interest to experts" is, IMO straying from simply describing the dispute and instead gives a reason why one side or the other is preferred. Again, important information, but IMO best put in the arguments section. What interests experts or non-experts is not part of the description of the issue, but rather is a reason for favoring one side over the other. Putting it in an argument section would actually make it a stronger argument.

Rick's original question

The dispute is whether the article should primarily satisfy

1) Wikipedia:Make technical articles understandable, with an initial, extended section focusing exclusively on "simple solutions" that makes no mention of any other solution approaches, in particular the approach using conditional probability. All other approaches will be relegated to later sections of the article intended for experts only. This structural outline (but not the content aspects) are shown in this version of the article.

or

2) Wikipedia:Neutral point of view, with initial sections of the article addressing the most common interpretation of the problem using various approaches specifically including both simple and conditional solutions. The version of the article following the May 2008 FAR (this version) was more or less along these lines, although the "Solution" section in this version of the article arguably expresses a bias in favor of the conditional approach.

Martin's modified version of Rick's question

The dispute is whether the article should primarily:

1) Have an initial section focusing exclusively on "simple solutions" that makes no mention of any other solution or approach (including reference to conditional probability). Other approaches, which will be of greater interest to experts, will be placed in later sections of the article.

or

2) Have the initial sections of the article addressing the most common interpretation of the problem using various approaches including both simple and conditional solutions.

Rick's response

Rick, comment here if you think I have seriously misrepresented you. Martin Hogbin (talk) 15:54, 21 August 2011 (UTC)

Since my stance is that this boils down to a POV issue, omitting any mention of WP:NPOV seems like a serious oversight. I want the discussion about this dispute focused on how to represent what the plethora of sources say without bias and with appropriate WP:WEIGHT and WP:STRUCTURE, not on what individuals think about the content. This should not be a popularity contest between "simple" solutions and conditional solutions. Frankly, I'd like to preface any statement of the dispute with a summary of sources (e.g. "many, many sources present simple solutions to the usual problem", "many, many sources (including essentially all introductory probability textbooks) present conditional solutions to the usual problem", "some sources express an explicit preference for conditional solutions, often using variations to show exactly how the simple solutions are deficient", "many variations of the usual problem are presented with solutions using conditional probability or game theory"). IMO this dispute should be focused on what the sources say, and nothing else. -- Rick Block (talk) 05:20, 22 August 2011 (UTC)

I have removed WP:NPOV because I and many others do not think that my proposed structure does promote a specific POV. I have always made clear that all solutions and approaches will be properly presented. We are both supposed to be writing a neutral statement of the dispute, not making a case for our opinion. Martin Hogbin (talk) 08:14, 22 August 2011 (UTC)

Without opining on whether it should have been placed or whether it should be removed, please review this list from http://en.wikipedia.org/wiki/Template:POV

When to remove:

This template is not meant to be a permanent resident on any article.

Remove this template whenever:

No discussion about neutrality issues was started on this article's talk page.

Discussion about neutrality issues is dormant.

There is consensus in the discussion that the problems have been resolved.

Removing this tag may be tendentious—just like placing it on the article may be tendentious—but it is not an act of vandalism. --Guy Macon (talk) 18:12, 1 September 2011 (UTC)

Martin didn't remove the tag on the article, he removed it from the description of the dispute. -- Rick Block (talk) 18:48, 1 September 2011 (UTC)

Making the two versions the same where there is no content dispute

Referring to...

Talk:Monty Hall problem/draft1

Talk:Monty Hall problem/draft2

and

Talk:Monty Hall problem/RfC

...I would like to make the two draft versions so that they only differ where there is an actual content dispute. Is reversing the order of "Simulation" and "Increasing the number of doors" really an integral part of the content dispute, or can we reverse the order in one or the other drafts?

In Draft2, the draft ends with "Discussion of all other variants, formulations, approaches and solutions" Could we cut and paste from draft1 to fill out this section and make them as close to each other as possible?

In those areas where draft1 and draft 2 are identical, could we add a note saying so to the section? Perhaps collapsing or using a different font to show what is different would work. I am looking for a way that the reader can instantly see the differences without doing a side-by-side comparison. Guy Macon (talk) 12:37, 20 August 2011 (UTC)

Would it be better to highlight where each differs from the present article? Each proposes to change the article in a different way, and I think the most salient difference for understanding these proposals is the difference vs. status quo. ~ Ningauble (talk) 13:57, 20 August 2011 (UTC)

There are pluses and minuses to that approach. One issue is that the statu quo reflects a long history of editors who hold positions in the content dispute temporarily stepping aside while editors holding the other position attempted to reach a compromise. The general feeling is that the attempts at compromise resulted in lower quality without achieving the goal of being acceptable to everybody - certainly the article has degraded since being a featured article.

On the other hand, you make an excellent point about salience, so perhaps we should highlight where each differs from the present article. It might be worthwhile to cut and paste sections of the current article into the drafts wherever doing so does not change the drafts being good examples showing the content dispute. Certainly making all three as close to identical as possible while still showing the content dispute is a Good Thing. Guy Macon (talk) 19:19, 20 August 2011 (UTC)

off topic comments about ownership, transparently by banned editor Glkanter

No one sees a continuing Page Ownership violation? Same minority editor viewpoint. Same specious arguments about what the reliable sources say. Same mis-interpretations of Wikipedia policies. Same editor found to be engaged in a MHP Page Ownership violation by arbcom. I agree with this old observation. Same techniques used to indefinately forestall needed improvements to the article. Well, I can see it. 71.166.38.174 (talk) 21:47, 20 August 2011 (UTC) — 71.166.38.174 (talk • contribs) has made few or no other edits outside this topic. Wrong Place. Wikipedia has a Dispute resolution noticeboard where you can report suspected Page Ownership violations. Wikipedia:Talk page guidelines says that "The purpose of a Wikipedia talk page (accessible via the talk or discussion tab) is to provide space for editors to discuss changes to its associated article or project page." and "If you have a disagreement or a problem with someone's behavior, please read Wikipedia:Dispute resolution." Continuing to complain about other editors on article talk pages will simply result in you being ignored. Complaining about other editors on the relevant noticeboard will result in your complaint getting the attention it deserves. Guy Macon (talk) 17:35, 21 August 2011 (UTC) Given their finding of Page Ownership earlier this year, perhaps arbcom is the appropriate venue to discuss the editor's continuing behavior? 76.190.236.207 (talk) 05:58, 22 August 2011 (UTC) If you want to do that, the proper place is Wikipedia:Arbitration/Requests/Enforcement. I cannot comment on which venue is more appropriate because to do that I would have to consider the details of the alleged page ownership, and I see no evidence of it. Nonetheless, if you think there is a page ownership issue, please don't let my opinion stop you from reporting it. You might want to read WP:BOOMERANG first. Guy Macon (talk) 09:08, 23 August 2011 (UTC)

As Guy says, the current article was explicitly edited by Martin (and others supporting his view about what the article should contain) as part of a preliminary attempt to create what is now intended to be embodied by /draft2, so I think differences relative to the current article are not really very informative since the starting point was not a "consensus" version. Perhaps these could be diffed relative to the version as of the last successful FAR (this version). There were some comments about /draft1 from Ningauble a while ago [12] that I have not responded to, essentially reflecting the fact that this draft is incomplete. I would be willing to work on it some more and invite anyone else who may be interested to do the same, although if Martin remains unwilling to edit /draft2 to show us what he wants the article to look like the comparisons will be fairly meaningless. -- Rick Block (talk) 15:48, 23 August 2011 (UTC)

Martin's original question

Should this article treat the MHP principally as an undergraduate exercise in conditional probability or should it treat it as a simple, well-known, probability puzzle that most people get wrong but which was correctly and simply solved by vos Savant and many other sources and also include a full discussion of all other aspects of the problem for the more specialist reader?

Rick's version of Martin's question

Should this article

a) include in the introductory sections sufficient clarification of the problem statement to ensure all solutions have the same answer (i.e. that a player who switches wins with probability 2/3) and an accessible solution based on conditional probability specifically showing a player who picks door 1 and sees the host open door 3 has a 2/3 chance of winning by switching to door 2, or

b) start with more or less a complete "introductory" article (based solely on popular sources such as vos Savant plus any academic sources that happen to use exclusively "simple" approaches) treating the MHP as a simple probability puzzle focused on the strategies of "always switching" as opposed to "always staying" without necessarily clarifying the exact question that is asked and without explicitly addressing the specific "player picks door 1 and host opens door 3" case, and only after these introductory sections then proceed with a discussion of all other aspects of the problem for the more specialist reader.

Martin's response

Martin, comment here if you think I have seriously misrepresented you. -- Rick Block (talk) 04:58, 22 August 2011 (UTC)

Rick, you are meant to be writing something based on my wording. You can remove or change things that you think are misleading or unfair but you need to write something that looks at least vaguely like my words, as I have done with your statement. Martin Hogbin (talk) 08:17, 22 August 2011 (UTC)

I honestly struggled with this. Your description of one side of the dispute is so far off the mark that there really wasn't anything to do but rewrite it. I've simply expanded the description of the other side to be more explicit about what you're actually talking about. Here's a marked up diff (original in bold, additions in italics):

should it treat itstart with more or less a complete "introductory" article (based solely on popular sources such as vos Savant plus any academic sources that happen to use exclusively "simple" approaches) treating the MHP as a simple, well-known, probability puzzle that most people get wrong but which was correctly and simply solved by vos Savant and many other sources focused on the strategies of "always switching" as opposed to "always staying" without necessarily clarifying the exact question that is asked and without explicitly addressing the specific "player picks door 1 and host opens door 3" case, and also include a full only after these introductory sections then proceed with a discussion of all other aspects of the problem for the more specialist reader?

I sincerely believe this accurately captures your stance, and it's definitely based on your words (and edits to the article). You do want the article to start with a more or less complete introductory article based on vos Savant (and other "simple solution" sources) treating the MHP as a simple probability puzzle focused on the strategies of always switching as opposed to always staying without clarifying the exact question and without explicitly addressing the specific case of "player picks door 1 and host opens door 3", don't you? Your description of your stance is so vague that nearly anyone would agree with it (for example, I agree with it if we consider an approachable [not based on Bayes theorem] analysis of the specific door 1/door 3 case as "simply solved" and include nearly all introductory probability textbooks in the scope of "vos Savant and many other sources"). Please correct me if I'm wrong, but hasn't your stance always been fundamentally based not on what you want IN the article but on what you want OUT of the early sections of the article (i.e. anything other than "simple" solutions based on analyzing "always switching" as opposed to "always staying", and most specifically anything whatsoever that even hints that the question is about the difference between the prior and posterior probabilities of the car being behind door 1 and door 2 before and after the host opens door 3)? -- Rick Block (talk) 15:51, 22 August 2011 (UTC)

The deal was that you rewrite my wording and I rewrite yours. If you are not willing to give that a try there is no point in proceeding. I though it was worth a try. I guess we will have to stick with the original statements then. Martin Hogbin (talk) 21:46, 22 August 2011 (UTC)

Does that mean you disagree with something I'm saying here? If so, what? -- Rick Block (talk) 00:17, 23 August 2011 (UTC)

Re: "I guess we will have to stick with the original statements then", actually, as the person requesting comments, I need to choose what I think is the best way to request comments (of course anyone else is free to write Their own RfC with whatever question they like). I am not going to present two wildly different descriptions of the content dispute just because you two cannot agree upon what you disagree upon. That does not allow outside opinions to choose between two clearly described positions. Instead, I will go with the basic logical principle of "whatever the heck Person X says the dispute is about, he has to write the page if consensus favors his position"` and present the two drafts (possibly after editing out trivial differences myself if I can't get cooperation in making them differ only where this an actual content dispute). I can understand that the two of you may disagree about what the dispute is, but I do not believe that either of you are incapable of editing the article to reflect your position should you prevail. Guy Macon (talk) 09:25, 23 August 2011 (UTC)

That is somewhat at odds with WP principles, which favour cooperative editing. I do not want to, or claim to be able to write the article by myself. My point is one of principle, that the article should principally represent the subject as a simple mathematical puzzle, solved simple and correctly by vos Savant and others. It should also deal with the subsequent media furore and the psychological reasons that people get the answer wrong. The 'conditional solutions' represent the narrow viewpoint of undergraduate probability and should have no special standing in the article but should, of course, be mentioned along with the many other methods of solution. Martin Hogbin (talk) 14:52, 1 September 2011 (UTC)

Do you believe this approach represents (per WP:NPOV) "fairly, proportionately, and as far as possible without bias, all significant views that have been published by reliable sources", or does this approach explicitly endorse those views with which you personally agree? -- Rick Block (talk) 15:31, 1 September 2011 (UTC)

Beware of false conclusions. "Significant views" vs. "insignificant views".

No circumvention, please. All you really "know" is that by staying you have a "1 in 3 chance", whereas by switching you have a "2 in 3 chance" to win the car. The illusion that you eventually "could" know better if you just knew better, the illusion that any (in real words) unavailable but just assumed additional information on the actual location of the car ever could recommend to stay and not to switch is not significant for the MHP, but is outmost insignificant for the MHP. So no outwitting, please. Such mental games are an illusion and belong to the realm of teaching and learning to do correct calculi in conditional probability theory, that's where they belong, but never to making the correct decision and to give the correct answer to the famous question. In the aricle it may be mentioned en passant, although it never is nor ever was "necessary" to make the correct decision. Gerhardvalentin (talk) 16:55, 1 September 2011 (UTC)

What measure do we use to, "fairly, proportionately, and as far as possible without bias, all significant views that have been published by reliable sources"? On the number of sources alone, simple solutions probably outnumber 'conditional' solutions by 10 to 1 or more. On the other hand if we consider only undergraduate level textbooks on probability then the 'conditional' solutions probably win. Should we take into account the source of the puzzle and its intended audience in our calculation? I think so. It was clearly intended to be a simple popular puzzle not an exercise in probability for students. What about game theory and other types of solution. Why should they get less exposure in the article than the 'conditional' solution? Martin Hogbin (talk) 17:48, 1 September 2011 (UTC)

What measure? Well, first, we need to agree that this is what we're trying to do. Then, we need to make some effort to honestly and objectively assess sources, paying particular attention to reliable secondary sources. Your 10-1 number is absurd - in my reading it's perhaps 2-1 but the 2 is dominated by popular sources which would be considered much less reliable than the predominantly academic sources constituting the 1. By any measure, both simple and conditional solutions are extremely common (many dozens of sources), and are thus both "significant".

The original source of the puzzle was Selvin's letter to the American Statistician (not vos Savant's column in Parade), so I suspect you don't actually want to consider the source of the puzzle but rather the source of the popularization of the puzzle. Since the puzzle itself originated in academia, and there are not an insignificant number of sources explicitly critical of its treatment in popular sources, it seems highly biased for the article to (in your words) "principally represent the subject as a simple mathematical puzzle, solved simple and correctly by vos Savant and others".

Sources presenting game theory and other types of solutions are MUCH less common than either simple or conditional solutions, and should be presented in a way reflecting their prominence. Clearly where we disagree is about the relative prominence of sources presenting conditional solutions and sources presenting simple solutions. I think these two are essentially equal. You do not, but it seems to me your view about this primarily reflects your own opinion about the topic itself rather than your familiarity with the sources. -- Rick Block (talk) 19:39, 1 September 2011 (UTC)

Moving Forward to RfC despite lack of agreement on what the Issue is

Clearly this content dispute is completely intractable. Having failed to get a brief description of the conflict that all can agree upon, I am going with the two draft versions.

References:

Talk:Monty Hall problem/draft1

Talk:Monty Hall problem/draft2

and

Talk:Monty Hall problem/RfC

I am rejecting any further claims that the plan of basing the RfC on the two versions is not what we should do, based upon two self-evident facts: First, no alternative has been proposed that all agree upon. Second, if an editor cannot translate his position into a version of the article now, he obviously will be unable to do so should the consensus favor him.

In have taken the liberty of making draft1 and draft2 closer in content, hopefully without erasing the differences that highlight the content dispute. Please review the changes and correct any places where I got it wrong, keeping in mind the goal that the two versions should differ only where they have to to show the dispute. Thanks! --Guy Macon (talk) 05:28, 2 September 2011 (UTC)

I appreciate your efforts to help, Guy. I suggest you proceed with and RfC any way you like. Rick and I will be able to comment in the RFC itself to make our positions clear. Martin Hogbin (talk) 09:46, 2 September 2011 (UTC)

I understand what Guy is trying to do here, but I must reject the rejection of rejecting a choice between these two alternatives. This is not simply a choice between X and not X, it proposes to force a choice between apples and oranges for replacing a banana. Yes, the banana is overripe, but I believe the choices being offered both involve too many disparate changes and are both too extreme in some respects.

To give just one example of a change that ought to be addressed as a separate question, both current draft versions (1&2) eliminate any mention an "equal goat" stipulation from the Problem description section, apart from retaining the interpolation of a single word "[uniformly]" in one of them. (Note that Martin's original draft proposal[13] did not do this.) I reject, as no choice at all, the choice between two ways of making what I consider to be the same mistake because, IMO, this needs to be brought out more clearly than in the current article,[14] not eliminated or obscured.

I made a feeble attempt to frame the main issue in contention as a yes-or-no question,[15] but folks wanted to argue the answers rather than the question of what the question is. That may have been the wrong question, but I still believe we need to find a better question than an either/or Morton's fork that is "flawed by the fact that its tines are not true opposites."(Amalya Lyle Kearse, Burroughs v. Metro-Goldwyn-Mayer, Inc., 683 F.2d 610 (1982)) ~ Ningauble (talk) 18:31, 2 September 2011 (UTC)

A completely reasonable position, and a valid argument supporting it. What I need is one of the following:

[1]: One brief description of what the conflict is that all can agree upon.

...or...

[2]: One draft page per person who disagrees, with the minimum amount of differences between the draft versions needed to show what the conflict is.

Clearly we are getting nowhere on [1], it looks like we never will, but of course someone may have a breakthrough tomorrow.

for [2], I don't need anyone to agree, nor do I care whether anyone chooses to participate. I can move forward with two, three or four draft versions, and I can ignore anyone who disagrees with all of the other draft versions yet has failed to write up an alternative draft version. --Guy Macon (talk) 19:51, 2 September 2011 (UTC)

I am, of course open to suggestions as to some other way to move forward. Discussing this for another year without a resolution is not an acceptable option. --Guy Macon (talk) 19:51, 2 September 2011 (UTC)

Very well then, since my proposed version of the question [1] has been ignored and since I am not going to undertake a singlehanded rewrite of the article [2], I consider myself duly banned from these proceedings. Good luck with that. ~ Ningauble (talk) 01:15, 3 September 2011 (UTC)

Thank you Guymacon for your efforts and thank you Ningauble, I appreciate your view and the view of Glrx. Basically, at present we are where we were years ago. No fresh air for the readers to clearly conceive the diverging aspects and to discern what the "dilemma" of that misty article is all about. Still crusted "secrets" of outworn perception. Let's finally put them into perspective. There are plenty of actual most reliable sources that enable us to make the article "such as what the subject of the article ought to be": No more stale, crusty one-sided Myopia. Let's renew the article as modern actual sources firmly require, not just tamper. Gerhardvalentin (talk) 21:51, 2 September 2011 (UTC)

Motion to close RfC discussions

A content dispute is one thing, but an unconstrained dispute about a murky dispute is madness. Move to close the discussion on multi-drafts and RfC. Glrx (talk) 02:11, 3 September 2011 (UTC)

• Support as proposer. Addressing smaller, specific, topics is a better thing to do. For example, Martin sought agreement on his items 1-6 at #Academic extensions; a result appeared to be a consensus to suppress the significance of door numbers in the article. Take smaller steps. Creating N drafts is pointless. Glrx (talk) 02:11, 3 September 2011 (UTC)

Proposer? While nobody has actually nominated an RfC yet, there is a draft RfC (still being refined) that I wrote, based upon draft versions prepared by Martin and Rick. You have not made a single edit to any of the three. [16] [17] [18] I don't know whether you proposed an RfC sometime in the past or whether you were the first to do so, but I am pretty sure you have not listed one (nothing at Wikipedia:Requests for comment/All), and the one I am preparing to nominate was entirely my idea. --Guy Macon (talk) 07:58, 3 September 2011 (UTC)

• Strong Oppose as nominator. Rfcs are Requests for Comments. Any editor can nominate a RfC without asking for permission, and I fully intend to propose this one no matter what motion you post or what the responses to the motion are.

I am glad that you made the motion, though. It is my contention that discussing smaller steps has not only been totally ineffective at resolving the ongoing content dispute, but has indirectly led to a lowering of article quality as evidenced by MHP being delisted as a Featured Article. I am pretty sure that the responses to this motion will show you that there is a general agreement that this is true, and a consensus to settle the issue rather than continuing to discuss it. --Guy Macon (talk) 07:58, 3 September 2011 (UTC)

Am I to understand that the "tendentious editing" of a currently non-involved [banned] editor is not the cause of this still-intractable stalemate, or of the article's quality degradation described above? How is that possible? Since there was this obvious cause and effect confusion, perhaps the "tendentious editing" (the "cause") never existed? Could it be the Page Ownership finding that is the real cause, instead? 76.190.225.244 (talk) 09:12, 3 September 2011 (UTC)

Something to consider

What is the most important thing about the MHP? I don't want you to respond with what you think it is; I just want you to think about what is most important. There may be a quiz later. Glrx (talk) 02:11, 3 September 2011 (UTC)