User:Sunray/Discussion of Monty Hall RfC

The purpose of this page is to develop an RfC for issues related to the Monty Hall problem. Discussion here will be between Rick Block, Martin Hogbin and me. The agreed upon steps are as follows:

Martin and Rick agree on an RfC statement, or statements.
They then agree on a decision rule
The RfC is then posted and opened to comment from all autoreviewed editors.

My suggested outline for discussion is below. You are welcome to suggest additions or changes. Once that is done, would each of you be willing to begin by preparing a draft of what you would like to see in an opening statement? Sunray (talk) 17:45, 28 April 2012 (UTC)

Looks good to me. I actually have a suggestion for how we might be able to create a single statement - I'll describe this below. -- Rick Block (talk) 18:39, 28 April 2012 (UTC)

Preparing an opening statement

Martin's draft

Introduction and aims

My aim is to get a swift conclusion to the argument, between supporters of the 'simple' solutions and supporters of the 'Morgan' solutions, that has been dogging the MHP article for years.

I do not think we will ever resolve that problem. The secondary/tertiary literature discusses that subject at length but comes to no clear conclusion on the matter. It is therefore hardly surprising that editors here cannot agree.

The answer, from the point of view of WP, however, is simple. Structure the article in a way that is most helpful to readers of all abilities and experience and which allows scholarly discussion of the disputed issues in a way that does not disrupt the article and which is of interest to more advanced readers.

We all agree that the MHP is one of the world's most unintuitive simple puzzles. There are two things that puzzle most people when they first see the problem. These are: that the probability of winning the car by switching is 2/3 and not 1/2, and that it matters that the host knows where the car is (or more accurately that the host reveals a goat with certainty). That these are the two main issues concerning the MHP is beyond dispute.

Because the two primary issues are so difficult for many people to grasp I believe that their solutions should initially be presented in the simplest way possible. Even taking the (disputed) view that the simple solutions are wrong, this approach is the same as that used by most technical authors; start with a simple explanation of the topic covering the essential features, even if this means glossing over some technical details, then go on to discuss deficiencies or extensions to the simple explanation.

It greatly hinders the reader who is still stuck on the basic issues above to have to read 'health warnings' in the first part of the article which say things like 'these solutions are wrong', 'these solutions answer a different question'. Once the reader has understood the basics of the problem, the more advanced issues are easily introduced. In fact they are much easier to understand than the basic basic puzzle itself.

Bearing in mind that the vast majority of WP editors and sources actually think the simple solutions are perfectly sound I can see no possible objection to this proposal.

My proposal

Simply follow the structure shown below

Problem description

Give the standard version of the problem as per vos Savant/Whitaker and K&W

Simple Solutions (with no disclaimers or health warnings)

Vos Savant's solution
Other simple solutions

Aids to understanding (with no disclaimers or health warnings)

Help people understand why the answer is 2/3
Help people understand why it matters that the host knows where the car is

Sources of confusion (with no disclaimers or health warnings)

Discussion over why people find the subject so hard to understand and what it is exactly that leads people to the wrong conclusions.

'Morgans solutions' (Not necessarily with this title)

Morgan's paper
Morgan solutions
Discussion and criticism of Morgan solutions
Problem variants (for example host does not choose uniformly)

The rest of the article

Simplified proposal

The article should be structure as shown below:

Problem description
Simple solutions (with no disclaimers)
Discussion and help concerning the simple solutions
'Conditional' solutions
The rest of the article

Proposed RfC question

Do editors prefer structure 1 or structure 2 (or structure 3 ...) for the article?

Rick's draft (analogous to Martin's draft above)

What we have here is a POV issue, plain and simple.

There is a vast literature about the MHP (thousands of sources), including a huge number of popular sources (nearly universally presenting "simple" solutions) and a smaller but also huge number of academic sources from a variety of fields (presenting solutions to the standard problem and numerous variants, analyzing why the problem is so counterintuitive, etc.).

OK, so what's the fuss?

The preponderance of academic sources in the field of probability, including virtually every introductory probability textbook, solves the MHP by showing the conditional probabilities the car is behind Door 1 and Door 2 are 1/3 and 2/3 (not 1/2 and 1/2) given the host has opened Door 3. Among these there are not an insignificant number that (in one way or another) explicitly criticize the popularly presented "simple" solutions, saying these solutions are "correct but ... shaky"[1], or do not "address the problem posed"[2], or are "incomplete"[3], or are "unconvincing and misleading"[4] or are (most bluntly) "false"[5]. Some clarify that these solutions answer a slightly different question - one phrasing is "you have to announce before a door has been opened whether you plan to switch" [6] (emphasis in the original). As one source says, "the distinction between [these questions] seems to confound many"[7].

Again, OK, so what's the fuss?

The fuss is that some editors apparently dislike the conditional approach, thinking it unnecessarily complicated. These editors want the article to begin with several sections exclusively presenting "simple" solutions as if these solutions are universally agreed to be complete and correct, with any mention of solutions based on (or anything else relating to) conditional probability relegated to a later section presented as if using conditional probability in the analysis of this problem is somehow controversial. This proposed structure obviously does not represent "fairly, proportionately, and as far as possible without bias, all significant views that have been published by reliable sources", as required by Wikipedia's fundamental policy of NPOV.

The counter proposal is to treat this as a POV issue, presenting both "simple" solutions and solutions based on conditional probability in an editorially neutral fashion.

Here is the structure proposed by one editor who dislikes the conditional approach:

<Martin's proposed structure here>

Here is the structure proposed by one editor favoring treating this as a POV issue:

<Rick's proposed structure here>

Rick's draft (attempt at a joint, neutral statement)

I think the statement should have the following basic structure, with the content of each section (essentially line by line) either agreed or prefaced with something like "Rick says" or "Martin says" as appropriate. Essentially this boils down to treating the RfC statement in the same way we'd treat an article where there are differing POVs. The "Rick says" or "Martin says" preface attributes what one of us is saying to whoever is saying it, which doesn't mean whatever is said is true but simply that it is what one of us is saying. In the content below I've used a "Rick says" preface for some content and included "Rick says ..." and "Martin says ..." as placeholders (mostly to show how it sort of might end up reading). In the final version, ideally there would be none of these - but realistically I suspect there will be at least a few. This is not a complete draft of "my" statement, just something to show the form I'm suggesting.

Brief summary of the MHP

The MHP may be the most counterintuitive probability puzzle ever devised.

Rick says the standard version creates a mental image of a player who has picked Door 1 deciding whether to take the host's offer to switch to Door 2, after the host has opened Door 3. It's exquisitely counterintuitive - you don't know which of only two places the car may be, but the probability is not evenly divided between them.

Martin says ...

Overall summary of the literature

There is a vast literature about this problem (thousands of sources), including a huge number of popular sources which nearly universally present what we'll call "simple" solutions and a smaller but also huge number of academic sources from a variety of fields which present different types of solutions to the standard problem and numerous variants, analyze why the problem is so counterintuitive, etc.

Summary of academic sources from the field of probability

Rick says ... (this content will be controversial so I'm omitting it for now)

Martin says ...

OK, so what's the fuss?

Martin is suggesting a change to the article's structure. Rick objects to this change and suggests a different structure. The two structures are inherently incompatible.

What structure is Martin suggesting?

Martin says ...

Rick says he understands Martin to be saying ...

What are Martin's reasons for suggesting this structure

Martin says ...

What are Rick's objections to this proposal?

Rick says ...

What structure is Rick suggesting?

Rick says he favors a single solution section including both "simple" and conditional solutions ("simple" solutions first) in a strictly NPOV manner using text like the following:

Different sources present solutions to the problem using a variety of approaches.
Some sources (naming them) present this solution. <solution 1 goes here>
Some sources (naming them) present this solution. <solution 2 goes here>
Some sources (naming them) present this solution. <solution 3 goes here>

Rick has written a full text draft of such a section, see [8]. [I'd be happy to move this to a new page if the surrounding context on the talk page might be distracting]

Martin says he understands Rick to be saying ...

What are Rick's reasons for suggesting this structure?

Rick says the intent of the structure he is proposing is to present the two kinds of solutions typically presented in popular and academic probability sources in an editorially neutral fashion - without favoring one or the other. Rick agrees with Martin that the explicit criticism of the "simple" solutions can come in a later section of the article, but disagrees that presenting a conditional solution is overcomplicated or constitutes an implied criticism of "simple" solutions.

What are Martin's objections to this structure?

Martin says ...

Summing up the conflicting positions

Martin says ...

Rick says ...'

Discussion

Martin - what do you think of the structure I proposed above? Most of your draft would go in the section describing your proposal with your introductory comments included either in the rationale section or in the background section. Are you willing to work toward a single statement? -- Rick Block (talk) 04:59, 4 May 2012 (UTC)

The structure above is in the wrong order for an encyclopedia. The first things 95% of our readers will want to know are: What is the problem? What is the solution (convince me you are right)? Why does it matter what the host knows? Why does everybody get it wrong? This should all be based on sources but we are not writing a literature review.

I do not understand your question about a single statement. Martin Hogbin (talk) 08:24, 4 May 2012 (UTC)

Or are you referring to a structure for the RfC? In that case I think it is plain crazy. We want an answer not more endless discussion. Martin Hogbin (talk) 08:26, 4 May 2012 (UTC)

The question is about the structure for the RFC. Are you saying you think it's crazy to try to work out a single statement that we can both agree to? I thought you had already agreed to try this. -- Rick Block (talk) 22:37, 4 May 2012 (UTC)

Well let is see if it can work. Do you agree with with my proposed statement?

Just to be clear, my proposed question for the RfC is, 'Do editors prefer structure 1 or structure 2 (or structure 3 ...) for the article?'. I have removed the names of the proposers as irrelevant. Martin Hogbin (talk) 08:51, 5 May 2012 (UTC)

Martin - are you saying you consider your statement as is to be a brief, neutral statement of the issue? It has some elements in common with the structure I proposed. Shall I try merging them together? -- Rick Block (talk) 23:24, 5 May 2012 (UTC)

What is the point of making the question put to the RfC complicated. It is hard enough to get people to participate as it is. If we propose a complicated mathematical/philosophical question we will get very few takers. We both know what we want to say, why not both say it then ask the community which approach they prefer? That is obviously a completely neutral approach so I cannot see what possible objection you could have. Martin Hogbin (talk) 08:18, 6 May 2012 (UTC)

The point is that two contradictory non-neutral statements (obviously!) do not add up to neutral. We have already discussed this and although you have agreed numerous times to try to work out a single neutral statement [9] [10] [11], you seem to be distinctly uninterested in actually doing this. Perhaps Sunray can comment here. -- Rick Block (talk) 17:30, 6 May 2012 (UTC)

Martin's structure has the potential to be fairly straightforward and economical of words. I think that is valuable in an RfC. It gets to the essence of the matter fairly quickly. While we are going to get commentary from the "usual suspects," :) we will also get comments from newcomers (the aim of an RfC is usually to get comments from the wider community). Thus, being able to simply and quickly explain the problem will likely be a boon to meaningful discussion. Of course, it is easier to say than to do. It will be hard work to agree on the actual statement. Rick, what to you think of this approach? Sunray (talk) 17:52, 6 May 2012 (UTC)

I'm confused. Martin is suggesting we present two statements, one from him and one from me, and (as far as I can tell) is simply refusing to do anything else. I'm suggesting we work on a single statement that we both agree to. I would prefer to present a single statement. -- Rick Block (talk) 18:10, 6 May 2012 (UTC)

If we're presenting two statements with no attempt to agree on a single neutral statement, I've drafted a version of mine (above). -- Rick Block (talk) 05:49, 7 May 2012 (UTC)

Just to be clear Sunray, what I am suggesting is that Rick and I (and anyone else who wants to do so) writes a statement giving their view on what the dispute is all about and then their proposed solution (with a word limit) . These statements will clearly not be neutral, I will present my opinion and Rick will present his. The RfC statement, which I suggest that you or Guy write, need only say something like, 'editors are asked to choose between proposal 1 and proposal 2'. If you also want to write a short neutral introduction to the problem that would be fine with me. If you would like input from Rick or myself to do that, that would also be fine. This is what I have described in Process below. I am not sure if Rick agrees with this or not. Martin Hogbin (talk) 09:15, 7 May 2012 (UTC)

Martin - are you willing to work on a single succinct neutral statement of the issue, yes or no? As I've repeatedly said, this would be my preference. I thought you had agreed to try this and it's what we were attempting to do here. If you are now saying you are completely unwilling to do this, then we'll obviously need to talk about alternatives. -- Rick Block (talk) 15:01, 7 May 2012 (UTC)

I wasn't clear. I was proposing Martin's basic structure. I do think that a single RfC statement would be preferable and the format Martin has given would be a good way of presenting the RfC. Sunray (talk) 15:07, 7 May 2012 (UTC)

Martin's RfC structure consists of "Introduction and Aims" discussing and justifying (IMO, in very non-neutral terms) the structure for the article he is proposing. There's no "as opposed to what?" included - it's missing the entire other side of the argument. I'm happy to try to work toward a single succinct statement, but to be neutral it seems to me it needs to present both sides of this argument and it should be followed by the two contrasting article structures we're talking about. Am I totally off base here? -- Rick Block (talk) 17:13, 7 May 2012 (UTC)

Not only was I not clear, I evidently misunderstood. Are you both saying that you each want to present a new article structure in the RfC? Sunray (talk) 18:12, 7 May 2012 (UTC)

I think Martin pretty clearly wants an up or down vote on his proposed structure. My response to his proposed structure has (for 2 or 3 years now) been a counter proposal that the way we should resolve this conflict is to treat it as a POV dispute, which suggests a different structure (although I'm far less attached to any particular structure than Martin seems to be). Since this is a proposal and counter proposal, it seems both need to be in the RfC (i.e. the choice is not "do nothing" vs. Martin's proposal, it's "change the article so that the simple/conditional argument in the sources is treated as a POV issue" vs. Martin's proposal). I have commented before that treating what amounts to a math problem in this way seems very odd - but since there are clearly strongly held POVs (among both sources and editors), I think it's a very reasonable resolution. The problem is how to present this in an RfC in a way someone commenting might understand. If you haven't gotten it yet, it would appear we're pretty far from our goal. -- Rick Block (talk) 20:04, 7 May 2012 (UTC)

Perhaps not so far from the goal. I am trying to find common interests and also to find a simple way to present an RfC. It seems to me that there is a considerable difference between implying a new structure and presenting that structure. Working out the eventual structure will surely flow from a decision about the best way to present the problem. What is the essence of the dispute? Can we not come up with a statement that describes that? I would like to hear from each of you on that. Sunray (talk) 20:19, 7 May 2012 (UTC)

Actually we might have almost reached agreement on what to do. I have written my proposal above and Rick has now written his. Surely all we have to do now is to give editors a choice between them in a neutral manner. In other words, 'Do you prefer 1 or 2'. Martin Hogbin (talk) 23:01, 7 May 2012 (UTC)

If the two of you want to present this, that's fine. Personally, I think it is far too complicated for an RfC. I do not see a clear problem statement. What are they responding to? Sunray (talk) 23:41, 7 May 2012 (UTC)

I'm with Sunray on this. My guess is almost anyone reading the two statements above will be EXTREMELY confused. -- Rick Block (talk) 05:48, 8 May 2012 (UTC)

All we are asking those commenting to do is to choose between two (or more) structures for the article. There is no way that this RfC is going to be simple. If it helps I can simplify my proposal for the article structure. Martin Hogbin (talk) 08:46, 8 May 2012 (UTC)

Martin - you never answered the question above. Are you willing to work on a single succinct neutral statement of the issue, yes or no? -- Rick Block (talk) 06:24, 9 May 2012 (UTC)

I was willing to give it a go but upon seeing the vast differences between our approaches on the subject I think it is a lost cause. Martin Hogbin (talk) 08:34, 10 May 2012 (UTC)

You don't think there's any way we can neutrally describe the structure you want for the article and that I think that this structure creates a POV issue (and, lest you've forgotten, I'm not the only who has objected to your proposed change on these grounds)? This just doesn't seem that hard to me.

For example, the format I originally suggested above [12] is completely neutral. It's perhaps a little longer than we want, but to describe the issue you need to describe the structure you want and why you're suggesting this, and I need to describe why I think your proposal creates a POV issue (which requires at least a brief description of the sources) and my counter proposal for how to structure the article in what I would consider an NPOV manner.

I really don't understand why you are apparently so reluctant to engage in this process. My impression is you think my opinion that your structure creates a POV is specious and therefor I must have some other agenda (presumably to push the "Morgan" POV, which I have repeatedly and again deny). I could in return say your claim that your goal here is help our readers understand the problem is specious and that you must have some other agenda (such as to push the "simple solutions are correct and complete" POV, which you deny). However, for the purposes of creating a neutral RFC statement I'm willing to take you at your word that you sincerely and honestly are only trying to make the article easier to understand. In return, you need to take me at my word that my opinion that the structure you're suggesting creates a POV is sincere (I also happen to disagree that the structure you're suggesting makes the article easier to understand, but given that I think it creates a POV problem this is a distinctly secondary consideration).

And, I agree (look, something we agree on!) Sunray should comment here. -- Rick Block (talk) 16:14, 10 May 2012 (UTC)

I do indeed think that your opinion that my structure creates a POV is specious but I do not presume to know your reasoning or motives.Martin Hogbin (talk) 15:58, 13 May 2012 (UTC)

Essence

IMO, the essence of the dispute is pretty much what my non-neutral statement says above - i.e. we have a POV dispute (reflecting a dispute in sources) about the "simple" solutions to the MHP.

I believe Martin thinks I'm trying to push the POV that the "simple" solutions are deficient in some way (which I deny). I think he's trying to push the POV that the "simple" solutions are complete and correct (which he denies).

I think it's that simple. -- Rick Block (talk) 05:48, 8 May 2012 (UTC)

The RfC can be about us each pushing our own opinion if you wish but I have moved on from that, I have suggested a structure for the article that I would support even if I held your opinion on the subject. I find it hard to see what possible objection there can be to it. Martin Hogbin (talk) 08:46, 8 May 2012 (UTC)

As I've said repeatedly, the objection is that the structure you're suggesting gives the impression the "simple" solutions are the "right" and undisputed way to approach the problem while solutions using conditional probability are somehow controversial - which (I believe) is the exact opposite of what the sources say! As I read the sources, solutions based on conditional probability are not only completely undisputed but are (according to what many sources explicitly say) the "right" way to approach the problem, while "simple" solutions are controversial. Rather than address this issue head-on as a POV issue, you seem to want a up/down vote on your structure (based on the tautologous premise that the article should start simple before proceeding to more complex) by people who won't have any familiarity with the sources - and thus won't have any way to judge whether what you're suggesting satisfies WP:NPOV. -- Rick Block (talk) 15:21, 8 May 2012 (UTC)

Sunray, I would appreciate your opinion on this. This has nothing to do with [[WP:NPOV]. I think this is a manufactured objection indicative of a degree of page ownership.

As I explained, even if thought that that Rick was correct, I would want to start with the simple solutions. Why? because that is what nearly all good text books and articles on technical subjects do. They start with a simple version (even if it is not completely correct) and the proceed to the more complicated aspects. In maths and physics, this approach is almost universal because it would be almost impossible to get off the ground if the book went straight in to the full complexity of the subject.

Of course, there are cases where a 'health warning' is included in the opening section saying that the simplified explanation is not totally correct but these are generally introductory undergraduate texts where the intention of the book is to lead the student from a school-level review to university level understanding. In the MHP case I think a 'health warning' is particularly unhelpful. Many people struggle to understand and accept even the simplest and clearest explanations of the two essential facts. Telling them that the explanation is actually wrong at that stage is likely to blow their minds completely.

Finally I think it is pointless and a waste of all our time for Rick to continue to assert that the sources support his POV and that he is the only one following WP policy. We have all discussed mathematics, sources, and policy at very great length and although a small group of editors have consistently supported Rick's position the vast majority of editors have taken the same view as me. I have accepted that there is an irreconcilable difference of opinion which we need to find a way round and I really thought that, by looking at the problem from the POV of our readers, I had found one. Martin Hogbin (talk) 09:17, 9 May 2012 (UTC)

When I first read the article, (as a general reader without much post-secondary mathematics training), I was grateful that the simple solution was presented first. I then became interested in that fact that the simple solution was problematic. As far as the "structure" is concerned, you have my opinion, above: Simpler is better. A neutral wording, agreed on by both of you would be the most desirable course, IMO. I was drawn to Martin's approach, because it seemed to move us in that direction. However, I think that it would need to be modified so as to be acceptable by Rick. Would the two of you be willing to leave aside detailed discussion of structure for the moment and see if we can begin writing an RfC statement?

Absolutely. I'd even be fine with copying Martin's statement above into a new section of this page and collaboratively editing until we're both satisfied. If we do it this way, I'd suggest any edits to the statement be done separately from making any other comments on this page so the changes can be easily determined using the version diff tool. So, Martin, how about it? -- Rick Block (talk) 19:31, 10 May 2012 (UTC)

I've started this in the section below. It is a work in progress, but I'll stop for now pending some indication from Martin that he's willing to participate in this process. -- Rick Block (talk) 04:48, 11 May 2012 (UTC)

I do not wish to take part in a disagreement between Martin and Rick. I make no special claim to control what is on this page, that should be decided by community consensus. This argument is between two groups of editors, one small group which includes Rick, who assert that the Morgan solutions are the correct ones and another much larger group, which includes me, who prefer the simple solutions and who consider the Morgan solutions as a sideline. The problem is that most editors from both groups have been driven away by the continued argument, leaving Rick and me to argue it out. There is no requirement for the article to be acceptable to Rick, or to me but I have offered a compromise proposal for which I would like to seek community support. Martin Hogbin (talk) 11:35, 11 May 2012 (UTC)

Collaboratively edited statement

Some discussion

I am not sure how this is meant to work or what it exactly refers to but if we are talking about an introductory statement to be placed on the page for the benefit of RfC attenders then I am happy to work on it with Rick to make it neutral.

However I still think our (Rick, me, anyone else who wished to make one) proposals should be presented intact and editors should be asked to choose between them.

I have indented my proposed changes below and put comments in square brackets. Martin Hogbin (talk) 12:30, 11 May 2012 (UTC)

The idea is to work on this in the same way we would work on an article (by collaboratively editing). I suppose inline comments are OK, but we'll eventually delete these. Given the version diff tool, there's no particular reason to mark changes (any change is reflected in the history of this page). -- Rick Block (talk) 16:33, 11 May 2012 (UTC)

That is fine, I have no problem with that. Please delete and refactor as you see fit below. The only thing I am not sure about is what we are producing. Is it just the introduction to the proposals?

Just FYI - I'll be traveling on business for a few days, so will not have much time to participate here until Thursday. -- Rick Block (talk) 20:33, 13 May 2012 (UTC)

Proposed RfC introduction

Introduction

The aim of this RfC is to resolve an ongoing conflict concerning the relative importance and prominence within the article of the 'simple' and 'conditional' solutions to the problem.

Discussion mostly about Martin's list

The long dispute has not been about structure but about the relative importance and prominence within the article of the 'conditional' solutions. My proposed structure was a relatively recent proposal to resolve the original dispute. I also think we need to show readers the fact that there has historically been much greater support for the simple solutions. If you want to go through my list with me that is fine.

I've changed "conditional" to "various", deleted "two groups", and deleted "first proposed by Morgan". The issue is not just the importance and prominence of conditional solutions, but (on the flip side) the importance and prominence of simple solutions as well (so "various" seems more neutral to me). The first conditional solution appears in Selvin's second letter about the problem, not Morgan et al. As I've said, I believe your list is highly biased and have no desire to go through it with you. If you want to, link to it from a comment you make during the RfC process.

I have clarified 'various' in a neutral way.

I cannot see how my list can be biased, it consists of verbatim quotes from all users who have expressed a clear opinion. How is it biased?

Rick you have not responded to this. You must face up to the fact that the clear majority of users have been in favour of giving prominence to the simple solutions.

Comment from a third party: Cherry picking quotes like this is very poor form. I could produce several statements by Rick Block himself that expressed clear opposition to giving prominent weight to conditional probability solutions. He might rightly object to claiming they show he supports your position since he changed his mind long ago.

I advise against introducing your list into evidence for the RFC. It is unnecessary for showing that there has been long running dispute, and it is inappropriate to claim or imply that remarks from people who have not commented on your specific proposal show support for it. 'Twere better to argue your proposal on its own merits and let respondents to the RFC speak for themselves. ~ Ningauble (talk) 16:36, 14 May 2012 (UTC)

I think this conversation should take place elsewhere such as here. The list has been around for some time without challenge but if you would like to check its accuracy and point out any errors you are welcome to do so on the related talk page. Martin Hogbin (talk) 17:38, 14 May 2012 (UTC)

If you insist you must have a reply from me it is very similar to what Ningauble says above. You are attempting to pidgeonhole commenters into two camps - and as yet a different third party (Glrx) has mentioned It is more complicated than that. In addition none of them were commenting on these specific proposals so referring to your list as if it represents previous discussions on exactly the same topic is at best misleading. It is also not clear how many of these commenters are expressing personal opinions as opposed to trying to judge wp:weight. As I said, I believe your list is highly biased and have no desire to go through it with you.

As my list shows, most editors have taken a more extreme position than I am proposing, which is that the simple solutions are the 'right' ones and the conditional solutions are an unnecessary complication. Including this fact, shows that my proposal is a compromise between the two extreme positions, intended to let both sides be represented fairly and in a scholarly fashion.

If you want to continue to claim that my list is biased then please tell me on the related talk page where the problems lie. Martin Hogbin (talk) 09:14, 15 May 2012 (UTC)

In point of fact, your argumentum e silentio is false – the list is not unchallenged. See discussion over a year ago at Wikipedia:Arbitration/Requests/Case/Monty Hall problem/Workshop#A small group of editors has exerted disproportionate control over the page content and structure. As if cherry picking quotes out of context were not bad enough, people actually had the temerity to twist my words and argue that they knew better than I what I meant. If you would like an explanation of the faulty inferences drawn from what I said, ask me on my talk page. If you would like a Wikiquotian to explain the fallacy of quoting out of context in general, just cite the list in the RFC and when it is open for comment I will try to keep my dissertation within the word limit. ~ Ningauble (talk) 17:21, 15 May 2012 (UTC)

You are not mentioned on my history page and I have not added you because you have not expressed a clear preference for the simple or conditional solutions. At the time of the RfC I went through the talk page archives to find every editor who had expressed an opinion on the simple/conditional argument. For each editor I copied verbatim the statement by them that gave the clearest indication of their views on the subject. On both sides, some are more polarised than others but, if you think anyone has been misrepresented, please say so on the appropriate page and stop disrupting this process in which Rick and I are trying to agree on the proposed RfC introduction.

If you wish to put your own proposal for the resolution of this dispute and join in this discussion that would be fine with me but, at the moment, this conversation is meant to be between myself and Rick, with the kind assistance of Sunray.

The background and history of the dispute is important to show that my proposal is a genuine compromise between the two opinions that have been endlessly argued on this article. Martin Hogbin (talk) 08:12, 16 May 2012 (UTC)

I have already said as much about your opinion survey as is appropriate here, and indicated where it may be pursued further. I am sorry you consider my advice disruptive, and you are free to ignore it. ~ Ningauble (talk) 09:43, 16 May 2012 (UTC)

The bottom line here is we're not adding a link to Martin's list, is that correct?

I was not aware of agreeing to that

Which is why I'm asking. Elsewhere you've suggested we not include things we disagree about - we clearly disagree about this.

One editor has made Proposal 1 as a way to resolve the argument and make the article easier for readers to understand the solution.

Another editor thinks this proposed structure would create a structural POV and has proposed Proposal 2 as an alternative. The proposer of 1 thinks this gives undue prominence to the 'conditional' solutions and makes the article harder to understand.

I thought the whole point of what we were doing here was to create a neutral statement for the RfC. As such, I don't see the rationale for linking to a "Martin-only statement" and a "Rick-only statement" introducing the proposed structures. Doesn't this effectively defeat the entire purpose of a neutral statement? Anything Martin or I want to say in our own voices (as opposed to the neutral voice we're using in the RfC statement) should be clearly separate. We could perhaps include initial statements from Martin and Rick following the neutral RfC statement (which I think includes the proposed structures) - but making these part of the neutral RfC statement seems like a bad idea to me.

What do you mean by RfC statement? If you mean the words that will appear on the list of RfC then I have no problem. I am not suggesting that we each have statements there. If it helps to remove the links from the neutral statement that is fine with me.

If, on the other hand you are referring to the article talk page I do not understand quite what you are suggesting. Are you suggesting that neither of us should be allowed to comment there throughout the RfC?

My suggestion is that we, and possibly others should be allowed only limited commentary on the article talk page to let others have their say. If you are OK with that you can regard the statements as pre-prepared comments for that page

By "RfC statement" I mean the section on the talk page that WP:RFC suggests starts with {{rfc}} and then includes a "brief, neutral statement of the issue" (just dated, or signed and dated - in this case just dated seems more appropriate, or dated and signed by Sunray). I'm imagining this statement would be the text we're working on - with the proposed structures - but not your rationale and not my rationale. These seem more like comments (our !votes) we'd add in response to the neutral RfC statement. BTW - can we move the text above (starting with "One editor ..." so that it follows the paragraph below starting with "An argument between ..."?

If the RfC statement is to be strictly neutral then it cannot contain either proposal. It seems bizarre to expect newcomers to choose between two options with no explanation of why each option has been proposed. I be happy just to have the agreed neutral statement. Of course, I would then add my proposal and supporting statement and you would, I presume, add yours in the following discussion.

If it would make you happy, I would have no objection to having: the neutral statement, the two proposals, and then in a different section immediately below (the start of the discussion section) the supporting statements by you and me. My point is that, outside of the neutral statement and the two proposals, we (and maybe others) should have a limited words for our supporting statements and subsequent discussion in order not to swamp discussion by others. Do you agree?

Regarding your comment about !votes, if you do not agree with my comments below about counting votes then please say so in the relevant section. Martin Hogbin (talk) 07:51, 18 May 2012 (UTC)

Sounds like we're both OK with neutral statement, structure 1, structure 2, your supporting statement (max words=x), my supporting statement (max words=x), statements from others (max words=<something, possibly different from x>), and then a section for !votes (perhaps divided into sections like "support structure 1", "oppose structure 1", "support structure 2", "oppose structure 2" - note that since the 2 proposals are not complementary supporting one does not necessarily imply opposing the other and vice versa). I'll comment on the decision rule later. Is it time to put this together in a draft that we continue to edit without interspersed commentary? It's getting a little hard to see the statement since it's dwarfed by the comments.

I was thinking the same. If you want to do it feel free. Martin Hogbin (talk) 19:15, 18 May 2012 (UTC)

The Monty Hall problem (MHP) may be the most counterintuitive probability puzzle ever devised. It's exquisitely counterintuitive - you don't know which of only two places the car may be, but the probability is not evenly divided between them. The intuition that the probability must be distributed evenly between the two remaining closed doors is so strong that many people have trouble believing the (correct) solution - which is that the player has a 1/3 chance of winning the car by staying with her original choice and a 2/3 chance of winning by switching.

I want to recognize the work that has been done here by each of you to create a neutral statement. Thank you. At this stage of the process, I find it useful to listen to one another. I see evidence of that here and encourage you to continue. As Covey put it: "Seek first to understand. Then to be understood." I will pose some questions about the RfC structure in another section. Sunray (talk) 17:45, 13 May 2012 (UTC)

Sources

There is a vast literature about this problem, including huge numbers of both popular and academic sources. The majority of sources, including the most well known source responsible for popularizing the problem (vos Savant), present what we'll call "simple" solutions. Academic sources from a variety of fields present both "simple" and other types of solutions to the standard problem, numerous variants of the problem, analyses and experimental results exploring why the problem is so counterintuitive, etc.

Editors disagree what academic sources in the field of probability say. Many introductory probability textbooks solve the MHP by showing the conditional probabilities the car is behind Door 1 and Door 2 are 1/3 and 2/3 (not 1/2 and 1/2) given the host has opened Door 3, and make no comment about "simple" solutions. Some sources in the field are clearly critical of "simple" solutions (e.g. "This [vos Savant's solution] is an elegant proof, but it does not address the problem posed" [13]). Others are supportive (e.g. "One must consider the matter with care to see that both analyses are correct." [14]). Yet others make somewhat ambiguous statements that some editors consider critical but others consider supportive (e.g. "This solution [a 'simple' solution] is actually correct, but I consider it 'shaky'" [15]).

I do not like, 'In the field of probability'. The whole problem is about probability

I agree the whole problem is about probability. This is precisely why it's important to include what sources from the academic field of probability have to say.

The sources are not really from the academic field of probability; this particular issue is not at the cutting edge of probability research. I have changed it to 'Academic sources'.

These most definitely are from the academic field of probability - just look at the journal titles. These aren't journals where groundbreaking research is reported, but they definitely are in the field. You keep deleting MOST from this sentence, which completely changes the meaning of the paragraph (and, since I've added "and make no comment about simple solutions" to the end of the sentence, this sentence has become essentially nonsensical). Do you actually disagree that most (if not "a preponderance of") sources in the field present conditional solutions (without commenting about simple solutions) or do you just not want this said in this neutral summary? You seem to agree sources in the field are relevant. How would you characterize what sources in the field say?

Why do we need to characterise sources here? You seem to want me to agree to our saying 'all the best sources support the conditional solutions'. We disagree about the exact position of sources on this dispute; what we disagree on we should leave out.

Why do we need to characterize sources here? It's the point of this section. You're apparently fine with saying above that most sources present simple solutions. I'd like a corresponding, neutral statement here about the sources from the field of probability. There's no dispute that this IS an academic field, and you apparently agree that what these sources say has specific relevance. You seem to be Ok with saying most introductory probability textbooks present conditional solutions (right?). I'm suggesting saying that it's not just textbooks, but indeed most sources from this field (and that most sources in the field say nothing at all about "simple" solutions). Do you dispute this? I thought you disputed some specific sources, and that this dispute is already covered with the Rosenthal quote. I'm really not trying to be difficult here, if this is something we disagree about it's news to me. I thought your stance was that most sources present simple solutions and you thought conditional solutions were simply too technical for most people to understand - which is completely orthogonal to what sources in the field generally do. If we disagree about this I really am curious what you think the majority of sources in the field say. I don't think we can expect folks commenting here to do their own literature survey so I think we need to say something. If the best we can do is something like "editors disagree what the majority of sources in the field say" so be it. I've changed the paragraph above to say this.

My problem is really with the your use of the term 'academic'. To say that academic sources support the claim that only the conditional solutions are correct is to suggest that ongoing academic opinion supports this view. The fact is that there has only really been one, somewhat lighthearted, paper that has raised the point about the condition that the host opens a specific door and this was criticised on publication. The authors have since substantially retracted their original claims. There have been academic papers that have cited the Morgan result and there have been text books introducing students to conditional probability that have used the Morgan analysis to introduce an unexpected condition into a problem. However, there are no papers reanalysing the problem and confirming the Morgan analysis and no great swell of academic opinion confirming that Morgan got it right.

We have argued endlessly about sources before and we have to agree to disagree about what overall academic opinion on the subject is. I have trimmed your statement a little but I think we have to say that we disagree in the neutral statement. Martin Hogbin (talk) 19:41, 16 May 2012 (UTC)

I'm not saying most academic sources in the field support the claim that only conditional solutions are correct - rather that most sources in the field present solutions explicitly using conditional probability (as opposed to "simple" solutions). Further, I'm saying most sources in the field are completely silent regarding "simple" solutions. This has absolutely nothing to do with Morgan et al.

I am happy to have this quote from a reliable secondary source but other sources that support one side or another should be in the individual proposals.

An argument between supporters of the "simple" solutions and supporters of "conditional" solutions has been dogging the MHP article for years. The secondary/tertiary literature discusses this subject at length but comes to no clear conclusion on the matter. It is therefore hardly surprising that editors here cannot agree.

Request to participants

Users are requested to briefly discuss the different proposals and indicate a preference for one or the other.

No new proposals will be considered unless there is a clear consensus for them including all current solution proposers.

Sorry folks but I just cannot see this working

If Rick and I could agree on a neutral statement of the problem then we probably would not be arguing in the first place. Can someone please explain to me what is wrong with Guy's suggestion we each (and anyone else) have a limited number of words to put our proposal, and explain why we think it is the best one. Maybe we then have fewer words to respond to the others' rationale. The we ask the community to chose with limited discussion and a with strict limit on words by the proposers. Martin Hogbin (talk) 18:12, 11 May 2012 (UTC)

There are several neutral statements that each of you have proposed (and even some that you agree on). My suggestion is to avoid disagreeing. Simply suggesting changes is more collaborative. As far as a limitation in number of words, I definitely agree. Simpler is better. How about working at finding things to agree on?

Sunray, I think you have misunderstood Guy's/my suggestion, which is that Rick and I (and anyone else who wants to) write separate proposals for the article and we also each write separate, limited wordcount, rationales in support for our proposals. There is no need for us to agree on anything. Is this your understanding and we just talking about a common introduction to the subject to be placed at the top of the RfC section on the article talk page or are you proposing something different? Martin Hogbin (talk) 15:48, 12 May 2012 (UTC)

My main concern here is to assist in preparing an effective RfC statement. The shorter and clearer the statement, the more likelihood of a reasonable result, IMO. The statement can certainly have two options (note I say "two options" rather than "Martin's proposal" and "Rick's proposal"). Neutral wording is likely to assist uncommitted readers to make a decision. I suggest that the goal be clarity rather than some arbitrary word limit. Would you be willing to support such an approach? Sunray (talk) 16:27, 12 May 2012 (UTC)

Thanks for your response but I am still in the dark as to how you expect the RfC to work. On the article talk page, in the RfC section I am envisaging two (or more) sections, one written by exclusively Rick, explaining what he proposes and why he thinks it is a good idea, and one written exclusively by me with my proposal and rationale. As you say above, the proposals will be just be numbered 1, 2 etc. Are you expecting this?

In addition I am expecting a strictly neutral introduction to the problem, maybe written here by Rick and myself and a request for editors to show their preference. Is this your expectation? Martin Hogbin (talk) 17:42, 12 May 2012 (UTC)

To take your last question first: Yes, a neutral opening statement agreed upon by both of you would be optimal, in my opinion. With respect to your first question, I think that the more the two of you can agree on in the wording of each option, the better. Does this make sense? Sunray (talk) 19:43, 12 May 2012 (UTC)

Yes your question does make sense and I agree with you that the more we can agree to start with the better it will be, however, history has shown that we are not going to reach complete agreement. I can therefore see no way that we will ever be able to make one single RfC statement.

If the suggestion is that we try to make an opening statement containing as much agreement as possible but still have two (or more) individual proposals between which RfC editors will choose then that is fine and I am happy to work towards a neutral opening statement but I can see no way that we will ever reach complete agreement on an useful RfC question here. Are you happy for there to be limited word-count individual proposals in the RfC? Martin Hogbin (talk) 08:49, 13 May 2012 (UTC)

Proposal 1 to resolve the dispute

We seem to be settling on having a neutral and agreed introduction followed by two individual proposals. This is my proposal, which only I should edit, although suggestions to improve clarity are welcome. I start with my rational for my proposal before giving the structure

Rick's proposal is below, which only he should edit. I would suggest that Rick adds a rationale section in which he says the things he wants to say that we cannot agree on for the neutral section.

My proposal is a compromise between both views and does not assume the superiority or correctness of either. I suggest that we:

Structure the article in a way that is most helpful to readers of all abilities and experience and which allows scholarly discussion of the disputed issues in a way that does not disrupt the article and which is also of interest to more advanced readers.

We all agree that the MHP is one of the world's most unintuitive simple puzzles. There are two things that puzzle most people when they first see the problem. These are: that the probability of winning the car by switching is 2/3 and not 1/2, and that it matters that the host knows where the car is (or more accurately that the host reveals a goat with certainty). That these are the two main issues concerning the MHP is beyond dispute.

Because the two primary issues are so difficult for many people to grasp I believe that their solutions should initially be presented in the simplest way possible. Even taking the (disputed) view that the simple solutions are wrong, this approach is the same as that used by most technical authors; start with a simple explanation of the topic covering the essential features, even if this means glossing over some technical details, then go on to discuss deficiencies or extensions to the simple explanation.

It greatly hinders the reader who is still stuck on the basic issues above to have to read 'health warnings' in the first part of the article which say things like 'these solutions are wrong', 'these solutions answer a different question'. Once the reader has understood the basics of the problem, the more advanced issues are easily introduced. In fact they are much easier to understand than the basic basic puzzle itself.

Bearing in mind that the vast majority of WP editors and sources actually think the simple solutions are perfectly sound I can see no possible objection to this proposal.

Proposed Structure

Problem description

Give the standard version of the problem as per vos Savant/Whitaker and K&W

Simple Solutions (with no disclaimers, criticisms, or any mention of conditional probability)

Vos Savant's solution
Other simple solutions

Aids to understanding (with no disclaimers, criticism, or any mention conditional probability)

Help people understand why the answer is 2/3
Help people understand why it matters that the host knows where the car is

Sources of confusion (with no disclaimers, criticisms, or an mention of conditional probability)

Discussion over why people find the subject so hard to understand and what it is exactly that leads people to the wrong conclusions.

'Conditional' solutions

Morgan's paper
Morgan solutions
Discussion and criticism of Morgan solutions
Problem variants (for example host does not choose uniformly) Discussion on the whether the conditonal nature of the problem is relevant to its unintuitiveness.

The rest of the article

Proposal 2 to resolve the dispute

Problem description

Give the standard version of the problem as per vos Savant/Whitaker and K&W

Solution

Vos Savant's solution
A conditional solution

Both presented in a completely NPOV manner with neither presented as "more correct" than the other, for example per this specific wording:

Proposed text for this section

According to the problem statement above, a car and two goats are arranged behind three doors and then the player initially picks a door. If the player has picked, say, Door 1, there are three equally likely cases.

Door 1	Door 2	Door 3	result if switching
Car	Goat	Goat	Goat
Goat	Car	Goat	Car
Goat	Goat	Car	Car

A player who switches ends up with a goat in only one of these cases but ends up with the car in two, so the probability of winning the car by switching is 2/3. In other words, there is a 2/3 chance of being wrong initially, and thus a 2/3 chance of being right when changing to the other door (vos Savant 1990).

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

Another way to analyze the problem is to determine the probability in a specific case such as that of a player who has picked Door 1 and has then seen the host open Door 3. Referring to the figure below or to an equivalent decision tree as shown to the right (Chun 1991; Grinstead and Snell 2006:137-138), the car is behind Door 2 and the host opens Door 3 with probability (1/3)x1=1/3 while the car is behind Door 1 and the host opens Door 3 with probability (1/3)x(1/2)=1/6. These are the only possibilities in which Door 3 is opened, so altogether the host opens Door 3 with probability (1/3)+(1/6)=1/2. Given the host opens Door 3, the probability the car is behind Door 1 is therefor (1/6)/(1/2)=1/3, and the probability it is behind Door 2 is (1/3)/(1/2)=2/3. The intuition behind this solution is that the host must always open Door 3 if the car is behind Door 2, but opens Door 3 only half the time the car is behind Door 1 - so if the player sees the host open Door 3, switching to Door 2 wins twice as often as staying with Door 1.

Other solutions and a formal proof that the conditional probability of winning by switching is 2/3 using Bayes' theorem are presented below, see Additional solutions.

Car hidden behind Door 3	Car hidden behind Door 1		Car hidden behind Door 2
Player initially picks Door 1

Host must open Door 2	Host randomly opens Door 2	Host randomly opens Door 3	Host must open Door 3

Probability 1/3	Probability 1/6	Probability 1/6	Probability 1/3
Switching wins	Switching loses	Switching loses	Switching wins
If the host has opened Door 3, these cases have not happened		If the host has opened Door 3, switching wins twice as often as staying

Aids to understanding

Help people understand why the answer is 2/3 including discussion based on conditional probability
Help people understand why it matters that the host knows where the car is

Sources of confusion

Discussion of why people find the subject so hard to understand and what it is exactly that leads people to the wrong conclusions including sources that say the reason people have so much trouble is that people have a hard time properly evaluating conditional probabilities.

Additional solutions

Other simple solutions
Game theory solutions
Formal proof the conditional probability of winning by switching is 2/3

Problem variants (for example host does not choose uniformly)

The rest of the article

Notes

Presenting the RfC statement

Here's what WP:RFC says about the RfC statement:

"Include a brief, neutral statement of the issue below the template, and sign it with ~~~~ (name and date) or ~~~~~ (just the date).

If possible, keep your statement or question simple and succinct, so that the RfC attracts a clear and actionable response. For example: "Should this article say in the lead that John Smith was a contender for the Pulitzer Prize?" The longer and more complicated your question or statement, the more diverse the responses will be, and the harder it becomes for the closing admin to interpret the consensus."

The guideline further states: "the first date stamp must precede any such sub-section headings or tables." You may want to use summary style introduce longer presentations on structure, etc.

Intent, process

What is the goal of the RfC? What do you want to achieve?
Who do you want to comment? The whole WP community or some subset (e.g. Wikiproject)?

Discussion

Determining the decision rule

The parameters for determining the outcome. What constitutes consensus?

Martin's suggestion

My suggestion is that if any proposal gets more than 50% support it should be accepted as a consensus regarding only the issues outlined in the proposal. If no proposal gets a majority vote then this method or resolution should be deemed to have failed and we carry on as before until a new proposal is proposed.

Rationale

I an fully aware of Wikipedia:Polling is not a substitute for discussion but in this case the subject has been discussed ad infinitum and, to the best of my knowledge, not one editor has changed their mind. A consensus on just the aspects of the article outlined in the winning proposal does not prevent others from changing other aspects of the article. Debates may well continue but one issue at least will have been settled so some progress will have been made.

My firm belief is that the structure that I have proposed will enable cooperative editing to resume. Martin Hogbin (talk) 08:20, 6 May 2012 (UTC)

Process

Posting of RfC, duration of process, etc.

Martin's suggestion

Get a proposal from Martin and one from Rick.

Ask if anyone else wants to make a proposal for solution of the simple/Morgan argument

Start an RfC asking editors to choose between the proposals. No new proposals will be accepted at that stage.

Give the proposers a strictly limited number of words for the whole RfC process to support their proposals.

Limit the number of words for recent or long term editors for the whole RfC process.

Encourage as many new editors as possible plus proposers and regulars to give a quick preference (vote).

After an agreed time count the votes and make a decision.

RfC Statement

Text of statement

The aim of this RfC is to resolve a longstanding and ongoing conflict involving many editors concerning the relative importance and prominence within the article of the 'simple' and 'conditional' solutions to the problem.

The Monty Hall problem (MHP) may be the most counterintuitive probability puzzle ever devised - you don't know which of only two places the car may be, but the probability is not evenly divided between them. The intuition that the probability must be distributed evenly between the two remaining closed doors is so strong that many people have trouble believing the (correct) solution - which is that the player has a 1/3 chance of winning the car by staying with her original choice and a 2/3 chance of winning by switching.

There is a vast literature about this problem, including huge numbers of both popular and academic sources. The majority of sources, including the most well known source responsible for popularizing the problem (vos Savant [16]), present what we'll call "simple" solutions. Academic sources from a variety of fields present both "simple" and other types of solutions to the standard problem, numerous variants of the problem, analyses and experimental results exploring why the problem is so counterintuitive, etc.

Editors disagree what academic sources in the field of probability say. Many introductory probability textbooks solve the MHP by showing the conditional probabilities the car is behind Door 1 and Door 2 are 1/3 and 2/3 (not 1/2 and 1/2) given the host has opened Door 3, and make no comment about "simple" solutions. Some sources in the field are clearly critical of "simple" solutions (e.g. "This [vos Savant's solution] is an elegant proof, but it does not address the problem posed" [17]). Others are supportive (e.g. "One must consider the matter with care to see that both analyses are correct." [18]). Yet others make somewhat ambiguous statements that some editors consider critical but others consider supportive (e.g. "This solution [a 'simple' solution] is actually correct, but I consider it 'shaky'" [19]).

An argument between supporters of the "simple" solutions and supporters of "conditional" solutions has been dogging the MHP article for years. The secondary/tertiary literature discusses this subject at length but comes to no clear conclusion on the matter. It is therefore hardly surprising that editors here cannot agree.

Two proposals have been made for ways to structure the article to resolve the conflict. Arguments for and against these proposed structures are presented below (see "Statements about this issue").

Proposed structure 1

Problem description

Give the standard version of the problem as per vos Savant/Whitaker and K&W

Simple Solutions (with no disclaimers, criticisms, or any mention of conditional probability)

Vos Savant's solution
Other simple solutions

Aids to understanding (with no disclaimers, criticism, or any mention conditional probability)

Help people understand why the answer is 2/3
Help people understand why it matters that the host knows where the car is

Sources of confusion (with no disclaimers, criticisms, or any mention of conditional probability)

Discussion over why people find the subject so hard to understand and what it is exactly that leads people to the wrong conclusions.

'Conditional' solutions

Morgan's paper and Selvin's solutions
Conditional solutions
Discussion and criticism of Morgan solutions
Problem variants (for example host does not choose uniformly)
Discussion on the whether the conditional nature of the problem is relevant to its unintuitiveness.

The rest of the article

Proposed structure 2

Problem description

Give the standard version of the problem as per vos Savant/Whitaker and K&W

Solution

Vos Savant's solution
A conditional solution

Both presented in a completely NPOV manner with neither presented as "more correct" than the other, for example per this specific wording:

Proposed text for this section

According to the problem statement above, a car and two goats are arranged behind three doors and then the player initially picks a door. If the player has picked, say, Door 1, there are three equally likely cases.

Door 1	Door 2	Door 3	result if switching
Car	Goat	Goat	Goat
Goat	Car	Goat	Car
Goat	Goat	Car	Car

A player who switches ends up with a goat in only one of these cases but ends up with the car in two, so the probability of winning the car by switching is 2/3. In other words, there is a 2/3 chance of being wrong initially, and thus a 2/3 chance of being right when changing to the other door (vos Savant 1990).

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

Another way to analyze the problem is to determine the probability in a specific case such as that of a player who has picked Door 1 and has then seen the host open Door 3. Referring to the figure below or to an equivalent decision tree as shown to the right (Chun 1991; Grinstead and Snell 2006:137-138), the car is behind Door 2 and the host opens Door 3 with probability (1/3)x1=1/3 while the car is behind Door 1 and the host opens Door 3 with probability (1/3)x(1/2)=1/6. These are the only possibilities in which Door 3 is opened, so altogether the host opens Door 3 with probability (1/3)+(1/6)=1/2. Given the host opens Door 3, the probability the car is behind Door 1 is therefor (1/6)/(1/2)=1/3, and the probability it is behind Door 2 is (1/3)/(1/2)=2/3. The intuition behind this solution is that the host must always open Door 3 if the car is behind Door 2, but opens Door 3 only half the time the car is behind Door 1 - so if the player sees the host open Door 3, switching to Door 2 wins twice as often as staying with Door 1.

Other solutions and a formal proof that the conditional probability of winning by switching is 2/3 using Bayes' theorem are presented below, see Additional solutions.

Car hidden behind Door 3	Car hidden behind Door 1		Car hidden behind Door 2
Player initially picks Door 1

Host must open Door 2	Host randomly opens Door 2	Host randomly opens Door 3	Host must open Door 3

Probability 1/3	Probability 1/6	Probability 1/6	Probability 1/3
Switching wins	Switching loses	Switching loses	Switching wins
If the host has opened Door 3, these cases have not happened		If the host has opened Door 3, switching wins twice as often as staying

Aids to understanding

Help people understand why the answer is 2/3 including discussion based on conditional probability
Help people understand why it matters that the host knows where the car is

Sources of confusion

Discussion of why people find the subject so hard to understand and what it is exactly that leads people to the wrong conclusions including sources that say the reason people have so much trouble is that people have a hard time properly evaluating conditional probabilities.

Additional solutions

Other simple solutions
Game theory solutions
Formal proof the conditional probability of winning by switching is 2/3

Problem variants (for example host does not choose uniformly)

The rest of the article

Statements about this issue

(limited to x words)

Martin's statement

My aim is to get a swift and lasting conclusion to the argument, between supporters of the 'simple' solutions and supporters of the 'conditional' solutions, that has been dogging the MHP article for years.

I do not think we will ever resolve that problem. The secondary/tertiary literature discusses that subject at length but comes to no clear conclusion on the matter. It is therefore hardly surprising that editors here cannot agree.

The answer, from the point of view of WP, however, is simple. Structure the article in a way that is most helpful to readers of all abilities and experience and which allows scholarly discussion of the disputed issues in a way that does not disrupt the article and which is of interest to more advanced readers.

We all agree that the MHP is one of the world's most unintuitive simple puzzles. There are two things that puzzle most people when they first see the problem. These are: that the probability of winning the car by switching is 2/3 and not 1/2, and that it matters that the host knows where the car is (or more accurately that the host reveals a goat with certainty). That these are the two main issues concerning the MHP is beyond dispute.

Because the two primary issues are so difficult for many people to grasp I believe that their solutions should initially be presented in the simplest way possible. Even taking the (disputed) view that the simple solutions are wrong, this approach is the same as that used by most technical authors; start with a simple explanation of the topic covering the essential features, even if this means glossing over some technical details, then go on to discuss deficiencies or extensions to the simple explanation.

It greatly hinders the reader who is still stuck on the basic issues above to have to read 'health warnings' in the first part of the article which say things like 'these solutions are wrong', 'these solutions answer a different question'. Once the reader has understood the basics of the problem, the more advanced issues are easily introduced. In fact they are much easier to understand than the basic basic puzzle itself.

Bearing in mind that, according to my survey of the history of this article, the vast majority of WP editors actually think the simple solutions are perfectly sound as do the majority of sources, I can see no possible objection to this proposal. Martin Hogbin (talk)

Executive summary/idiot's guide

My aim is to get a swift and lasting conclusion to the argument between supporters of the 'simple' solutions and supporters of the 'conditional' solutions that has been dogging the MHP article for year

My proposal is to give both types of solution equal prominence within the article but do what most good text books do and start with just the simple solutions and then proceed to the more complicated stuff. Martin Hogbin (talk) 17:42, 26 May 2012 (UTC)

Rick's statement

This is a draft. Included here so Martin has some idea what I'll be saying.

This is a POV dispute, plain and simple.

There are (at least) two ways to interpret the question - each supported by numerous sources.

1) It asks whether as a strategy switching is better than staying. Many secondary sources agree this interpretation is implicitly taken by "simple" solutions.

2) It asks whether a player should switch in a specific case, such as after picking Door 1 and then seeing the host open Door 3. This interpretation is implicitly taken by sources presenting only "conditional" solutions, and is explicitly supported by a number of sources.

As one source says, "the distinction between [these questions] seems to confound many".

The RfC statement above says the majority of sources present "simple" solutions. True enough. But this includes an immense number of popular sources as well as academic sources from many fields which essentially parrot vos Savant's solution. Within the field of probability, the textbook solution (literally and figuratively) is to compute the conditional probabilities the car is behind Door 1 and Door 2 given the player selected Door 1 and the host opened Door 3. Most sources in the field say nothing (good or bad) about "simple" solutions. However, saying or implying that solving the MHP using conditional probability is uncommon or controversial is nothing less than a Big Lie.

There is a controversial, but by no means fringe, POV expressed by a number of sources that "simple" solutions are deficient, and that "conditional" solutions are a better way to address the problem. To be NPOV the article must not endorse this view (as it arguably did following its last successful featured article review), but it equally must not endorse the opposite view that "simple" solutions are the best way to address the problem. IMO, proposed structure 1 does exactly this. It creates a structural POV strongly suggesting "simple" solutions are the primary, undisputed approach to solving the MHP.

The player initially picks Door 1. The host then opens Door 3 revealing a goat, and offers to let the player switch to Door 2.

Furthermore, the claim most readers would not be interested in a "conditional" solution and find "simple" solutions easier to understand is contradicted by Krauss and Wang. They say 97% of their test subjects created a mental image of a player who has picked Door 1, deciding whether to switch to Door 2 after the host has opened Door 3 (like the image to the right), and that once formed this image makes the "simple" solutions inaccessible. This situation is precisely addressed by the "conditional" solutions.

The resolution here is simple. Follow Wikipedia's core content policy of NPOV. Include both "simple" and "conditional" solutions in an initial "Solution" section, without saying or implying either is "more correct" than the other.

Support/opposition of Structure 1

Support

(please sign)

Oppose

(please sign)

Support/opposition of Structure 2

Support

(please sign)

Oppose

(please sign)

Comments about the statement above

I think it will be helpful if we can confine further comments here, rather than interspersing in the text above (which is not to say that we shouldn't edit the text above, just that we shouldn't include inline discussion). I've deleted the subsection headings from the statement (didn't seem necessary, it's pretty short), and moved the text referring to the proposals to follow the text saying there's been an argument.

AFAICT, we're not yet agreed on the following:

Including a link to Martin's "history" page (although my stance is absolutely not, Martin hasn't agreed with this yet)

I will put a link my supporting section, where it is clearly identified as my survey.

The exact wording about what sources in the field of probability say (Martin hasn't responded to my last comments about this)

I think it is best to say that we cannot agree, as we cannot.

Deleting the headings from the statement and moving the text referring to the proposals (a change I've made Martin has not OK'd)

That is fine with me.

Presenting the proposed structures in show/hide sections (seems reasonable to me, but if Martin doesn't like this for some reason we should talk about it)

Also OK with me

I think the text introducing the two structures could use some additional work as well. Before getting into this, is this where we currently are? In particular, is there anything I've overlooked, anything to which I haven't responded, or anything else in the above to which we haven't agreed? -- Rick Block (talk) 04:56, 19 May 2012 (UTC)

We need to agree the decision rules and some housekeeping

Can we wait just a bit on decision rules? What housekeeping? And have we agreed how many words we'll allow in the "statement" sections?

Why do you want to wait on the decision rules? Sunray suggested we consider them at the start.

By housekeeping I meant more some general, and hopefully non contentious, rules,

I'm not overly happy with the "One editor has proposed ..." and "Another editor ..." text introducing the proposed structures. Can we either make these flatly descriptive somehow, perhaps something like

Two suggestions have been made to resolve the argument.

In Structure 1 the article is divided into two sections. The first presents exclusively "simple" solutions and analyses of the problem based on these solutions, while the second presents other solution approaches (including addressing the problem using conditional probability) as well as a discussion of the pros and cons of various solution approaches.

In Structure 2 the article treats the "simple vs. "conditional" argument as a POV issue within the sources, with an initial solution section presenting both of these kinds of solutions in an NPOV manner (remaining editorially neutral about whether one is in any sense "better" than the other), also with other solution approaches and a discussion of the pros and cons of various approaches in later sections of the article.

Or, perhaps just simply say there are two proposed structures - e.g.

Two suggestions have been made to resolve the conflict, Structure 1 and Structure 2. Arguments for and against these proposed structures are presented below (see "Statements about this issue").

I think either of these would be better than what we have now.

Your second suggestion is fine with me so I have changed the text to that, although I would prefer Proposal 1 and Proposal 2

I reworded it slightly - better?

It is not that important but why include 'structure' in the statement? We have two proposals, both happen to involve the article structure but it need not be that way.

I wanted to wait on the decision rules to keep us focused on one thing at a time. Since we're more or less agreed on the text at this point, I'm fine with moving on to the decision rules. Since it's an RfC about the fundamental structure of the article directly involving core Wikipedia content policies, I think supermajority consensus, as determined by any uninvolved admin, is a reasonable rule. I think the more interesting question is what happens if neither of the proposed structures generates a supermajority consensus. I would suggest that we then solicit other alternatives.

To address your second point first, this is my worry. If we do not get a conclusion here I can see no prospect of this dispute ever being resolved. There is no consensus for the current version so we are left with an impasse.

For the above reason, I think we should accept a simple majority; it is our best chance to finally end this dispute. We could say that if more that 50% of editors who express a valid (see below) opinion support one or other proposal that is a decision. Note that that is stronger than a simple majority vote between the two proposals because you made the voting non-exclusive. An editor could vote for neither or both proposals.

I think that we should discourage users from making alternative proposals or voting on such new proposals.

We should explain in some text, possibly written by Sunray or agreed here, why we are taking this unusual approach to the dispute.

I suggest that we agree to ignore the view users who clearly do not understand the problem at all. In particular anyone who argues against the universally agreed facts, for example that the correct answer is not 2/3 or that it does not matter that the host must reveal a goat, should have their views ignored. Brief and polite explanations to these users should be exempt from any word-count limit that we set.

I see no reason why Sunray (if willing) should not close the RfC on the basis agreed here. I would object strongly to an uninvolved admin attempting to close on the basis of the strength of the arguments.

I agree there's no consensus for the current version, but if there's no consensus for either of these two proposed structures that doesn't mean we're at an impasse. It means we both need to seek other alternatives. You would have to agree that your vision of the article, where there's no mention of conditional probability in a series of initial sections devoted exclusively to "simple" solutions, does not meet the community's desires - so you should back off from this stance. I would have to agree that my vision of this article, where there's a single solution section presenting both "simple" and "conditional" solutions, does not meet the community's desires - so I should back off from this stance. There are many, many, many ways to structure the article. These two are not the only ones.

Deciding this based on counting votes and not based on strength of arguments seems wrong to me. For example since my objection to your proposal is based on NPOV, if this objection is not reasonably addressed a "consensus" of editors doesn't matter (from WP:NPOV: The principles upon which this policy is based cannot be superseded by other policies or guidelines, or by editors' consensus).

Perhaps Sunray could comment here.

There is absolutely no point in mentioning NPOV. You think that logic, mathematics, the sources, and WP policy, including NPOV, all support your position but I think the majority of editors, logic, mathematics, the sources, and WP policy, including NPOV, all support my position. We can go over the last few years' arguments if you like but I fear it will serve no purpose as neither of us is likely to be swayed by the other. We thus have to accept that the matter must be decided by community consensus.

The reason that I will not accept closure by an admin on the strength of the arguments is that if the admin that turns up happens to think like me they will clearly judge arguments for my position to be the stronger, on the other hand, if they happen to think like you, they will clearly judge arguments that support your position to be the stronger. It is just a matter of luck who turns up. Admins have no special powers of logic or understanding of WP policy, they are just editors with access to the administrative features of this wiki and with a mandate to apply community consensus.

Other editors too may not fully understand the long arguments that editors have been having here for the last few years but at least we have the advantage of numbers. To a large degree WP works on the principle that one person can be wrong but many people are usually not all wrong. In the absence of some properly appointed superperson a vote is the best we can do.

There are many potential ways to resolve this problem but, in the light of the continuous argument we have had over the years, I doubt that any will get a clear consensus. All the time we wait for solution the article and consequently our readers suffer.

OK. You won't accept closure by an admin. I won't accept simple majority. I'd be OK with a supermajority consensus. I again suggest it's time for Sunray to comment here.

I'm traveling on business again this week. I'll participate as much as possible, but responses may be delayed.

I will accept closure by admin but only in accordance with the rules agreed here.

OK. Ignoring clueless users seems fine. Is there anything else we need to agree on other than what constitutes consensus?

I have two comments, one about the structure of the RfC, one about the decision rule. I've elaborated further in the two sections below. Sunray (talk) 01:45, 24 May 2012 (UTC)

Structure

I appreciate the work you have both done in creating the draft statement. It is probably as simple as you can make it given the two alternative, and I like the "show" boxes. There is question niggling at me, though: Can it work as an RfC? My sense is that it is still too complicated. It is possible that only editors who have been dealing with the problem will be able to answer it. You probably already know what these editors think already. Therefore, I wonder whether the RfC would produce anything new. The only remedy to this would be to craft a an understandable statement that puts the question simply (omitting the details of structure). The structure would follow from the decision. Sunray (talk) 01:45, 24 May 2012 (UTC)

Understanding my proposed structure requires no understanding of the Monty hall problem or its associated mathematics at all. My proposal accepts that there are two ways of dealing with the problem and suggests that we do what most good technical books do; start with the easy stuff then go on to the hard stuff.

Why do we not each write an executive summary/idiots guide to our proposals so that anyone can quickly see what we are getting at. Martin Hogbin (talk) 08:33, 24 May 2012 (UTC)

I solicited comments from Ningauble. See his reply here. I think he's basically echoing Sunray's sentiment that the question we're attempting to ask is not very clear. I'm not sure there's a "simple" statement of the conflict on which we can agree.

I think the essence is that Martin wants the initial sections of the article to mention only "simple" solutions, specifically excluding any mention of conditional probability (without even a forward reference). My primary objection is that this creates a "pro simple" bias contrary to NPOV since both 1) most sources (by far) in the field of probability present "conditional", not "simple" solutions and 2) a fair number of sources (enough that this POV cannot be considered "fringe") explicitly criticize "simple" solutions. I have a secondary objection that the "simple" solutions, although simple in form, are not easily understood by most people (who form a conditional mental model of the problem) so Martin's claim that the structure he favors better serves the non-technical reader is simply incorrect.

IMO, the issue is how we present this in a neutral way given that Martin denies the legitimacy of my points. How can we neutrally say that I think most sources in the field present conditional solutions (but Martin disagrees), that I think there's a non-fringe POV critical of the "simple" solutions (but Martin disagrees), and that I think K&W say the mental image most people create of the problem is more consistent with a conditional solution (but Martin disagrees)? -- Rick Block (talk) 07:15, 28 May 2012 (UTC)

Let me explain one more time. This is not an argument between Rick and Martin over the 'correct' solutions to the MHP. Most editors (including myself) do not see that point of the 'conditional' solutions and think they have no place (or a very minor place) in the article. A persistent minority of editors prefer the 'conditional' solutions. It is very unlikely (see Guy's latest post on the article page) that anyone will ever change their mind on that subject so we have to find a way round that disagreement.

This discussion is about two proposals to resolve that argument. My proposal is not that hard to understand and requires no mathematical or specialist knowledge, it is a proposal that anyone can understand. Exactly as Rick says above, 'Martin wants the initial sections of the article to mention only "simple" solutions, specifically excluding any mention of conditional probability (without even a forward reference)'. I then want the later sections to discuss, with equal prominence, the conditional solutions and their significance. Put very simple 'easy stuff' on its own then 'hard stuff'. This approach gives the 'conditional' solutions far greater prominence than most editors think they should have. What is there to object to? Martin Hogbin (talk) 09:01, 28 May 2012 (UTC)

I see real progress in the foregoing two posts, towards an agreement in principle on what the principal difference of opinion is that the two "proposed structures" reflect. I encourage you to focus on formulating a succinct question for RFC respondents that identifies this difference without having to incorporate entire structural schemata by reference within the question.

To wit: I would suggest a separate prose section of 100 words or less, following the background material about the dispute, that states the question of principle for respondents to answer. I recommend that if structural outlines are used to illustrate how the principles might be applied, they should be presented after the question itself, in a side by side format to facilitate comparison.

My take on Sunray's opening post in this thread is that without a clear question that succinctly indentifies the disagreement in principle, too many respondents will miss the essential issue or focus on particulars, and the underlying dispute will remain unresolved. To be clear, the principles I am referring to are matters of what, in principle, should the article present?, which is separate and distinct from principles used in supporting answers to that question. In your contrasting statements above, I think the two of you are close to agreement on articulating that question, if you are agreeable to doing so. ~ Ningauble (talk) 17:08, 28 May 2012 (UTC)

Ninguable, does my 'Executive summary/idiot's guide' above not conform to your suggestion.

If you want to ask a simple question then forget my compromise solution and ask this question. What relative prominence should the 'simple' solutions be given compared to the 'conditional' solutions? Split marks from a total of 10 to the prominence you think each should be given, for example Simple-8, Conditional-2, (more or less my opinion) meaning give much more prominence to the 'simple solutions'.

Finally I am not willing to participate in any process that characterises this as a dispute between Rick and myself. I have proposed a compromise between the 25 users who prefer the simple solutions and the 7 users who prefer the conditional solutions. You may quibble about the list (although you have not pointed out any errors in it) but it is my honest assessment of editors' opinions.

Just to be clear, by "conditional" solutions above Martin means any solution using conditional probability, such as a solution presented in nearly any introductory textbook showing P(car behind Door 2|player picks Door 1 and host opens Door 3) is 2/3 (i.e. not Morgan et al.'s solution of what they consider to be vos Savant's problem where the host's probability of picking between two goats is left as a variable rather than fixed to be 1/2). If Martin really were seeking "equal prominence" we wouldn't be having this discussion, since that is exactly what the structure (with text) I've proposed does (if anyone disagrees, please tell me how). Since Martin apparently won't accept this proposal, my assumption is he wants something else - which by contrast would almost have to be called "greater prominence" for "simple" solutions.

I'd be fine with the RfC statement being something like Martin wants the initial sections (solution, aids to understanding) devoted exclusively to "simple" solutions, specifically excluding any mention of conditional probability. Rick wants the article to give equal prominence to "conditional" solutions (as commonly presented by sources in the field of probability), by including in the initial "solution" section an approachable solution showing the conditional probability the car is behind Door 2 given the player picks Door 1 and the host opens Door 3 is 2/3.

The objection is that IMO what Martin wants makes the article violate NPOV. Since judging this requires familiarity with the sources, the claim that folks can comment on this with no understanding of the Monty Hall problem or its associated mathematics is simply incorrect. Refusing to admit this is a POV issue is not helpful and doesn't get us anywhere. Another RfC statement I'd be fine with would be something like This is a POV issue concerning the prominence of "simple" and "conditional" solutions. Martin wants the article to endorse the view that "simple" solutions are sufficient. Nijdam wants the article to endorse the view that the solution must be "conditional" [I'm pretty sure this is Nijdam's stance - I'm including it here just to show the "opposite" of what I believe is Martin's stance]. Rick wants the article to be neutral, giving equal prominence to both of these types of solutions. -- Rick Block (talk) 18:19, 28 May 2012 (UTC)

Yes, why not have,Martin wants to promote his POV by having the initial sections (solution, aids to understanding) devoted exclusively to "simple" solutions, specifically excluding any mention of conditional probability contrary to all WP policy. Rick, in accordance with WP policy and natural justice, wants the article to give equal prominence to "conditional" solutions (as supported by by all the good sources), by including in the initial "solution" section an approachable solution to the actual question asked by showing the conditional probability the car is behind Door 2 given the player picks Door 1 and the host opens Door 3 is 2/3.

To wit: As to the actual academic literature, textbook-"conditional solutions" for use in maths classes on conditional probability theory never address the correct distinct scenario of the world famous paradox with its well-defined and exact certain information content, but address just only distant rarities of quite other scenarios, ignorably offside the well defined world famous paradox, just useful in training conditional probability theory in maths classes, yes in training pernicious, strange "conceited" additional information that give quite other "solutions". evidently just to train Bayes. All of that belongs not to the well defined and world famous paradox. All of that, if ever, belongs to a later section of ancillary information on Bayes, but never to the famous paradox. Please, Sunray, can you help me to make an appropriate proposal of logically consistent article-structure. Gerhardvalentin (talk) 00:21, 30 May 2012 (UTC)

You are not alone Gerhard when you say of the 'conditional solutions', "All of that, if ever, belongs to a later section of ancillary information on Bayes, but never to the famous paradox". I and many others agree with you.

Unfortunately a small minority insist that the 'conditional' obfuscation is given top billing and included right from the start of the article, making it incomprehensible and unconvincing to most first-time readers. My proposed compromise between the views held by you, me and the majority of editors and the views held by a small but persistent minority is being treated as my own extreme position rather than a major concession to the 'conditionalists' in an attempt to end the deadlock here. Martin Hogbin (talk) 08:36, 30 May 2012 (UTC)

Well, if you insist. :) Actually, you seem to agree that I have fairly accurately described your stance (per [20]). How, exactly, would you succinctly describe my stance?

You do not seem to understand the meaning of the word 'neutral'. Presenting the stance of 25 users as:

Martin Hogbin's stance
Not in agreement with the sources
POV
Contrary to WP policy
Not answering the actual question asked

and the minority stance as:

The natural choice of editors here
In full agreement with the sources
NPOV
Fully in accordance with WP policy
The only way to answer the actual question asked

when you know that I disagree with all of your assertions is so biased that I have to question whether this process can ever work. Martin Hogbin (talk) 08:50, 30 May 2012 (UTC)

I'm confused. You were being sarcastic. I acknowledged you were being sarcastic (see the smiley?). Are you saying the text you quoted after saying "Exactly as Rick says ..." does not capture the essence of your stance? I understand you're not happy with the text I suggested to capture my stance - so I asked how you would phrase it (succinctly). The two alternatives I suggested above are to 1) contrast your stance (avoid any mention of conditional probability in the initial sections of the article) with mine (give equal prominence to solutions using conditional probability), or 2) contrast your stance with its actual opposite (i.e. present a conditional solution as THE solution, with "simple" solutions discussed later as controversial approaches - which I believe is still Nijdam's preference) with my stance shown as a compromise where both approaches are given equal prominence with neither presented as more correct than the other.

If I have your stance incorrect, then by all means suggest something else. Since you clearly don't like the way I'm describing my stance, please suggest an alternative. Saying what my stance is does not mean you agree with it. And, BTW, it's definitely NOT that "the 'conditional' obfuscation is given top billing and included right from the start of the article, making it incomprehensible and unconvincing to most first-time readers". And, another BTW, you really need to drop the "25 editors agree with me" claim. As far as I can tell, even Gerhard (even Glkanter!) is not arguing the same thing you are. Per [21] all Gerhard seems to be saying is that the initial sections of the article should address the fully symmetrical problem. I agreed to this over two years ago [22]. I could put up a page and count him as on my side - and I honestly think he is. Actually, this is one reason I want you to write down what you think my stance is. From what you say, it seems to me you may not actually understand it. Perhaps I don't understand yours either since you keep saying your proposal is a "compromise", but I see no compromise whatsoever.

Are you seriously telling me that you cannot see what is not neutral with your proposed RfC statement, Martin wants the initial sections (solution, aids to understanding) devoted exclusively to "simple" solutions, specifically excluding any mention of conditional probability. Rick wants the article to give equal prominence to "conditional" solutions (as commonly presented by sources in the field of probability), by including in the initial "solution" section an approachable solution showing the conditional probability the car is behind Door 2 given the player picks Door 1 and the host opens Door 3 is 2/3?

Are you seriously refusing to provide your own description of what you think my stance is? Collaborating works better if more than one person participates. If you want me to suggest wordings until you're happy we might be here a while, but if you insist how about this? Martin proposes the initial sections including 'Solution' and 'Aids to understanding' be based exclusively on "simple" solutions (as presented by vos Savant and many, many other sources), specifically excluding any mention of conditional probability. Rick proposes the article give equal prominence to "conditional" solutions (as commonly presented by sources in the field of probability), by including in the initial "solution" section an approachable solution showing the conditional probability the car is behind Door 2 given the player picks Door 1 and the host opens Door 3 is 2/3?

Or, we could leave the "as presented by" for subsequent discussion, leaving something like Martin proposes the initial sections including 'Solution' and 'Aids to understanding' be based exclusively on "simple" solutions, specifically excluding any mention of conditional probability. Rick proposes the article give equal prominence to "conditional" solutions, by including in the initial "solution" section an approachable solution showing the conditional probability the car is behind Door 2 given the player picks Door 1 and the host opens Door 3 is 2/3.

Or, we could add something about what the "simple" solutions show (with or without a parenthetical about sources) like Martin proposes the initial sections including 'Solution' and 'Aids to understanding' be based exclusively on "simple" solutions showing the chances of winning by switching are 2/3, specifically excluding any mention of conditional probability. Rick proposes the article give equal prominence to "conditional" solutions, by including in the initial "solution" section an approachable solution showing the conditional probability the car is behind Door 2 given the player picks Door 1 and the host opens Door 3 is 2/3.

This might go faster if you'd provide at least a "warmer/colder" sort of indication.

Final attempt

The aim of this RfC is to resolve a longstanding and ongoing conflict involving many editors concerning the relative importance and prominence within the article of the 'simple' and the more complex, 'conditional' solutions to the problem. The 'simple' solutions do not consider which specific door the host opens to reveal a goat (see examples). The 'conditional' solutions use conditional probability to solve the problem in the case that the host has opened a specific door to reveal a goat (see examples).

The larger group of editors considers that the 'simple' solutions are perfectly correct and easier to understand and that the, more complex, 'conditional' solutions are an unimportant academic extension to the problem.

The other group believes that the 'simple' solutions are essentially incomplete or do not answer the question as posed and that the conditional solutions are necessary to properly solve the problem.

That argument is unlikely to ever be resolved but two proposals have been made to resolve the dispute. Both proposals give equal prominence and weight to the two types of solution.

One proposal to resolve this dispute is for the initial sections including 'Solution' and 'Aids to understanding' to be based exclusively on "simple" solutions (with no disclaimers that they do not solve the right problem or are incomplete) then to follow that, for those interested, with a section of equal prominence giving a full and scholarly exposition of the 'conditional' solutions.

The other proposal is for the article to include in the initial "solution" section "conditional solution showing the conditional probability the car is behind Door 2 given the player picks Door 1 and the host opens Door 3 is 2/3 Martin Hogbin (talk) 08:13, 31 May 2012 (UTC)

What do you mean by final attempt? Am I not allowed to edit this at all? Assuming I can, I would make the following changes (bold is only to show diffs):

The aim of this RfC is to resolve a longstanding and ongoing conflict involving many editors concerning the relative importance and prominence within the article of the 'simple' and the more complex 'conditional' solutions to the problem. The 'simple' solutions, as presented by vos Savant and many, many other sources, do not consider which specific door the host opens to reveal a goat (see examples). The 'conditional' solutions, as presented by many other sources, use conditional probability to solve the problem in the case that the host has opened a specific door to reveal a goat, for example the player picks Door 1 and the host opens Door 3 (see examples).

~~The larger~~ One group of editors considers that the 'simple' solutions are perfectly correct and easier to understand and that the, more complex, 'conditional' solutions are an unimportant academic extension to the problem.

The other group believes, as claimed by some sources, that the 'simple' solutions are essentially incomplete or do not answer the question as posed and that the 'conditional' solutions are necessary to ~~properly~~ solve the problem.

That argument is unlikely to ever be resolved but two proposals have been made to resolve the dispute. ~~Both proposals give equal prominence and weight to the two types of solution.~~

One proposal ~~to resolve this dispute~~ is for the initial sections including 'Solution' and 'Aids to understanding' to be based exclusively on 'simple' solutions (with no disclaimers that they do not solve the right problem or are incomplete, and no mention of conditional probability) then to follow that, for those interested, with a section ~~of equal prominence~~ giving a full and scholarly exposition of the 'conditional' solutions.

The other proposal is for the article to include in the initial 'Solution' section both one or more 'simple' solutions and an approachable 'conditional' solution ~~showing the conditional probability the car is behind Door 2 given the player picks Door 1 and the host opens Door 3 is 2/3~~ with neither presented as "more correct" than the other, and to include in some later section of the article a discussion of the criticism of the 'simple' solutions.

Other than what I hope are uncontroversial editorial changes, there are three basic changes here. One is to include a mention that numerous sources present both kinds of solutions with "many, many" presenting 'simple' and only "many" presenting 'conditional', and that the "anti-simple" belief reflects the view of "some" sources. The point is that the dispute here reflects a dispute in sources - it's not that some editors like or don't like certain solutions. The second is to delete your characterization of one group as being larger than the other. You're describing editors' POVs here - and frankly how many editors hold what POV is completely irrelevant to any Wikipedia process (even if your assessment of how many editors agree with you is correct). The third is to delete the claim that both proposals present 'simple' and 'conditional' solutions with equal prominence. I understand you seem to think that your proposal does this, but I think it manifestly does not.

Again, I don't know if by "final attempt" you mean you're unwilling to consider any changes - but these are the changes I'd suggest. -- Rick Block (talk) 19:42, 31 May 2012 (UTC)

The aim of this RfC is to resolve a longstanding and ongoing conflict involving many editors concerning the relative importance and prominence within the article of the 'simple' and the more complex 'conditional' solutions to the problem. The 'simple' solutions do not consider which specific door the host opens to reveal a goat (see examples). The 'conditional' solutions use conditional probability to solve the problem in the case that the host has opened a specific door to reveal a goat (see examples).

One group of editors considers that the 'simple' solutions are perfectly correct and easier to understand and that the, more complex, 'conditional' solutions are an unimportant academic extension to the problem.

The other group believes that the 'simple' solutions are essentially incomplete or do not answer the question as posed and that the 'conditional' solutions are necessary to solve the problem. Both sides ~~have sources supporting~~ claim sources support their views.

That argument is unlikely to ever be resolved but two proposals have been made to resolve the dispute. Both proposals aim to give equal prominence and weight to the two types of solution.

One proposal is for the initial sections including 'Solution' and 'Aids to understanding' to be based exclusively on 'simple' solutions (with no disclaimers that they do not solve the right problem or are incomplete) then to follow that, for those interested, with a section ~~of equal prominence~~ giving a full and scholarly exposition of the 'conditional' solutions.

The other proposal is for the article to include in the initial 'Solution' section both one or more 'simple' solutions and an approachable 'conditional' solution (showing the conditional probability the car is behind Door 2 given the player picks Door 1 and the host opens Door 3 is 2/3) with neither presented as "more correct" than the other, and to include in some later section of the article a discussion of the criticism of the 'simple' solutions.

By 'final attempt' I refer to this series of changes to agree a single statement. If we cannot reach agreement here I will drop my compromise proposal.

I have accepted some of your changes, including all that relate to your proposal. I have accepted none that relate to mine. I see no point in saying anything more about sources than 'Both sides have sources supporting their views'.

I say, '...aim to give equal prominence' now because I do.

Is there anything now that you cannot agree to? Martin Hogbin (talk) 22:43, 31 May 2012 (UTC)

I've taken the liberty of unbolding a portion you accidentally left in bold and made the "showing the conditional probability ..." phrase a parenthetical (it's kind of a long sentence - I think this might make it easier to read).

You do mean to exclude any mention of conditional probability in the initial sections of the article, don't you? Why do you not want to mention this?

I have agreed to call the 'Morgan style' solutions the 'conditional' solutions for reasons of neutrality and conciseness only. All solutions to the MHP are conditional, the dispute is actually about what exactly you take as your condition. To explain all this in the statement is too complicated and to suggest that your perferred solution is the only one to use conditional probability is misleading and biased.

I accept that you're "aiming" for equal prominence, but I completely disagree that you're achieving it. How about deleting "of equal prominence" in the description of the first proposal (as struck above) and letting whoever responds to the RfC decide for themselves whether each proposal meets this aim or not? Perhaps you mean "at the same heading level" (which I'd be OK with).

Of course you disagree with me about equal prominence but I think it is important to show that we both are trying to present compromises between the hard-line positions of 'only the conditional solutions are correct' and ' the simple solutions are the only right ones'. By saying 'aiming' we do as you suggest and leave the success of our aims to be judged by our responders.

Regarding sources, the way things are phrased now strongly suggests there are sources that say simple solutions are "perfectly correct" and that they are "easier to understand", and conditional solutions are "an unimportant academic extension to the problem". I don't mean to be difficult, but what sources are these, exactly? As far as I recall the only sources you've ever offered that in any way criticize "conditional" solutions are Seymann's comment following the Morgan et al. article, and the comments by Rosenhouse in his book. I'll agree with "perfectly correct", but I don't think either of these says anything like "easier to understand" or "an unimportant academic extension to the problem". I believe these are strictly your opinions, not opinions offered by (at least these) sources. Are there other sources you're thinking of? I understand the neutrality issue if the beliefs of one group of editors are explicitly said to be "as claimed by some sources" while the beliefs of the other group are not - but it's also not neutral to imply sources say things that they don't. If you could clear this up with references that'd be great. If not, then I think we're not quite done yet.

And, BTW, I appreciate the effort you're making here. We clearly have a deeply rooted disagreement that we're likely never going resolve, but I don't think that has to mean we can't work together.

I would be happy with any neutral statement along the lines that both sides claim that the sources support them or that the sources have been carefully considered but they have not enabled a resolution of the argument. I want to avoid users coming to the RfC and saying 'it is easy, just follow the sources'. Been there, tried that, did not work. I think it would be a bad thing to start the very complicated discussion of sources and exactly what each says in the RfC statement, so we should not mention specific sources or groups of sources. Martin Hogbin (talk) 08:54, 1 June 2012 (UTC)

Re conditional: Without a little more description of what constitutes a 'simple' solution your proposal seems kind of vague. I thought "no conditional probability" captures it pretty well. Just to clarify, I think you are proposing the words "conditional probability" would not appear in the initial sections. Is this right? And, similarly, I think you are proposing there must not be any table like the one I recently created at the talk page in this section (and, by extension, the tree diagram and large figure currently in the Decision tree section of the article), nor any enumeration or discussion of the 6 possible combinations of initial player pick and door the host opens. Also right? I'm not sure how to clarify this in a neutral way, but what I hear you saying (and I'm not trying to say this in a neutral way) is there must be no mention or implication that the case of interest is specifically player picks door 1 and host opens door 3.

I think my statement "The 'simple' solutions do not consider which specific door the host opens to reveal a goat" explains exactly what I mean. I have also suggested links to examples.

<slight digression> Would you be OK with a "Solution" section with a progression of solutions (with no hint any should be considered "better" than another) considering first the player picks "a door" and the host opens "a door", then second the player picks door 1 and the host opens "a door" (e.g. vos Savant), then third the player picks door 1 and the host opens door 3? The first two are what we're calling 'simple' and the third 'conditional', right? If you'd be OK with this we could maybe skip the whole RfC thing. Just a thought. (and, yes, I've suggested this before) </slight digression>

No! Of course not. That is exactly what I and many others are trying to avoid. Just as the reader is getting to grips with the simple explanation they are thrown into a pointless ad unnecessary complication. Martin Hogbin (talk)

Re equal prominence: "Aiming" is in the paragraph before the two proposals are listed. The "of equal prominence" I'm suggesting deleting is the one in the paragraph about the first proposal (which doesn't say "aiming" - it is asserting the follow on section is of equal prominence). This is not letting our responders decide.

I would be OK with 'at the same heading level' for the one on the first proposal.

Re sources: I've changed "have sources supporting" to "claim sources support". OK?

That is fine with me. Martin Hogbin (talk) 10:33, 3 June 2012 (UTC)

Possible draft and next steps

I think what we have at this point is this:

The aim of this RfC is to resolve a longstanding and ongoing conflict involving many editors concerning the relative importance and prominence within the article of the 'simple' and the more complex 'conditional' solutions to the problem. The 'simple' solutions do not consider which specific door the host opens to reveal a goat (see examples [23] [24]). The 'conditional' solutions use conditional probability to solve the problem in the case that the host has opened a specific door to reveal a goat (see examples [25]).

One group of editors considers that the 'simple' solutions are perfectly correct and easier to understand and that the, more complex, 'conditional' solutions are an unimportant academic extension to the problem.

The other group believes that the 'simple' solutions are essentially incomplete or do not answer the question as posed and that the 'conditional' solutions are necessary to solve the problem. Both sides claim sources support their views.

That argument is unlikely to ever be resolved but two proposals have been made to resolve the dispute. Both proposals aim to give equal prominence and weight to the two types of solution.

One proposal is for the initial sections including 'Solution' and 'Aids to understanding' to be based exclusively on 'simple' solutions (with no disclaimers that they do not solve the right problem or are incomplete) then to follow that, for those interested, with a section at the same heading level giving a full and scholarly exposition of the 'conditional' solutions.

The other proposal is for the article to include in the initial 'Solution' section both one or more 'simple' solutions and an approachable 'conditional' solution (showing the conditional probability the car is behind Door 2 given the player picks Door 1 and the host opens Door 3 is 2/3) with neither presented as "more correct" than the other, and to include in some later section of the article a discussion of the criticism of the 'simple' solutions.

I've added links to examples (permanent links to sections of specific versions of the article). I'm still somewhat concerned about the vagueness of proposal 1. Perhaps it won't affect the wording, but for my own understanding of your proposal can you answer the questions I asked above? I think it would be good to solicit comments on this wording as well. Assuming you don't object, we could add a link at the article's talk page (making it VERY clear we're soliciting comments on the wording, not on the issue). We also need to agree on the decision rules. Is there anything else we need to do before going "live" with this?

OK, let us go with that.

I suggest that we two (and maybe some of the other regulars) should have a limited number of words to support our proposals during the RfC and that all editors should be encouraged to express a simple preference for one of the options rather than give long expositions of their opinions. No other proposals should be accepted unless unanimously agreed (I am just allowing for the possibility that someone comes up with the perfect resolution). Maybe we could add words to this effect at the end of the first paragraph above.

We should do all we can to get the maximum number of users to respond and I would suggest that we set a minimum number for the result to be valid. It would not do the years of discussion justice for one side to win with just 2 votes to 1.

Regarding the decision rule we can discus that below.

I suggest that we can drop the font colours now. Martin Hogbin (talk) 21:19, 3 June 2012 (UTC)

Are you not going to answer the questions I asked above? -- Rick Block (talk) 05:11, 4 June 2012 (UTC)

What exactly do you think is vague about proposal 1.

No I do not think we should solicit comments on the wording, that would lead to endless further discussion and delay and the whole thing would end in disaster. So that no one feels left out we might ask if anyone else wants to add a short proposal (similar in length to the two given). Martin Hogbin (talk) 08:30, 4 June 2012 (UTC)

I think it's fairly clear you're suggesting the initial "Solution" section of the article only include solutions addressing Richard Gill's "Proposition 1" (from [26]), but that you don't want ("no disclaimers that they do not solve the right problem...") any discussion clarifying the difference between Proposition 1 and Proposition 3 (or anything that says the solutions in this section address Proposition 1 as opposed to Proposition 3). What's not clear is what you're suggesting be included in the "Aids to understanding" section. For example, the discussion that was in this version of the article shows a table enumerating possible outcomes given the player initially picks Door 1 where the host is opening specifically Door 2 or Door 3. Would this be "allowed", or not? The basic point is that without clear rules people responding may not know what they're being asked to decide between, and if there's consensus for your structure future editors may not know what is allowed to be put where. -- Rick Block (talk) 18:44, 4 June 2012 (UTC)

That is an interesting point but I am happy to leave it open for future editors to decide. The solution section should be as simple as possible. The objection of most editors is to solutions in which the host choice of door when the player has originally chosen the car (the Morgan solutions) is considered important. If in giving a more in depth explanation of why it matters that the host always reveals a goat in the, 'Aids to understanding' section, a consensus should arise to use the explanations you quoted then I would not object. It is the hosts choice of goat door which is irrelevant to the standard problem. Martin Hogbin (talk) 13:35, 5 June 2012 (UTC)

Decision rule

RfCs, like all content decisions for Wikipedia articles, are determined by consensus. Consensus is distinguished from majoritarian decision-making. Clearly consensus does not have to be unanimity, however, when the decision rule is not unanimity it is a supermajority. Two thirds or 75% are common supermajorities used in WP. I think we should settle on one of these. Sunray (talk) 01:45, 24 May 2012 (UTC)

I'd be fine with 2/3, which I suspect is closer to what Martin is wanting which seems to be 50%+1. With 2 proposals and for/against possibilities for each one I think we may need to be more explicit about what we're actually talking about. There are three comparisons that seem relevant:

1. (for #1) / ( for #1 + against #1)

2. (for #2)/(for #2 + against #2)

3. For #1 / (for #1 + for #2)

A clear consensus would be one of the first two of these and the third are both greater than 65%. If the head to head but not the for/against is greater than 65% then my guess is we didn't phrase the question in the right way. There are 8 possible outcomes. I guess we ought to enumerate them and agree about each one.

This is a very unusual situation. The dispute has been running for years and it is no nearer resolution that it ever was despite Arbcom intervention. All the time it is not resolved the article and its readers suffer and if this attempt at a solution fails I can see no prospect of any other solution working, especially if a supermajority is required for acceptance. Ultimately we should be acting in the best interests of Wikipedia and in working together to make it a better encyclopedia for all readers. If this requires us to accept a simple majority here than that is what we should do. My suggestion is that if more that half the valid votes support a proposal then it should be accepted.

One thing we should perhaps do is ask if anyone else wants to make proposal to resolve this dispute.

The dispute: This famous paradox (2/3 and not 1/2) is based on an accurate "problem description", and based on such correct description no conditional probability is "necessary" to make the correct decision asked for: to switch and not to stay. A clean split between the accurate scenario of this famous paradox and quite other scenarios is necessary to show respect for the readers. Such clear split has finally to determine the structure of the article that is not on conditional probability theory per se, but is on a counterintuitive paradox that just exists in an accurately fixed scenario only. See Distinguishing between different scenarios. --Gerhardvalentin (talk) 13:42, 24 May 2012 (UTC)

Gerhard, I meant that others might want to make a proposal for resolution of this dispute, not to comment here. If you do not support either of the two proposals here then you might make one of your own. Martin Hogbin (talk) 18:50, 24 May 2012 (UTC)

Your comment about arbcom is curious since the arbcom action was related to egregious user misbehavior making progress during mediation impossible, not the content dispute we're talking about here. The notion that we need to pick one of these alternatives, even without what would ordinarily be viewed as consensus seems fundamentally flawed to me. There are many, many ways to structure the article. If this RFC fails to show a consensus one possibility might be that we resume mediation.

You are correct that the Arbcom case was about user behaviour. You might also remember that two editors were sanctioned for page ownership. Regarding mediation it failed to get off the ground lasts time, what makes you think it will be different this time? Martin Hogbin (talk) 18:50, 24 May 2012 (UTC)

One thing you might agree with is that there should be a minimum number of editors responding to the RfC for the vote to be valid. Martin Hogbin (talk) 18:56, 24 May 2012 (UTC)

How about we just offer three options: for 1, for 2, neither, with a consensus if, for 1/(for 1 + for 2 + neither) > 50%? That makes the calculation easier and only assumes a consensus if on side has an absolute majority. Martin Hogbin (talk) 21:34, 3 June 2012 (UTC)

What justification, in policy, might we reference for deciding an RfC by a simple majority? Sunray (talk) 15:55, 5 June 2012 (UTC)

Is there any existing policy on the majority required? Martin Hogbin (talk) 21:50, 5 June 2012 (UTC)

The policy on consensus guides all editorial decisions. There are further guidelines that explain why polling for a majority is contrary to WP policy. Sunray (talk) 01:33, 7 June 2012 (UTC)

You are putting things a bit strongly when you say that the WP:POLL#Why regard polls with caution? states that polling is contrary to WP policy. I agree that polls should be treated with caution but in this case we have, over a period of several years, exhausted every other possibility. Martin Hogbin (talk) 08:29, 7 June 2012 (UTC)

One further point. I am not proposing a simple majority but an absolute majority; there is quite a difference. For a proposal to be accepted it will need to get more votes that the other proposal plus the 'neither' combined. Martin Hogbin (talk) 13:25, 7 June 2012 (UTC)

Perhaps I wasn't clear. I am saying that consensus is the way that decisions are made. That includes RfCs. Sunray (talk) 06:28, 8 June 2012 (UTC)

Yes, I have read the consensus article and we have tried everything. There is no clear indication of exactly what a consensus is or any statement that it is not a majority. In this particular case we would by justified in saying that an absolute majority represents a consensus. I should also point out that there is no consensus for the current version, it represents a stalemate but not, under the normal meaning of the word a consensus. There is no evidence that it is even supported by a majority. Martin Hogbin (talk) 15:33, 8 June 2012 (UTC)

As I've mentioned, we have not tried everything (for example, we could restart mediation). You are seeking to permanently impose a specific structure on the article, which in the opinion of several editors would make it violate NPOV. Rather than address this concern, you want to put it up for a community vote. IMO, such a decision should have a stronger consensus than majority. -- Rick Block (talk) 16:40, 9 June 2012 (UTC)

What percentage of editors you suppose support the current article?

In the interests of getting things moving and compromise, how about 60% of the total vote? Martin Hogbin (talk) 16:48, 9 June 2012 (UTC)

60% would be fine with a proviso that we can't declare consensus in favor of anything that a significant percentage (how about if you suggest a number) are saying violates NPOV. This implies either changing how the question is asked or asking more questions. For example, instead of

Do you favor proposal 1, proposal 2, or neither?

something like

Do you favor proposal 1, proposal 2, or neither? Also, please indicate whether you see an NPOV issue with either.

Regarding minimum number of respondents - how about 20? -- Rick Block (talk) 17:09, 10 June 2012 (UTC)

We would be very lucky to get 20 respondents although I fully support our making every effort to maximise the number. 10 might be a better number.

I can see no reason or logic for letting a minority of editors veto the consensus because they have mentioned a specific WP policy. There are many WP policies that might be raised as reasons for choosing one version over another and there is no justification at all for giving one policy precedence over all others.

The NPOV issue is in any case just a figment of your imagination. No one else has mentioned it regarding my proposal and you have never presented a cogent argument as to why organising an article like most other encyclopedia articles or good text books should be POV. Martin Hogbin (talk) 23:44, 10 June 2012 (UTC)

So, hypothetically, you'd have no problem making a change to the article that, say, 40% of the respondents thought made the article violate NPOV? I accept that you don't think your proposal introduces any POV issues but others HAVE agreed with me, you just refuse to listen us. If more than, say, 25% of the respondents said they thought your proposal was POV is that enough that you'd take this objection seriously? The justification for NPOV trumping nearly anything else is because it is one of the three fundamental content policies (WP:V and WP:NOR being the other two). If you think no one other than me would object based on NPOV grounds, what harm is there in naming a percentage like 25%? -- Rick Block (talk) 00:32, 11 June 2012 (UTC)

We have no right to make up new rules saying that one policy trumps another, especially when discussing a specific argument. If you feel really strongly that NPOV trumps all other rules then you should bring it up on the appropriate policy forum after this dispute is over.

We are both throwing our proposals to the mercy of WP users. If the majority of readers were to choose your proposal for what we both agree are stupid or invalid reasons, and even after a brief discussion they stick to their guns, that is too bad for me; your proposal is accepted. You are, of course, free to try withing the limits that we set, to persuade users that my proposal is sufficiently NPOV that they should not support it but if a user decides that there is a NPOV element to my proposal but, on balance they still prefer it, that is too bad for you. I cannot agree to rule-fixing at this stage. Martin Hogbin (talk) 08:18, 11 June 2012 (UTC)

We are making progress. Actually, determining consensus is not all that difficult. As the policy says: "decision-making involves an effort to incorporate all editors' legitimate concerns, while respecting Wikipedia's norms." The supermajority decision rule is a fall back position. I would say that 60% is minimal. Though I've participated in consensus decision-making in a variety of settings, I've never actually seen the bar set that low. A higher supermajority makes it easier to determine a stable consensus. It is the role of the individual picked to determine consensus to attempt to incorporate all concerns. If you want me to play that role, and you are both in agreement with the question and the decision rule, I'm willing to do so. Sunray (talk) 18:41, 10 June 2012 (UTC)

Sunray, are you saying that you would be prepared to close the RfC on the basis of a 60% majority, if agreed here?

I am still not sure what the logic is for ignoring the many editors over the years who have supported a much stronger position than my compromise against the 'conditional' solutions. A consensus is not meant to me a snapshot taken at one instant. A 60% preference at the RfC plus over 3:1 majority over the history of the article for a more extreme position must surely constitute a clear and enduring consensus. Martin Hogbin (talk) 23:51, 10 June 2012 (UTC)

Martin, the concern you express seems to illustrate why consensus is usually far higher than 60 %. Sunray (talk) 08:20, 12 June 2012 (UTC).

Sunray - can you comment on the discussion above about the primacy of WP:NPOV, WP:V, and WP:NOR relative to other Wikipedia policies? It sounds to me like Martin is not understanding what it means for these to be the "fundamental" content policies. -- Rick Block (talk) 04:11, 12 June 2012 (UTC)

When I say "legitimate concerns" I mean concerns raised with respect to WP policies. Sunray (talk) 08:20, 12 June 2012 (UTC)

Just as we are reaching agreement, Rick pulls a special rule out of a hat which allows users who agree with him to veto a supermajority decision. I understand and support the relevant WP policies but that does not justify this form of veto and I am not willing to participate such in a process. Martin Hogbin (talk) 08:36, 12 June 2012 (UTC)

Martin Hogbin (talk) 08:36, 12 June 2012 (UTC)

Martin - if you want to roll everything into a single decision, that's fine but then I'll have to insist on an actual consensus of something like 75%. You seem to think this is simply a matter of personal preference between structure A and B that are more or less equivalent except regarding how easy they are to understand. I do not agree that this is the case. How about two simultaneous rfcs, one addressing whether there is an NPOV issue here and the other picking between the two suggested structures. If NPOV is not an issue like you claim then there should be a strong consensus indicating this. -- Rick Block (talk) 15:58, 12 June 2012 (UTC)

Rick you are just trying to rig the vote with a special rule that you proposed only a few days ago. I am not trying to roll anything into anything, that was the basis on which we started this discussion, if you remember, a single RfC statement. It was your idea, which I reluctantly agree to. After we arrived at an agreed statement you threw in a special rule which would allow supporters of your bogus POV argument to veto a supermajority decision If users have legitimate concerns about my proposal relating to WP policy they will not support it; it is as simple as that. Martin Hogbin (talk) 18:01, 12 June 2012 (UTC)

Martin, I don't understand what you mean when you say "trying to rig the vote." I don't read what Rick is saying that way, at all. As I've said, Wikipedia editorial decisions are made by consensus. On the other hand, voting is deprecated. Consensus involves considering all legitimate concerns (such as a concern based on WP policy). If we were to use a supermajority, it would be a fall back position. That is why the bar should be set fairly high. The WP article on supermajorities is misleading in that it implies that 60% is acceptable. The example given, though, is not from a consensus decision-making environment, but rather a legislative one. Legislatures in the English-speaking world use Robert's Rules of order, which is majoritarian. I hope this is clear.

Rick, I understand Martin to be saying that the purpose of you two being here is to write an RfC statement. One RfC, not two. I am simply trying to help the two of you work out a process that will have some chance of success.

Given the complexity of this discussion about the MHP, I'm thinking that we may need a subject matter expert well-versed in WP policy to advise whoever is moderating the RfC. Would the two of you be able to agree on someone who might fit that role? Sunray (talk) 18:57, 12 June 2012 (UTC)

Sunray, thank you for your attempt to help but it has unfortunately failed.

The article that you refer to, which I had not read before, contains, 'In the United States Senate, a three-fifths majority is required to bring out a vote of cloture, to end a filibuster'. We would do well to follow their example here.

I do not think that there is any point in continuing this discussion. Maybe we should go back to Arbcom. Martin Hogbin (talk) 19:24, 12 June 2012 (UTC)

The U.S. Senate goes by their rules, we must follow WP policies. Arbcom does not seem to be an option at this point. They deal with behavioral violations, not content disputes. Sunray (talk) 21:42, 12 June 2012 (UTC)

I think Sunray means Arbcom is not an option at this point. I'm puzzled why Martin is saying this has failed, or that I'm introducing new rules. I think I've been pretty consistently talking about NPOV for at least two years. I've even quoted this from wp:npov before: The principles upon which this policy is based cannot be superseded by other policies or guidelines, or by editors' consensus. Surely the threshold for a decision to do something that anyone claims would violate NPOV should be quite high. I think we've made enough progress here that whether Martin agrees or not we may want to go ahead with the RFC with normal closing rules (i.e. consensus). -- Rick Block (talk) 06:21, 13 June 2012 (UTC)

Whether Arbcom is an option or not is up to Arbcom. I may approach then to see what they think.

You have indeed been pretty consistent with your bogus NPOV argument for at least two years.

We should indeed follow WP policy and avoid anything that is POV in WP but, fairly obviously, that is not the same as 'something that anyone claims would violate NPOV'.

Who is 'we' above? I do not want to go ahead with an RfC based on a bogus POV argument. I guess you are free to do so but you do have an obligation to present the arguments in a neutral manner. Bearing in mind that you have been sanctioned for page ownership by Arbcom and you still improperly trying to pass off my proposed compromise as POV I doubt that this will be possible. Martin Hogbin (talk) 09:13, 13 June 2012 (UTC)

"We" would be Sunray and I. You are of course free to approach arbcom with whatever you'd like - I was simply correcting Sunray's obvious typo. IMO your notion that my POV concern is bogus simply reflects how deeply attached you are to your own POV. How you can continue to deny that this is a POV issue completely baffles me. -- Rick Block (talk) 05:32, 14 June 2012 (UTC)

Closing discussion?

It looks like the discussion has stalled. We don't seem to be much closer to a viable RfC statement. Without agreement on the basic terms of an RfC statement, I don't believe we can go much further. I've I'm missing something, please let me know. Otherwise, I think we should close. Sunray (talk) 08:36, 1 June 2012 (UTC)

I think we have actually made some progress in the past couple of days, and that it would be useful to continue. It looks to me like we could have an agreed version of the RfC statement by the end of the weekend. We haven't gotten very far with the decision rule part of this yet. -- Rick Block (talk) 14:01, 1 June 2012 (UTC)

Evidently I did miss something! By all means please continue. :) Sunray (talk) 19:16, 1 June 2012 (UTC)

Where are we?

I think we have what Martin and I essentially agree is a neutral statement for an RFC. Seems like we hit a snag attempting to agree on a decision rule. Martin wants a 60% majority to be taken as consensus, while I've suggested that since one of the alternatives creates what IMO is an NPOV violation the consensus should be considerably stronger (like 75%). I've suggested separating the NPOV concern as its own issue. It appears Martin is refusing to participate in this discussion any further.

Martin - is this correct (I guess silence should be taken as agreement)? -- Rick Block (talk) 03:52, 18 June 2012 (UTC)

What you call NPOV violation is an obvious attempt to rig what should be a straight choice.

1 There are very few, if any, sources which clearly state that for the standard interpretation of the problem (in which the host is defined to open an unchosen goat-hiding door uniformly at random) we must take into account which door the host opens in order to get a (numerical) solution to the problem. The disagreement is therefore one between editors of WP and not sources and thus not covered by WP:NPOV.

2 You suggestion was that if a lesser (than the agreed supermajority) fraction of editors thought that there was an NPOV issue, which happens to be your opinion, this should override the consensus. In other words, if a minority of editors raise the NPOV issue, even if the great majority believe that there is no such issue, the minority will have the power to veto the majority.

3 You have never presented any cogent argument as to how using the structure used in most technical, mathematical, and scientific text books can be assumed to be supporting a POV. There are crazy people who think that Einstein's theory of relativity is wrong and Newtonian physics is is perfectly correct but no one has ever suggested that a mechanics book that starts with pure Newtonian mechanics and then proceed to relativity is in any way promoting the POV of these crazy people. If there is any POV promotion going on here it is by you.

4 You brought up the issue of a POV veto right at the last minute ~~as what now seems to be a tactic to insist upon an unrealistically large supermajority.~~ perhaps you would be kind enought to explain why you did this. I have already moved substantially from my original absolute majority position. We both want a resolution of this dispute and setting unrealistic demands will fail to achieve this.

5 You are ignoring the fact that my proposal is a compromise between your position and a clear and continuing supermajority of editors who believe that the Morgan-style solutions should have much lower prominence within the article. If my proposal were to be accepted I would probably find myself having to defend it against hard-line simplists. Continuing to ignore the opinions of other editors in this way is WP:page ownership.

So to explain my position, I have no interest in continuing an endless discussion with you that fails to ultimately help improve the article. I have moved a long way from my original stance that the Morgan-style solutions do not answer the question asked and are merely an academic diversion just in the hope that this dispute can be ended. You have not changed your position at all, you are still promoting the 'combined solutions' concept that you started with. Martin Hogbin (talk) 09:34, 18 June 2012 (UTC)

Martin - it is the nature of POV disputes that those involved see things differently. What I'm proposing is a compromise between a) your stance (which AFAICT you have never varied from) that 'simple' solutions should be presented as if they are the undisputed, correct approach to fully explain the MHP, and b) the actual opposing stance (which I was arguing for at one point, but changed long ago in favor of a neutral presentation) that the 'simple' solutions are deficient and the MHP should be explained in terms of the conditional probabilities in a specific case, such as that of a player who has initially picked door 1 and has then seen the host open door 3. Your stance reflects the (implicit) POV of a large number of sources. The opposing stance (again, NOT what I'm proposing for the article) also reflects the implicit POV of a large number of sources (those presenting conditional solutions without commenting on 'simple' solutions) as well as the explicit POV of a smaller number of sources. The compromise I'm suggesting is to present both 'simple' and 'conditional' approaches, as equally valid. How you can deny that this is a compromise, or that there is a POV issue among sources is beyond me.

Sunray - once again, any ideas for how to proceed? -- Rick Block (talk) 19:48, 18 June 2012 (UTC)

Rick, as you have not meaningfully addressed any of the points raised above I do not propose to continue this discussion. Martin Hogbin (talk) 20:05, 18 June 2012 (UTC)

Martin - I'm not the unreasonable ogre you are making me out to be. Once upon a time, I argued the very same things you are arguing (start reading about here in the archives). Unlike you, however, I listened to the arguments presented by an anonymous (!) user and strove to include his (assuming it's a him) views in the article. In hindsight, this version of the article (the version following the last successful FAR) is perhaps not NPOV, but the fix is definitely not to roll it back to this version (the version following the previous FAR). The fact is there are a significant number of sources, not just Morgan et al., who say 'simple' solutions are not adequate. For the article to start with an extended section including only 'simple' solutions, presented as if they are the undisputed, correct approach fully explaining the MHP (IMO) means the article is not NPOV.

It's obvious you don't agree with this. How about if we ask whether there's an actual community consensus either way? Since this question is not a matter of personal preference, but rather a matter of fundamental Wikipedia policy, "consensus" here should clearly mean a VERY strong consensus. I'm at least as tired as arguing with you about this as you are with me. The reason I'm still at it is because I very strongly believe in Wikipedia's core content policies. I'm not sure what your motivation is here. -- Rick Block (talk) 06:56, 19 June 2012 (UTC)

Sunray - Any ideas for how to proceed?

-- Rick Block (talk) 03:52, 18 June 2012 (UTC)

I guess I'll think about creating an RfC specifically to resolve the issue of whether the structure Martin is proposing is NPOV. It seems a little silly to do this and then (assuming there's a strong consensus it is) to initiate another RfC asking "which one of the following structures do you prefer", so perhaps following up the NPOV question with a preference question is the way to go. Perhaps the statement we've worked out here will do, with something like the following questions:

1) Do you agree or disagree that both of these proposals satisfy NPOV (if you disagree, please explain)? Please limit your response to no more than 500 words.

2) If you agree both satisfy NPOV, do you prefer proposal 1, proposal 2, or neither?

What this does is resolve the NPOV issue first. If, as Martin claims, this concern is completely bogus there should be a strong consensus that both proposals satisfy NPOV. On the other hand, if there is not a strong consensus about this then I hope Martin would be willing to work on a more neutral proposal satisfying his concerns about understandability of the article.

Sunray - does this seem like a reasonable way forward?

Martin - you're welcome to comment as well, but given your comments above I'm not expecting you to. -- Rick Block (talk) 19:16, 21 June 2012 (UTC)

Well, it is one way to go, no doubt. Another would be to get an opinion from the NPOV Noticeboard. You may have already done that, but if not, I could see it as being one in a series of steps towards getting resolution. Sunray (talk) 08:11, 23 June 2012 (UTC)

We tried NPOV noticeboard a long time ago [27]. We didn't get a single response. -- Rick Block (talk) 16:57, 23 June 2012 (UTC)

Maybe there was a good reason for that? Martin Hogbin (talk) 21:49, 23 June 2012 (UTC)

I know what you're implying, but I think Glkanter's disruptive comment basically telling people there not to bother was the direct reason. -- Rick Block (talk) 22:43, 23 June 2012 (UTC)

Per feedback from Ningauble, perhaps a single question like

Do you prefer proposal 1, proposal 2, or neither? Consider all Wikipedia policies and guidelines, in particular WP:NPOV and WP:Technical, and please limit your response to no more than 500 words.

might be preferable. I think this hits the basic disagreements in a reasonably neutral manner. Anyone watching this page is welcome to comment. If no one comments by, say, Monday (of course Martin will interpret this not to mean Monday in particular, but rather any day of the week that we're calling Monday - to be clear, if you comment on, say, Tuesday, you'll be too late), I'll initiate an RFC with the statement and question as above. I'm perfectly willing to let Sunray (or any administrator) close this RFC using whatever criteria he/she thinks is reasonable. -- Rick Block (talk) 04:13, 24 June 2012 (UTC)

It would be reading too much into my remarks to suggest, as your post might be taken as doing, that I have endorsed framing the question thusly. Such was not my intent, and I apologize if my remark about problems with question (1) may have been so vague as to give the impression of expressing an opinion about question (2). (I had not thought this was the case because, subsequent to my remarks and prior to your post above, you asked me directly.[28] I have not yet responded to your latter inquiry, and will endeavor to do so when I have collected my thoughts.) ~ Ningauble (talk) 20:21, 24 June 2012 (UTC)

I am perfectly happy with, 'Consider all Wikipedia policies and guidelines' but I see no reason why we should draw special attention to guidelines you think support your proposal.

I would only accept closure in the basis of a count of opinions stated in the RfC. To accept a decision by a passing admin based, 'on the strength of the arguments' give would be absurd. It would be like asking a passer by to look at all the arguments for and against the existence of God and make a final decision on the matter based on the strength of those arguments; the final decision would depend entirely on who happened to be passing by.

If Sunray is happy to accept the task of assessing consensus based only on the views expressed in the RfC that might be a way forward. If we end with no consensus then we will have to continue to argue for other resolutions.Martin Hogbin (talk) 11:22, 24 June 2012 (UTC)

I'm drawing attention to the policy that I think is at issue, and the guideline you think is at issue. Seems pretty neutral to me. If you're going to insist on a count, I'm going to insist it be a strong consensus, like 75%. -- Rick Block (talk) 18:02, 24 June 2012 (UTC)

I have never based my argument on WP:Technical why not drop both policies from the question and let the users decide for themselves if any policies have been broken.

Regarding your 75% requirement, reviewing the history of the talk page, do you think that there is any realistic possibility that 75% of the editors will support your position? I seriously doubt that, which makes your 75% requirement just a spoiling tactic to prevent any kind of conclusion to this dispute. Martin Hogbin (talk) 21:41, 24 June 2012 (UTC)

You've never based your argument on WP:TECHNICAL? Must be some other Martin Hogbin who made these edits: [29] [30] [31] [32]. If we're going to be hurling bad faith accusations around, I might say your insistence that NPOV not be mentioned is just an attempt to avoid a discussion you might find uncomfortable. For me, the whole point of this RFC is to determine whether the community agrees with you that my POV concern here is bogus. If there is a strong consensus, I will drop this argument. Either way, the RIGHT thing for you to do would be to try to address the concern I'm raising. The fact that you absolutely refuse to do this makes me strongly suspect that your actual intent here is not what you claim. -- Rick Block (talk) 22:57, 24 June 2012 (UTC)

I have not based my argument around WP:Technical although I do agree that it does indeed support my proposal. The idea came from text books.

Regarding addressing your concerns, that is exactly what I did in my five points above, which you completely ignored. That is why I stopped discussing the matter with you any more. If you want to have a good faith discussion on the subject that is fine with me but you will need to respond to the five points that I made above. You could also respond to my last question, 'Do you think that there is any realistic possibility that 75% of the editors will support your position?'. Martin Hogbin (talk) 08:19, 25 June 2012 (UTC)

By "address my concerns" I mean change your proposal to address my concerns, not argue with me. This was my reply to your points 1,3, and 5 above. Is there anything not clear about this? Points 2 and 4 seem like little more than oblique personal attacks, so I ignored them. I don't know if either proposal will be supported by 75% of the respondents, but I think we'll find out soon. -- Rick Block (talk) 14:29, 25 June 2012 (UTC)

Of course I am not going to change my proposal to suit you. This whole discussion has been about two different proposals on which we cannot agree.

I cannot see how you have addressed points 1,3, and 5 by what you have written. Perhaps you would give a response below each section so that we can discuss things.

I cannot see anything in point 2 that might be though of as a personal attack . Perhaps you could read it again respond.

I am sorry of the wording of point 4 was a bit harsh. I will change it. Martin Hogbin (talk) 18:14, 25 June 2012 (UTC)

I'm sorry, but I cannot see how continuing to discuss this here would have any value. -- Rick Block (talk) 05:04, 26 June 2012 (UTC)

So why do we not go with:

''Do you prefer proposal 1, proposal 2, or neither? Consider all Wikipedia policies and guidelines, and please limit your response to no more than 500 words.

We do not need to lead WP users by the nose to the policy that we might think supports our position. Sunray would you be willing to officiate on this basis? Martin Hogbin (talk) 08:56, 26 June 2012 (UTC)

We don't go with that because it strongly implies the only issue here is one of personal preference. The point is not which presentation people prefer, but which is best for this Wikipedia article in consideration of the WP:NPOV policy and WP:Technical guideline (and any other policies or guidelines anyone might think are relevant, but I really can't think of any that have anything to do with the issue at hand). A consensus based on personal preference, no matter how strong, cannot override WP:NPOV. NPOV MUST be considered, and if we're not going to separate it out as its own issue we need to at least explicitly mention it. -- Rick Block (talk) 15:20, 26 June 2012 (UTC)

We say, 'Consider all Wikipedia policies and guidelines.' There is no need for that really because editors should always consider WP policies and guidelines. You will also of course be free to state that you think there is a POV issue during the RfC. Martin Hogbin (talk) 19:33, 26 June 2012 (UTC)

I've asked Sunray if he might be able to help. My stance is that without mentioning NPOV in the question, this RfC will not address what I have been saying for over two years is the primary issue with Martin's proposal. This is not "Martin likes his approach" vs. "I like my approach" - it's "Martin likes his approach" vs. "I think Martin's approach violoates NPOV and suggest an alternative (which is wholely unlike what my approach would actually be)". -- Rick Block (talk) 15:57, 27 June 2012 (UTC)

I think there is no POV issue. You are of free to state that you think there is a POV issue during the RfC but that is your opinion and it must not be presented in the RfC statement, which should be neutral and not favour one proposal over the other.

If you are going to continue to insist that your opinion should form part of the RfC statement then I am not interested in going any further, and the record will clearly show why. Martin Hogbin (talk) 20:55, 27 June 2012 (UTC)

It seems to me that a process for clearing up the NPOV question would be helpful. Awhile back I suggested getting an opinion from the NPOV noticeboard. Rick responded that this had been tried but there had been no response. Perhaps if you worked on how the question was framed, it would increase the likelihood of a response. If there was still no response, you could do an RfC on that specific question. What do you think? Sunray (talk) 23:56, 27 June 2012 (UTC)

"you could do an RfC on that specific question" - as I've said, IMO that's the principal thing we're doing here. There isn't any universe in which I'd argue about "this structure" vs. "that structure" for two years without some fundamental principle being at stake. -- Rick Block (talk) 03:39, 28 June 2012 (UTC)

The place to start with the NPOV question is discussion but Rick resolutely refuses to address my arguments above. Martin Hogbin (talk) 07:20, 28 June 2012 (UTC)

Your insistence on having NPOV in the RfC statement would be like my insistence in having 'page ownership' in the statement. Let us just keep it neutral, as agreed at the start. Martin Hogbin (talk) 11:58, 28 June 2012 (UTC)

Lets be clear who's refusing to do what. I refused to engage in further pointless arguing, taking you at your word that you absolutely refused to change your proposal to address my POV concerns ("Of course I am not going to change my proposal to suit you."). If you insist, how about

Proposal 1, Proposal 2, or neither?

Considering all Wikipedia policies and guidelines, in particular WP:NPOV, WP:Technical, and WP:OWN, do you favor Proposal 1, Proposal 2, or neither. If you choose to include extended comments in a section below, please create your own subsection and limit your comments to no more than 500 words.

This seems extraordinarily odd to me (NPOV and Technical are content issues, while OWN is a behavior issue), but if it makes you happy I'd be OK with this. -- Rick Block (talk) 14:41, 28 June 2012 (UTC)

Or, how about if we get another opinion about whether it's appropriate to include NPOV in the question from, say, User:Elen of the Roads? -- Rick Block (talk) 19:02, 28 June 2012 (UTC)

I've asked her. -- Rick Block (talk) 19:18, 28 June 2012 (UTC)

Please let me know if I can do anything to help, otherwise I will go back to reading without commenting. --Guy Macon (talk) 19:43, 28 June 2012 (UTC)

(You mean there's more than just me lurking over here in the darkness? : )

I'll be happy to comment if you would like, but I need to re-read all this a couple times I think. Because I'm missing why RB wants the higher threshhold (75%). - jc37 22:03, 28 June 2012 (UTC)

From the amount of stuff I had to read doing the RfAR, I seem to recall that the original problem wasn't conditional in its expression, but as soon as the mathematicians moved in, they started tossing in the "does it make a difference if Monty is standing in a kitchen sink" and lost me at that point. I suspect that there are probably no more than six Wikipedia editors who can understand the gist of the argument as you guys have presented it, and they've been arguing it round for years. If you guys were physicists, you'd just agree that the simple answers are approximations that are true on a macro scale only (<--Quantum joke).

In terms of the RFC, POV/NPOV features frequently in RFCs. One man's terrorist is another man's freedom fighter after all. But I think is only a "POV issue" because you have opposing POVs, not because it's impossible to reconcile differing POVs in the real world (like arguments over Gibralter for instance). I also think that trying to set % terms for a 'vote' are futile. This isn't a policy RFC, this is a content RFC, and the closer will go with whatever seems most likely to get a compromise. Between you (and I'm sure unintentionally) you have written the terms of this RfC to exclude anyone except the aforementioned half dozen who understand what you are talking about and I don't think telling those guys to bear the word salad in mind will really achieve much.

I appreciate that this is probably not helping, but if you could phrase the question in a different way, you could perhaps get more input from the general readership. If you could explain that there are many 'rough and ready' answers which work well enough to satisfy the general reader (the "thousand doors" explanation for example is completely analogue - it's not mathematical at all), and there are answers at undergraduate level that use mathematical language and notation, but the serious mathematicians pooh pooh all of these - to the extent of saying most are wrong or rubbish or both - and advance the most erudite theoreticals, so how should this be represented in the article, perhaps you might get more opinions from general editors to throw in the mix. Perhaps not. I just think that presenting it as a POV problem is too recherche. Elen of the Roads (talk) 22:30, 28 June 2012 (UTC)

Elen, tell me if I am misunderstanding you but it looks to me as though you agree with me about most things. The reason that the Monty Hall problem is so well known is that most people, from all walks of life, initially think the answer is 1/2 and not 2/3. Many also find it hard to believe that it matters that the host knows where the car is. The great majority of editors here, including myself agree and consider the 'conditional solutions' argument to me an academic sideline. I say 'academic sideline' but in fact it is not even that, there has been no serious academic discussion of the subject at all and the few secondary sources that mention the issue make rather vague and equivocal statements on it. So, when you say, 'the serious mathematicians pooh pooh all of these', even that is not true, serious mathematicians have much better and more interesting things to do. In reality, there no points of view on the subject in academia or in the sources. The only different points of view are between the 5 editors here who have steadfastly clung to the opinion that the 'conditional' solutions are the only correct ones and pretty well everyone else who has ever commented here.

My proposal is to do what most good books and encyclopedia articles do, which is to give the simple stuff first and full cover what makes this problem so remarkable then to give a full and scholarly description of the 'conditional' solutions. I really cannot see how anyone could call this POV.

I am a physicist by the way. Martin Hogbin (talk) 16:41, 29 June 2012 (UTC)

Quotes from critical sources

Whether you've read these sources or not, I know you've seen these quotes before:

"Ms. vos Savant went on to defend her original claim with a false proof and also suggested a false simulation" [33]
"This [vos Savant's solution] is an elegant proof, but it does not address the problem posed, in which the host has shown you a goat at #3. Instead it is still considering the possibility that the car is at #3-whence the host cannot have already opened that door (much less to reveal a goat). In this game-you have to announce before a door has been opened [emphasis in the original] whether you plan to switch." [34]
"any proposed solution to the MHP failing to pay close attention to Monty's selection procedure is incomplete"[35]
(about vos Savant's solution) "what could and should have been a correct and enlightening answer to the problem was made unconvincing and misleading" [36]
"This solution [the 1/3 chance the car is behind the initially chosen door does not change because you know the host will open a door showing a goat] is actually correct, but I consider it shaky" [37]

They're obviously sources, and certainly seem to be expressing a POV (that "simple" solutions are deficient - which, again is not the POV I want the article to take, but I don't want the article taking the opposite POV either). Would you care to explain your comment that "In reality, there no points of view on the subject in academia or in the sources"? Perhaps "in reality" means something different to you than it means to me. -- Rick Block (talk) 19:48, 29 June 2012 (UTC)

So, based on the below, "in reality" apparently means "ignoring sources I disagree with". The POV is not that the simple solutions are wrong (which no one is claiming) - it's that they are deficient. The POV expressed by these (and other) sources is that simple solutions come up with the right answer (2/3 chance of winning by switching), but they answer a different question than most people think the problem is asking (i.e. they're "correct, but ... shaky", or they're "misleading", or they're "incomplete", or they do not "address the problem posed" or they are [most bluntly] "false"). This can be shown by (admittedly artificially) creating a variant of the original problem where they produce the wrong answer. The POV of these sources is that "simple" solutions (correctly) address the question of whether a strategy of switching is better than a strategy of staying (which no reliable source disputes), but that this is not the same as addressing the question of whether it's best for a player who's initially picked Door 1 and has seen the host open Door 3 should switch. And it's worth noting the latter is how nearly everyone (according to Krauss & Wang) interprets the question. Once again, I'm not arguing that the article MUST endorse this POV, but that it MUST NOT endorse the opposite POV (i.e. that "conditional" solutions are of academic interest only). -- Rick Block (talk) 05:18, 30 June 2012 (UTC)

Discussion of the sources

Whether you've read these sources or not, I know you've seen these quotes before

Good to see that you at last willing to discuss what the sources actually say, and about what exactly they say it about. Martin Hogbin (talk) 20:35, 29 June 2012 (UTC)

As anyone following this discussion knows, we've talked about these sources innumerable times before. Your implication that I've never been willing to discuss what sources say is simply a Big Lie (which is going to be sort of a theme here). -- Rick Block (talk) 06:29, 30 June 2012 (UTC)

Firstly, I do not think those quotes and their sources represent a significant body of academic opinion that the simple solutions are wrong. But let us look at them in more detail anyway. Martin Hogbin (talk) 20:35, 29 June 2012 (UTC)

Right. You dismiss them since you don't agree with them. Virtually the definition of POV. -- Rick Block (talk) 06:29, 30 June 2012 (UTC)

I do not dismiss them completely but I contest that a small number of of papers that make rather unlear criticism of the standard problem represents a significant body of opinion. Martin Hogbin (talk) 08:41, 30 June 2012 (UTC)

Morgan et al

"Ms. vos Savant went on to defend her original claim with a false proof and also suggested a false simulation" [38]

I am fairly familiar with this one. Morgan et al address the problem in which the host's choice (of an unchosen goat-hiding door) is not defined to be uniform; that is not the standard problem.

Later on, as you know, the authors graciously and admit their error in formulating the problem and all but withdraw their original claims. 20:35, 29 June 2012 (UTC)

Yet another Big Lie. They admit their error in computing the Bayesian probability with an uninformative prior. They also say "to wit, had we adopted conditions implicit in the problem, the answer is 2/3, period". Interpreting this to mean they "withdraw their original claims" is sheer fantasy - see user:Coffe2theorems comment about this. -- Rick Block (talk) 06:29, 30 June 2012 (UTC)

How would you interpret this comment then? What do you understand by, 'conditions implicit in the problem'?

Gillman

"This [vos Savant's solution] is an elegant proof, but it does not address the problem posed, in which the host has shown you a goat at #3. Instead it is still considering the possibility that the car is at #3-whence the host cannot have already opened that door (much less to reveal a goat). In this game-you have to announce before a door has been opened [emphasis in the original] whether you plan to switch." [39]

Lucas

"any proposed solution to the MHP failing to pay close attention to Monty's selection procedure is incomplete"[40]

This clearly refers to the possibility that Monty does not choose an unchosen goat-hiding door uniformly, the authors refer to a variant that they call 'High-Numbered Monty'

Right. The variant unequivocally shows that "any proposed solution ... failing to pay close attention to Monty's selection procedure is incomplete" - meaning any "simple" solution as you've defined them. -- Rick Block (talk) 06:29, 30 June 2012 (UTC)

Yes, but only in the case that the host does not choose evenly. Martin Hogbin (talk) 08:31, 30 June 2012 (UTC)

Eisenhaeur

(about vos Savant's solution) "what could and should have been a correct and enlightening answer to the problem was made unconvincing and misleading" [41]

That is just a cite of Morgan. The paper proceeds to say that the simple solutions relay on an 'unstated assumption'. That assumption is, of course that the host chooses uniformly, which is the case in the standard version of the problem. Martin Hogbin (talk) 20:35, 29 June 2012 (UTC)

Indeed. Like Lucas says, "any proposed solution ... failing to pay close attention to Monty's selection procedure is incomplete". Eisenhauer says "misleading", but he's making EXACTLY the same point. Lucas and Eisenhauer are both saying the "simple" solutions - meaning any "simple" solution as you've defined them - are deficient. -- Rick Block (talk) 06:29, 30 June 2012 (UTC)

No, Eisenhaeur says that the simple solutions are based on an 'unstated assumption'. However, that unstated assumption is now generally taken to be part of the standard formulation of the problem.

Rosenthal

"This solution [the 1/3 chance the car is behind the initially chosen door does not change because you know the host will open a door showing a goat] is actually correct, but I consider it shaky" [42]

This is exactly what I was talking about when I said that secondary sources were equivocal. You can hardly call a statement that starts: 'This [simple] solution is actually correct...' evidence that there is a significant body of opinion calling the simple solutions incorrect!

The meaning here is obvious, and no less an authority than Jeff Rosenthal himself has clarified it [43]. Your continued insistence that this is unclear is yet another Big Lie. Here are his exact words "I would say that the Shaky Solution can be 'made' to be correct, but only by providing a clear justification for why this conditioning does not change the probabilities; without such justification, the solution is incomplete and insufficient". -- Rick Block (talk) 06:29, 30 June 2012 (UTC)

The justification is simply an obvious and intuitive symmetry in the problem. Martin Hogbin (talk) 08:41, 30 June 2012 (UTC)

Discussion

They're obviously sources, and certainly seem to be expressing a POV (that "simple" solutions are deficient - which, again is not the POV I want the article to take, but I don't want the article taking the opposite POV either). Would you care to explain your comment that "In reality, there no points of view on the subject in academia or in the sources"? Perhaps "in reality" means something different to you than it means to me. -- Rick Block (talk) 19:48, 29 June 2012 (UTC)

'In reality' means for me, in the case of the Monty Hall problem with the standard assumptions. Martin Hogbin (talk) 20:35, 29 June 2012 (UTC)

"In reality" to the rest of us means what is verifiable according to reliable sources, not Big Lies. -- Rick Block (talk) 06:29, 30 June 2012 (UTC)

The common line in all the sources you cite is that the simple solutions fail if the host is not defined to choose evenly. In our article we give the standard assumptions, that the host does choose evenly.

Is there a single source that clearly and unequivocally states that given that the host chooses an unchosen goat-hiding door uniformly the simple solutions are wrong? The sources you cite all answer a different question. Martin Hogbin (talk) 08:43, 30 June 2012 (UTC)

Put up or shut up

Rick despite all your indignation you have not managed to give one single source which clearly considers only the standard version of the problem in which the host chooses (an unchosen goat-hiding) door uniformly and which unequivocally says about this specific formulation that the simple solutions are wrong. Martin Hogbin (talk) 11:13, 1 July 2012 (UTC)

And you are clearly not reading what I'm writing, for example this. Are you claiming you do not agree that the POV expressed by the sources we're talking about is that the simple solutions are deficient, specifically that the question they (correctly) answer is NOT whether a player who has chosen Door 1 and has seen the host open Door 3 should switch to Door 2? Note that you do not have to agree with this POV to agree that it is the POV expressed by these sources. -- Rick Block (talk) 18:22, 1 July 2012 (UTC)

No, I mean exactly what I say above. The sources do not address the standard version of the problem in which in which the host chooses (an unchosen goat-hiding) door uniformly. They all cover a variant in which the host may have a preference for one door or another. In the WP article we clearly quote from K&W who say of the host 'If both remaining doors have goats behind them, he chooses one [uniformly] at random'. The sources that you cite do not say this, they all refer to the case in which the host might not chose uniformly at random. Martin Hogbin (talk) 21:09, 1 July 2012 (UTC)

I guess we'll just have to agree to disagree here. As I read them, ALL of these sources are talking about solutions to the standard problem. And they are ALL saying these solutions are deficient in one way or another. -- Rick Block (talk) 04:12, 2 July 2012 (UTC)

Not correct, Rick (pardon for intruding) It is on the well defined "standard version" of the "standard Monty Hall paradox" as presented here in the article.
Of course you "can" regard before and after, no doubt, and you "can" express that in a mathematically correct "cure-all" way, no doubt, giving a probability of "2/3" (what else?) for the "standard version" of the "standard paradox". No question. Some (esp. one editor here) may find it deficient and incomplete without such mathematical "cure-all", even for the "standard paradox". A matter of pure opinion and unsourced, as you will remember.

It is on the question put in the well-defined scenario of the "standard paradox", of the world famous "standard Monty Hall problem" as presented here in the article: "is it to your advantage to switch? (Yes or no).

So please name just the one source that says, in order to get the only correct answer to the question put in the famous "standard Monty Hall paradox", that you *MUST* do it this way, that you HAVE to do it this way.

Again: for the "standard Monty Hall problem" and its well-defined scenario, as presented here in the article.

Rick, you say "All sources". Please name just the ONE source that says "you MUST do it the mathematical cure-all way to make the correct decision asked for in the well-defined "standard version" (of advantage, yes or no). Please name that source. (pardon for intruding) Gerhardvalentin (talk) 09:02, 2 July 2012 (UTC)

Rick, this is not a matter of opinion or conjecture it is a matter of verifiable fact.

Do you agree that in the WP article we say of the host that,'If both remaining doors have goats behind them, he chooses one [uniformly] at random' and that this is therefore the problem that we undertake to solve?

Do you agree that this statement excludes the possibility that the host may have a preference for one door or another?

Is it not true that none of your cited sources states that the host most open a legal (by which I mean not chosen by the player and hiding a goat) door uniformly at random?

In fact thay all state or imply that there is a possibility that the host might have a door preference. In their paper Morgan parameterise this preference but later they withdraw this saying, 'had we adopted conditions implicit in the problem, the answer is 2/3, period'. The very condition that Morgan are referring to is the condition that the host opens a legal door. In other words they agree that they did not answer the standard formulation ofthe problem that we address in the article. Martin Hogbin (talk) 08:56, 2 July 2012 (UTC)

uniformly at random (or do you think that they mean something else).

Once again, I AGREE none of these sources are saying the "simple" solutions produce the WRONG answer (given all the standard assumptions). Do you DISAGREE they're saying they produce the RIGHT answer to the WRONG question which happens to be the same as the answer to the RIGHT question given all the standard assumptions? Do you DISAGREE they all show this to be the case is by varying the question slightly so the issue is exposed (so that the answers to the WRONG question and the RIGHT question are different)? I've used this analogy before - it's like asking what is N^N for N=2 and being given the answer "2+2=4, so the answer is 4". 2+2=4 is a correct statement. It is actually related to the correct answer in an intrinsic sort of way (it uses the unmentioned but "obvious" simplification that for N=2, N+N and N*N and N^N are all identical). And 4 is the correct (numeric) answer. But yet there's something not quite right about this answer. It might be described as "correct, but ... shaky" (which you might later clarify as "incomplete and insufficient"), or perhaps "misleading", or maybe "incomplete", or perchance as "doesn't address the problem posed" or possibly [bluntly] "false" - and the issue can be shown by using this same solution to attempt to solve N^N for any other value of N. We've been through this so many times either you don't (and apparently never will) understand this or you do understand but continue to argue about it for reasons known only to yourself. Either way, like I say, we're just going to have to agree to disagree. -- Rick Block (talk) 15:19, 2 July 2012 (UTC)

(Once again, pardon for intruding) That splendidly highlights your mission. Relevance? Importance? Significance? Weight? – The right question? The question is "to switch, yes nor no?", not what is N^N. Reliable modern sources (dominance) say that you don't even need probability at all to give the only correct answer to the question put, to "solve" the paradox. Probability is not a necessity to give the correct answer. And other reliable modern sources that use clear probability explicitly say that, due to the symmetry of the "standard version", it makes no sense to use conditional probability. In symmetry, they say, it is not necessary to condition on door numbers. They say that no conditional probability is needed. Full-stop. Anyone may use conditional probability if he likes, yes, in showing quite differing scenarios outside the MHP. But never as an expedient and indispensable necessity for the standard version. So all of that clearly highlights the "weight". Show important and relevant aspects, yes, show it apprehensible, and show it there, where it belongs. Please show respect to the relevant sources, and, in respect for the readers, please show respect to the "weight". Gerhardvalentin (talk) 17:06, 2 July 2012 (UTC)

Rick, this is a section about the sources not your invalid analogies.

Can you provide one source that clearly says that it is addressing the standard problem (as defined in the article) and which also says that the simple solutions to that problem are wrong. If not, you must withdraw your claim. Martin Hogbin (talk) 17:46, 2 July 2012 (UTC)

I "must withdraw my claim"??? My claim is that multiple reliable sources describe the "simple" solutions using words like "correct, but ... shaky" (later clarified as "incomplete and insufficient"), "misleading", "incomplete", "doesn't address the problem posed", and (most bluntly) "false". These are direct quotes (provided with more context above). I'm not withdrawing this "claim". You apparently disagree that these sources are saying what it seems completely obvious to me that they're saying. And, once again, I suggest we simply agree to disagree about this (I will not respond to further badgering). -- Rick Block (talk) 05:55, 4 July 2012 (UTC)

Rick, you are quite correct in that some sources criticise the simple solutions, but to what problem?

None of the sources you cite say that they are referring to the problem formulation in which the host chooses a legal door uniformly. You seem to be ignoring this fact. Martin Hogbin (talk) 20:38, 4 July 2012 (UTC)

As I've said, all of the sources I'm citing are referring to the problem formulation in which the host chooses a legal door uniformly. There is someone ignoring facts here, but it's not me. -- Rick Block (talk) 17:33, 7 July 2012 (UTC)

Really? perhaps you can show me where each source says that. Martin Hogbin (talk) 20:09, 7 July 2012 (UTC)

Morgan et al

To avoid any confusion, here is the situation: The player has chosen door 1, the host has then revealed a goat behind door 3, and the player is now offered the option to switch. Thus is player having been given additional information, faced with a conditional probability problem. (emphasis added) In their analysis they indeed cover the more general case where the host may have a preference between two goats, but the highlighted statement applies to the "standard variant" as well. Indeed, in their rejoinder to vos Savant's reply they say One of the ideas put forth in our article, and one of the few that directly concerns her responses, is that even if one accepts the restrictions that she places on the reader's question, it is still a conditional probability problem. (emphasis added).

Most of your emphasised sections are irrelevant. In the article, we state in the problem description, before we consider any solutions, If both remaining doors have goats behind them, he chooses one [uniformly] at random. In other words we 'do not consider the possibility that the host might be biased.

Once the possibility that the host might choose unevenly is countenanced then, clearly, it might be important which door the host opens.

Morgan consider the more general case first and then consider the problem that we address in the article as a special case of this. If you never consider it possible that the host might choose unevenly then you do not need to do this because of the obvious symmetry in the problem as pointed out by mathematician Boris Tsirelson. This is also essentially what Morgan later stated.

Gillman

Restates the Parade problem description like this: A TV host shows you three numbered doors, one hiding a car (all three equally likely) and the other two hiding goats. You get to pick a door, winning whatever is behind it. You choose door #1, say. The host, who knows where the car is, then opens one of the other two doors to reveal a goat, and invites you to switch your choice if you so wish. Assume he opens door #3. Should you switch to #2? He calls this "Game I" and says of vos Savant's solution This is an elegant proof, but it does not address the problem posed, in which the host has shown you a goat at #3. Instead it is still considering the possibility that the car is at #3-whence the host cannot have already opened that door (much less to reveal a goat). In this game-Game II-you have to announce before a door has been opened [emphasis in original] whether you plan to switch. He then goes on to say Game I is more complicated: What it the probability P that you win if you switch, given that the host has opened door #3 [emphasis in original] ? This is a conditional [emphasis in original] probability, which takes account of this extra condition. When the car is actually at #2, the host will open #3. But when it is at #1, he may open either #2 or #3. The answer to the question just asked depends on his selection strategy when he has this choice [emphasis in original] ... Like Morgan et al., he then goes on to solve the more general case where the host's preference between two goats may be anything (not just 1/2), but all the comments pertain regardless of the value of this preference.

So where does Gillman say the the host must choose a legal door uniformly? In fact he says the exact opposite as you quote above,depends on his selection strategy when he has this choice. In the problem in the article the host does not have this choice. Gillman answers a different, and more complicated question.

Lucas et al.

They present a statement equivalent to the K&W statement (without door numbers!) and start with the naive, two doors so the probability must be 1/2, incorrect solution. In showing why this solution is wrong they say When Monty opens door X, there is a tendency to think, "I have learned that door X conceals a goat, but I have learned nothing of relevance about the other two doors." This is what we mean by "focusing on the doors". The proper approach involves focusing on Monty, specifically on the precise manner in which he chooses his door to open. We should think, "Monty, who makes his decisions according to strict rules, chose to open door X. Why this door as opposed to one of the others?" (emphasis added) They then go to show a conditional solution using the example case of player picks door 1 and Monty opens door 2, showing Monty opens door 2 1/6 of the time if the car is behind door 1 but 1/3 of the time if the car is behind door 3. Following this, to show the importance of paying attention to the exact rules the host follows, they show a variation where Monty opens the highest-numbered goat door where it doesn't matter whether you switch if you've picked door 1 and the host has opened door 3. They conclude this section with Take this as a cautionary tale. Whether we are playing Classic Monty or High-Numbered Monty, it is certain that Monty will open a goat-concealing door. In the former case the probability that our initial choice concealed the car did not change while in the latter case it did. This shows that any proposed solution to the MHP failing to pay close attention to Monty's selection procedure is incomplete. (emphasis added) They really can't be any more clear then this.

Again Lucas do not make clear that the host must choose a legal door uniformly. In fact, they clearly refer to a case where he does not, calling it High-Numbered Monty. In the problem that we address in the article High-Numbered Monty is excluded.

Eisenhauer

Here's his description of the controversy When asked the probabilities of winning by switching and not switching, the vast majority of respondents answer that with two doors unopened and a prize behind one of them, the doors are equally attractive: the chance of winning is 1/2 in either case. On the other hand, it is sometimes argued that since one knows in advance that Monty will reveal a zonk [goat], the revelation provides no relevant information to the contestant (see, for example, Nalebuff 1987). In this view, which Falk (1992) calls the 'no news' argument, the probability that the prize is behind the chosen door is 1/3, just as it was a priori, whereas switching doors gives a 2/3 probability of winning. ... Consequently, what could and should have been a correct and enlightening answer to the problem was made unconvincing and misleading. Subequent work by Gillman (1992) and Falk (1992) applied the correct Bayesian mathematics to derive the general solution, but several other authors continued to perpetuate the 'no news' argument, which at best relies on an unstated assumption (see, for example, Engel and Ventoulias 1991; Gilovich et al. 1995) He's clearly talking about the standard problem, and the "simple" solutions here. He goes on to show three different solutions, for an equivalent of the "high-numbered Monty" variant, for the "standard" variant (where P=1/2), and for the general case where the host's preference between goats is left as a variable - but this is obviously to show (just like Lucas et al.) the importance of paying close attention to the rules governing how the host picks between goats.

Exactly the same. Eisenhauer refers to 'the rules governing how the host picks between goats'. In other words, it is considered possible that the host may implement a different rule from that described in our article.

Rosenthal

I've already cited his clarification of what he meant by This solution is actually correct, but I consider it "shaky". I really don't know how to make this may more clear to you.

It is already perfectly clear to me.

Discussion

AFAICT YOU disagree with these sources and think that they're wrong (in a WP:TRUTH kind of way). Your refusal to admit that they are clearly expressing a POV that conditional solutions are BETTER than "simple" solutions (or, equivalently, that "simple" solutions are deficient) is not an unbiased reflection of their views, but rather reflects your own personal POV that "simple" solutions are just fine. My point is (and remains) that the article must be NPOV, meaning it must not endorse either your POV or the POV expressed by these sources. Frankly, we're never going to get anywhere until you admit that these sources say what they clearly say. -- Rick Block (talk) 04:46, 8 July 2012 (UTC)

No, the sources, as the quotes you have given above show, clearly refer to the situation in which it is possible that the host might not choose a legal door uniformly. In the article this possibility is excluded. Thus your sources answer a different question.

My POV does not in any way conflict with that of the sources you cite. Martin Hogbin (talk) 08:53, 8 July 2012 (UTC)

No, these sources refer to the situation where the player is deciding to switch AFTER seeing which door the host opens. They're saying knowing the original pick (say it's door 1) and which door the host has opened (say it's door 3), means the probabilities of interest are the conditional probabilities the car is behind the remaining doors given these events. They're saying these probabilities are a function of how the host chooses which door to open in the case where he has a choice and constraining this to be a uniform choice means the probability of winning by switching is 2/3 - but this is still a conditional probability. As Morgan et al. put it (also in their rejoinder to vos Savant): One may argue that the information necessary to use the conditional solution is not available to the player, or that given natural symmetry conditions, the unconditional approach necessarily leads to the same result, but this does not change the aforementioned fact [that it is still a conditional probability problem].

We're apparently not even going to agree about what these sources say, so I think it's best we simply agree that we disagree. And I'll note once again I'm NOT saying the article should criticize "simple" solutions at every turn, rather that it should be written in a way that it remains NPOV with respect to these sources which (IMO) clearly express the POV that conditional solutions are better. -- Rick Block (talk) 18:16, 8 July 2012 (UTC)

Just bandying the word 'conditional' about means nothing. All probability problems are conditional and I have no objection to using the term in relation to the MHP. The point of contention is, does it matter which legal door the host opens. I use the word 'conditional' to refer to the Morgan-style solutions for brevity only, the 'simple' solutions are also conditional.

But please just answer these two simple matter-of-fact questions.

In the article do we state, before we give any solutions, that the host must choose evenly between legal doors?

Do any of your cited sources state, before they give any solutions, that the host must choose evenly between legal doors? Martin Hogbin (talk) 19:25, 8 July 2012 (UTC)

Yes to both. -- Rick Block (talk) 20:08, 8 July 2012 (UTC)

Which sources state, before they give any solutions, that the host must choose evenly between legal doors? can you quote the text where they say this please. Martin Hogbin (talk) 22:24, 8 July 2012 (UTC)

Lucas et al. In Version 1 (Classic Monty), presented at the very beginning of their paper (which you evidently have not bothered to read), If Monty can open more than one door without violating rules one and two, then he chooses his door randomly. I have previously provided Grinstead & Snell in response to this demand as well. If you're looking for quotes, here's what G&S say Finally, we assume that if Monty has a choice of doors (i.e., the contestant has picked the door with the car behind it) he chooses each door with probability 1/2. As you should know by now, they then present a "simple" solution to what they call a simpler, related problem (what is the probability of winning using a "stay" or "switch" strategy, selected BEFORE seeing which door the host opens) and go on to say This very simple analysis, though correct, does not quite solve the problem that Craig posed. Craig asked for the conditional probability that you win if you switch, given that you have chosen door 1 and that Monty has chosen door 3. They're saying the "simple" solutions are the ones addressing a different question - exactly the opposite of your claim above that the sources I'm citing answer a different question. Lets flip this around. Can you provide a single source that says solutions computing the conditional probabilities the car is behind door 1 and door 2 given the host has opened door 3 are not addressing the "standard" problem? Or is this simply an WP:OR claim on your part matching your POV? -- Rick Block (talk) 23:46, 8 July 2012 (UTC)

(Intrusion: The article, dealing with the standard version, still brashly says "but this does not necessarily mean the probability of winning by switching is 2/3 given which door the player has chosen and which door the host opens." – Chief aim of the article to forever befog the reader and forever to remain unclear and opaque? Gerhardvalentin (talk) 06:35, 9 July 2012 (UTC)

In the light of Morgan's retraction (quoted br Rick above) I suggest that we remove that error. Martin Hogbin (talk) 08:01, 9 July 2012 (UTC)

Perhaps you should read Lucas more carefully. There is no criticism of the simple solutions in the Lucas paper until after Lucas change the problem, by saying, 'To further illuminate this point, let us consider an altered version of the problem...'. Before you mention the preceding sentence, 'The general principle here is that any-thing affecting Monty’s decision-making process is relevant to updating our probabilities after Monty opens his door', (my emphasis) in defence of your cause, let me point out that a random choice is not a 'decision making process'. Martin Hogbin (talk) 08:25, 9 July 2012 (UTC)

Martin - I believe you know perfectly well a random choice is a decision making process. I also believe you know perfectly well Lucas et al. (and all the others) are criticizing "simple" solutions (whether or not the host is constrained to choose evenly between legal doors) - but, for whatever reason, you're incapable of admitting this. My conclusion is further discussion with you about this would be pointless. -- Rick Block (talk) 15:42, 9 July 2012 (UTC)

The host randomly choosing a legal door is no more a decision-making process than the fact that he opens a door at all; both are part of the problem setup. The host has no element of choice and the player knows exactly how the host will decide which door to open - randomly. Martin Hogbin (talk) 21:23, 9 July 2012 (UTC)

To explain a bit more: if the host could decide whether to choose a legal door randomly or in some other manner then there would be e decision-making process involved, and this is exactly what Lucas are referring to, the fact that the host might have chosen a legal door in some other way, namely High Numbered Monty. But the host does not have this choice. In the standard problem formulation the host must always choose a door randomly, he has no decision to make. Martin Hogbin (talk) 21:33, 9 July 2012 (UTC)

Conclusion

So, at best, we have two sources, one contested source (Lucas) and an online textbook supporting the concept that there is a significant body of opinion asserting that the simple solutions do not correctly solve the standard version of the problem. Hardly enough for even the equal prominence compromise that I am suggesting.

If you like, I can explain exactly why there are no sources claiming that the simple solutions do not solve the standard problem. Martin Hogbin (talk) 08:25, 9 July 2012 (UTC)

I will explain anyway. Had the problem stated right from the start that the host must always choose a legal door randomly then if Morgan et al had been foolish enough to have submitted their paper it would not have been published, being at best a piece of pointless pedantry and, at worst, wrong. How do I know that? Because that is exactly what happened years earlier with Selvin. He forgot to mention the host's uniform choice of unchosen goat-hiding door, this was pointed out to him so he corrected his omission (and added a version for pedants). No papers, no drama. Martin Hogbin (talk) 21:41, 9 July 2012 (UTC)

The discussion seems to have stalled. Would one, or both, of you care to describe where things are at? Sunray (talk) 22:34, 10 July 2012 (UTC)

Per just below, we're stuck on the exact wording of the question following the description of the conflict. I think we're agreed about everything in the show/hide box except the five words highlighted in yellow. -- Rick Block (talk) 14:26, 11 July 2012 (UTC)

Outside comments on including NPOV in the question

Full text of proposed RFC

The aim of this RfC is to resolve a longstanding and ongoing conflict involving many editors concerning the relative importance and prominence within the article of the 'simple' and the more complex 'conditional' solutions to the problem.

00:53, 29 June 2012 (UTC) By adding a date here, the above will be copied to the RFC announcement page

The 'simple' solutions do not consider which specific door the host opens to reveal a goat (see examples [44] [45]). The 'conditional' solutions use conditional probability to solve the problem in the case that the host has opened a specific door to reveal a goat (see examples [46]).

One group of editors considers that the 'simple' solutions are perfectly correct and easier to understand and that the, more complex, 'conditional' solutions are an unimportant academic extension to the problem.

The other group believes that the 'simple' solutions are essentially incomplete or do not answer the question as posed and that the 'conditional' solutions are necessary to solve the problem. Both sides claim sources support their views.

That argument is unlikely to ever be resolved but two proposals have been made to resolve the dispute. Both proposals aim to give equal prominence and weight to the two types of solution.

Proposal 1 is for the initial sections including 'Solution' and 'Aids to understanding' to be based exclusively on 'simple' solutions (with no disclaimers that they do not solve the right problem or are incomplete) then to follow that, for those interested, with a section at the same heading level giving a full and scholarly exposition of the 'conditional' solutions.

Proposal 2 is for the article to include in the initial 'Solution' section both one or more 'simple' solutions and an approachable 'conditional' solution (showing the conditional probability the car is behind Door 2 given the player picks Door 1 and the host opens Door 3 is 2/3) with neither presented as "more correct" than the other, and to include in some later section of the article a discussion of the criticism of the 'simple' solutions.

Proposal 1, Proposal 2, or neither?

Considering all Wikipedia policies and guidelines, in particular WP:NPOV and WP:Technical, do you favor Proposal 1, Proposal 2, or neither. If you choose to include extended comments in a section below, please create your own subsection and limit your comments to no more than 500 words.

Proposal x Brief rationale. -- ~~~~

Comments from User 1

User 1's comments here

Comments from User 2

User 2's comments here

Discussion

The text in the show/hide box above is what we've agreed on for the RFC. The issue at this point is the yellow highlighted text in the question part. Martin objects to this on the grounds that he apparently thinks it supports the claim I've been making for two years that Proposal 1 is not NPOV (which is the whole reason I've suggested Proposal 2, which I think is NPOV, but apparently Martin disagrees with this). Resolving whether Proposal 1 is NPOV or not is the primary outcome I'm looking for from this RFC. I believe Martin is simply looking for a decision regarding whether editors prefer Proposal 1 or Proposal 2.

If anyone watching this page could comment about the yellow highlighted text in the question (good idea? bad idea? OK? not OK?), I would be grateful. -- Rick Block (talk) 00:53, 29 June 2012 (UTC)

And, to add slightly more context, here's a draft of the comment I'll be adding assuming we ever go live with this RFC. -- Rick Block (talk) 02:41, 29 June 2012 (UTC)

Rick's comments

This is a POV dispute, plain and simple.

There are (at least) two ways to interpret the question - each supported by numerous sources.

1) As a strategy, is switching better than staying? Many secondary sources agree this interpretation is implicitly taken by sources presenting "simple" solutions, although these sources generally do not say this themselves.

2) Should a player switch in a specific case, such as after picking Door 1 and then seeing the host open Door 3? This interpretation is implicitly taken by sources presenting only "conditional" solutions, and is explicitly preferred by a number of sources.

As Morgan et al. say, "the distinction between [these questions] seems to confound many".

No one disputes that an immense number of sources present "simple" solutions. But this includes popular sources and academic sources from many fields which uncritically parrot vos Savant's solution. Within the field of probability, the textbook solution (literally and figuratively) is to compute the conditional probabilities the car is behind Door 1 and Door 2 given the player selected Door 1 and the host opened Door 3. Saying or implying that the "conditional" solution is at all uncommon or remotely controversial is simply a Big Lie.

What is controversial, but by no means fringe, is the POV expressed by numerous sources, e.g. [47] [48] [49] [50] [51] [52], that "simple" solutions are deficient and "conditional" solutions are better. To be NPOV the article must not endorse this POV (as it arguably did at one point). But it equally must not endorse the opposite view. IMO, proposal 1 does exactly this. Rather than "give equal prominence and weight", it presents "simple" solutions as if they are the TRUTH (with no disclaimers, no criticism, and no mention of what interpretation of the problem they address) and treats "conditional" solutions as if they are incomprehensible academic jibberish. This creates a strong structural POV, which (hardly coincidentally) exactly matches the POV of one group involved in this conflict.

Should a player who picks Door 1 and then sees the host open Door 3 switch to Door 2?

Furthermore, the claim most readers would be better served by "simple" solutions is at best dubious. Krauss and Wang say 97% of their test subjects drew an image of the (conditional!) situation where the player has picked Door 1 and the host has opened Door 3 (like the image to the right), and that once formed this image "prevents the problem solver from gaining access to the intuitive [simple] solution". As Eisenhauer says [of vos Savant's solution] "what could and should have been a correct and enlightening answer to the problem was made unconvincing and misleading."

The resolution here is simple. Follow Wikipedia's core content policy of NPOV. Include BOTH "simple" and approachable "conditional" solutions in the initial "Solution" section, without saying or implying either is "more correct" than the other - i.e. Proposal 2.

Rick, it's not the pov that's the issue here. The policy you want to refer to is WP:WEIGHT - the weight given to content should reflect the weight given by the sources. The majority of sources treat the Monty Hall question as a brain teaser or parlour puzzle - the kind I first encountered as a schoolgirl in a book called "Who owns the zebra" that came free with Readers Digest. The vast majority of solutions are good enough to satisfy the audience for that market, who probably also watch game shows, but would have no appetite for recherche mathematical expositions. The more 'complex' ones seem designed to show undergrads how to use probability notations.

The few mathematicians who take it further should - in terms of Wikipedia policy - have only the weight that their number warrants, in just the same manner as say the article on the timeline of Pharaonic Egypt should refer to David Rohl, but not criticize every date in line with his observations (which may well be right, but which are not yet reflected by the majority mainstream view). I believe the problem is that those editors who wish to reflect the higher maths rather than the parlour puzzler answers do so out of a belief that these answers reflect the truth. It may be that they do in respect of the answer as a higher mathematics conjecture, but Wikipedia editors are not in the business of THE TRUTH, they are in the business of reflecting the sources.

The question for the RfC should, to my mind, not be 'should the parlour puzzler solutions be demolished at every turn' but 'to what extent should the higher maths be allowed in the article.' It certainly should be reflected - these are reliable sources - but in terms of weight and significance they appear to be somewhat of an aside - a respectable but minority view if you like. Elen on the Roads:talk to me 09:46, 30 June 2012 (UTC) (<--still me, just the account without the admin tools for less secure situations)

Speaking as someone who has, off and on, attempted to help to resolve this dispute since shortly after the arbcom decision, I would make one observation: I have never, ever been able to get the main parties to this dispute to agree on what the dispute is about. Again and again I have seen mediation, third opinions, noticeboard discussions, etc. all crash and burn because of claims that what the dispute is really about has not been accurately described. Because of this history of failed attempts, I would caution anyone who attempts to resolve this to make sure that the latest attempt does not, once again, contain a description of what the dispute is about that has not been agreed to by all involved parties. If you don't get that, you are likely to end up going down the "I accept the answer, but you asked the wrong question!" rabbit hole. --Guy Macon (talk) 11:00, 30 June 2012 (UTC)

I agree WEIGHT is an issue, but I really can't see how NPOV is not an issue as well. The source situation is that there are

1) lots and lots of popular sources presenting "simple" solutions

2) a reasonable number of academic sources, most of them not from the directly relevant field (probability) presenting "simple" solutions

3) lots of sources (the vast majority) from the field of probability presenting conditional solutions

4) a fairly small number (by comparison) of sources like the ones being discussed here which explicitly criticize the "simple" solutions

The WEIGHT question is how do you judge the relative prominence of sources #1, #2, and #3. Since #3 are the sources from the directly relevant field in my mind these are the ones that should receive the most weight. The numbers are skewed the other way (largely because of the number of popular sources, but you'd expect there to be more popular sources), so overall I think this is probably essentially a tie (i.e. "simple" and "conditional" solutions should be given equal weight). The WEIGHT of the 4th group of sources is clearly not as high, and I don't think anyone is saying the "simple" solutions should be criticized at every turn (I'm certainly not).

The separate POV issue involves only the 4th group of sources. These sources clearly express the POV that the "simple" solutions are deficient. However, Martin's proposal has the article present "simple" solutions as complete and correct, which is not remaining neutral with regard to the POV expressed by these sources. The criticism should not be overweighted, but to be NPOV the article cannot take the POV that the criticism is invalid. -- Rick Block (talk) 16:22, 30 June 2012 (UTC)

Rick, I'm not clear on the distinction you are making, above. According to WP:NPOV, "[e]diting from a neutral point of view means representing fairly, proportionately, and as far as possible without bias, all significant views that have been published by reliable sources." Since WP editors must also respect WP:NOR, what aspect of WP:NPOV do you think applies other than WEIGHT? In answering, would you be able to quote the specific line(s) of policy? Sunray (talk) 17:00, 30 June 2012 (UTC)

From WP:NPOV (emphasis added):

(the first sentence) Editing from a neutral point of view means representing fairly, proportionately, and as far as possible without bias, all significant views that have been published by reliable sources.
Martin's proposed structure biases the article in favor of the (only implicitly held) view that "simple" solutions are complete and correct, and against the explicitly stated view that these solutions are deficient.
(from WP:STRUCTURE) Segregation of text or other content into different regions or subsections, based solely on the apparent POV of the content itself, may result in an unencyclopedic structure, such as a back-and-forth dialogue between proponents and opponents. It may also create an apparent hierarchy of fact where details in the main passage appear "true" and "undisputed", whereas other, segregated material is deemed "controversial", and therefore more likely to be false. Try to achieve a more neutral text by folding debates into the narrative, rather than isolating them into sections that ignore or fight against each other.
Martin's proposed structure presents "simple" solutions in the "main" part of the article, structurally suggesting these are complete and correct. This is certainly related to WEIGHT but it creates a bias as well. Imagine an article on Religion, that started with several sections on Christianity (paraphrasing Proposal 1) with no disclaimers [that other religions even exist] and then to follow that, for those interested, with a section at the same heading level giving a full and scholarly exposition [of other religions]. The topic here is math, but imagining this structure for an article in virtually any other field makes the bias completely obvious.
(from Impartial tone) The tone of Wikipedia articles should be impartial, neither endorsing nor rejecting a particular point of view.
Martin's proposed structure endorses the view that "simple" solutions are complete and correct, rejecting the view that they are deficient.

Clear? -- Rick Block (talk) 18:00, 30 June 2012 (UTC)

Yes clear. The structure of an article can create imbalances in WEIGHT and thus bias the article. Ellen's opinion seems to address this. WEIGHT is the primary concern. However, as Rick has noted, the WEIGHT issue is complex. Sunray (talk) 18:12, 30 June 2012 (UTC)

Of course a structure can create imbalances in weight as indeed Rick's example about religion would but my structure does no such thing.

I am just proposing that we do what most good text books do, which is to start with a simple exposition then move to a more complicated one. On that basis most text books would seem to be pushing the POV that the simple expositions are the 'correct' ones. That is an absurdity. Martin Hogbin (talk) 23:27, 30 June 2012 (UTC)

Since outside comment has evidently been solicited, I would like to remark on a couple points raised by Elen of the Roads on 28 – June 30 June, in an effort to shed some light on whence POV's found in the literature arise, because this may be germane to deciding on their weight and the relationship between them.
1. The original problem as formulated and popularized by Selvin and vos Savant, respectively, does not speak of a probability distribution for Monty's behavior. (It has been criticized for ambiguity in some other regards that are not relevant to this dispute.) This is very unsatisfactory from the perspective of strict frequentist probability analysis because, from that POV, without a frequency distribution to work with it just ain't a question of probabilities.
There are essentially three ways out of this conundrum:
1. One might assume, for purposes of analysis, that Monty's behavior is a random variable, leading to the answer that the probability of winning by switching lies between 1/2 and 2/3. This can be a problematic approach in general because one can not just assume every unknown is a random variable (e.g. there is no frequency distribution for right- and left-handed Montys: there is only himself), and because chasing unknown unknowns is bootless (no one is embarrassed, e.g., to disregard the frequency distribution of black holes randomly generated by quantum fluctuations in the vicinity of new cars); and this approach does not work at all in the case of a unique, one-time situation (where, again, it just ain't a question of probabilities from a frequentist POV).
This leaves only two completely unassailable responses for a strict frequentist:
1. One can always redefine the question in terms of explicit frequency distributions for the placement of the car and for Monty's choice. This can be criticized as defining the question to fit the answer, not unlike vos Savant's teleological insistence that "The original answer defines certain conditions, [...] Anything else is a different question" (Parade Magazine, 17 February 1991), but at least it has the virtue of being explicit.
Or, if one wants to be really stubborn about it:
1. One can refuse to answer the question, on the grounds that there is not sufficient information to give an answer in terms of the frequentist interpretation of the fundamental meaning of probability. While this may be regarded as a Zen-like non-answer to the question of a vos Idiot, it might leave one wondering how frequentists deal with real life problems where frequency distributions are unavailable. The original problem is, after all, a perfectly realistic scenario for a question involving incomplete information.
The academic literature has largely focused on option #2, giving answers that are more satisfying than #1 and less embarrassing than #3, although these also receive some mention.
The popular literature has remained focused on the original question #0, giving answers that are quite satisfactory from the perspective of Bayesian probability based on available information, without assuming or stipulating additional information. Dogmatic frequentists may insist that Bayesians are doing something that does not meet their definition of probability but, whatever you call it, it answers the question. As Nassim Nicholas Taleb observed: "While in theory randomness is an intrinsic property, in practice, randomness is incomplete information." (The Black Swan (2007), p. 198, italics in original)
Lest anyone get the impression I am just beating up on frequentists, let me say that the conditional probability solution is quite illuminating for the small number of people who understand it, and that Bayesian probability is fraught with opportunities for error for those who do not understand it. Indeed, the naive 50:50 answer may be understood as a flawed Bayesian analysis that only takes into account that one of the three doors has been eliminated and ignores the contextual information that one of the two un-chosen doors has been eliminated.
So what does all this mean for the question of how to present these points of view with due weight and significance? In my opinion, fractious dispute about the article is giving undue weight to a very abstruse difference in philosophy, a difference that some people here and in the literature may not even understand. In my opinion, the two ways of looking at the problem are complementary, and treating them as oppositional gives completely unwarranted attention to a very few people who are either ridiculously dogmatic or who do not even address what the other perspective is about. (This includes the rudely outspoken Morgan, et al., but not many of the other sources Rick cites.) In my opinion, Elen's perspective on the question of due weight is about right.
Bottom line (at last) – On the question of how much weigh to give "simple" solutions and "conditional" solutions: Yes, that is a reasonable question. On the question of how to cover disagreements about points of view: Don't, they are not significant. (Or give the tempest in a teapot a very small footnote. But go ahead and write scandalous BLP articles about how Morgan is a cad and vos Savant is a dolt.)
~ Ningauble (talk) 01:52, 2 July 2012 (UTC)

Ninguable, perhaps you do not realise how much you agree with me. I agree with your analysis . If fact it is pretty much what is on my Morgan criticism page. If you are consistent in choosing your unknown distributions the problem is either insoluble or the answer is 2/3.

I agree the POV issue in essentially non-existent, in fact I say so several times on this page.

I do not want to come down hard on the side of either the 'simplists' or the 'conditionalists'. I want to write an article that starts with the simple stuff that confuses most people and proceeds to the more complex stuff, thus making the article accessible and useful to the widest range of readership.

My only real sticking point is that I do not want 'health warnings' in the simple section because at this stage many readers will be struggling to understand the basic problem and to tell them that the solutions and explanations presented are actually wrong/incomplete/do-not-answer-the-question will probably put them off to the degree that they lose interest in the problem altogether.

Can I ask you straight, is there anything that I have said that you actually disagree with? Martin Hogbin (talk) 09:19, 2 July 2012 (UTC)

No, I believe I do agree with much of what you have said, and I have said so in the past. But in the last couple years, whenever I have attempted to explicitly state what I agreed with, you protested that it did not capture the essence of your position, and raised points with which I disagree.

Although you disavow that POV is an issue, it seems very present to me. Just as Rick tends toward caveats about "non-conditional" solutions being inadequate, you seem to tend toward caveats about "conditional" solutions being pedantic or irrelevant. To the extent that efforts to make the RfC straightforward and succinct, itself a worthy goal, end up glossing or obscuring this disagreement, then the RfC is not really going to settle the dispute.

I quite disagree with your assertions, made repeatedly over the past couple years, that the "conditional" approach is an irrelevant sideshow, and with your proposal earlier on this page to have the article discuss "whether the conditional nature of the problem is relevant". It should be borne in mind that the Raison d'être of an encyclopedia is pedagogy. Although the line between pedagogy and pedantry is subjective, a sophomore-level treatment of the problem is entirely relevant in a general encyclopedia even if some might find it risibly sophomoric.

To digress a little bit about how pervasively POV has muddied the waters, let me point out what I see as a major problem shared in common by the current article and proposals put forward by both parties in this dispute. (I refer to the four numbered approaches in my previous post above.) In the opening sections of the article, before solutions of any kind are addressed, #0 is thrown on the rubbish heap and #2 is adopted as the question at hand! I tried to point out last year how this confuses the presentation of "simple" solutions that do not refer to the frequency distributions of #2, and when I proposed a way around this problem a ton of bricks was dumped on my head.[53] Admittedly, the particulars of my proposal were a bit abstract for our readership, and distinguishing between frequentism and Bayesianism is an epistemological subtlety beyond the reach of typical sophomores; but the problem I attempted to address has been completely ignored: interposing the #2 question between the #0 question and the "simple" #0 answers is downright confusing and, for those with a superficial understanding of the difference, casts the latter in a prejudicial light. It seems that the #2 "POV" is so pervasive that others don't see what I perceive to be a problem.

(To confess my own personal POV, which does not belong in the article: from a Bayesian perspective, given the very interesting question of #0, #1 is rubbish and #2 is a cop-out that is good enough for sophomores. Nevertheless, I respect the frequentist POV, which definitely has fruitful applications, though I disapprove when people sometimes mistake epistemology for ontology.) ~ Ningauble (talk) 17:48, 2 July 2012 (UTC)

Ninguable, you seem not to be making the distinction (that you make for yourself) between what I personally think about the MHP, which is that the 'conditional solutions are an academic sideshow (still with a place in the article though) and the compromise position that I am proposing here.

I am proposing to give equal prominence to both solutions with a full and scholarly discussion of all the issues involved, such as you mention above (supported by sources of course). I am a little puzzled by your out-of-context quotation from me above. I said, 'Discussion on the whether the conditional nature of the problem is relevant to its unintuitiveness'. If it is not clear to you what that means you only have to ask.

If you want to have a discussion concerning my views on the MHP and yours that is fine, but let us do it somewhere else. It would be more fruitful if you were to turn you attention to what I am proposing as a solution to this dispute rather than what you perceive my views on the subject to be. Martin Hogbin (talk) 19:31, 2 July 2012 (UTC)

You asked if there is anything you said that I disagree with, and that is the question I answered. I actually intended an explicit distinction between "assertions made repeatedly over the past couple years" (opinions), and "your proposal earlier on this page to have the article discuss..." (article content). I am sorry if that was not sufficiently clear.

The fragment I quoted from one of your proposals was chosen to emphasize that having the article discuss whether conditional probability is relevant, in that regard or any other regard, strikes me as spin. Others may not see it that way.

(I also have a problem with the phrase "the conditional nature of the problem" (not your fault, many pedagogical authors use this careless manner of expression): conditional probability is a means of analysis, not the nature of the problem. This is what I mean by mistaking epistemology for ontology. It is like saying the question of how many spaces are in a tic-tac-toe grid is "a problem of counting on your fingers", or is "a problem of squaring integers". There are several ways to analyze it (some of which exploit symmetry more than others), but the choice of analysis does not define the problem.)

Relax, we agree about far more than we disagree about. ~ Ningauble (talk) 14:47, 5 July 2012 (UTC)

Can I just remind you all

Can I just remind you all that Rick and I have already agreed on an RfC statement. Here it is copied from above. After we agreed all that Rick pull this POV nonsense out of a hat and now seems to be proposing his own biased RfC statements. Martin Hogbin (talk) 23:36, 30 June 2012 (UTC)

What? Isn't the statement I quoted above identical? All we haven't agreed on is a few words in the directions to respondents, which I highlighed in yellow. What biased RfC statement are you accusing me of proposing? -- Rick Block (talk) 04:13, 1 July 2012 (UTC)

As you can see there is no mention of WP:POV in the agreed statement, but you want to add partisan directions to the respondents in which you will essentially be stating your opinion as fact by drawing respondents' attention to a WP policy which you think supports your opinion.

To make what I mean clear, you insist on drawing users' attention to WP:POV which you think supports you, and to WP:Technical which you think I think is my main supporting policy, which is not the case. My opinion is that WP:Technical does indeed support my proposal but it is not the basis in which it has been made. I think that WP:POV is irrelevant here, so to draw special attention to it is to try to push users your way.

As I have said, I have no objection to drawing users' attention to WP policy in general but it is too late to a sneak some support for your proposal in. We have an agreed neutral statement, let us keep the remaining directions strictly neutral. Martin Hogbin (talk) 11:06, 1 July 2012 (UTC)

Agreed statement

Martin's copy of the agreed statement

The aim of this RfC is to resolve a longstanding and ongoing conflict involving many editors concerning the relative importance and prominence within the article of the 'simple' and the more complex 'conditional' solutions to the problem. The 'simple' solutions do not consider which specific door the host opens to reveal a goat (see examples [23] [24]). The 'conditional' solutions use conditional probability to solve the problem in the case that the host has opened a specific door to reveal a goat (see examples [25]).

One group of editors considers that the 'simple' solutions are perfectly correct and easier to understand and that the, more complex, 'conditional' solutions are an unimportant academic extension to the problem.

The other group believes that the 'simple' solutions are essentially incomplete or do not answer the question as posed and that the 'conditional' solutions are necessary to solve the problem. Both sides claim sources support their views.

That argument is unlikely to ever be resolved but two proposals have been made to resolve the dispute. Both proposals aim to give equal prominence and weight to the two types of solution.

One proposal is for the initial sections including 'Solution' and 'Aids to understanding' to be based exclusively on 'simple' solutions (with no disclaimers that they do not solve the right problem or are incomplete) then to follow that, for those interested, with a section at the same heading level giving a full and scholarly exposition of the 'conditional' solutions.

The other proposal is for the article to include in the initial 'Solution' section both one or more 'simple' solutions and an approachable 'conditional' solution (showing the conditional probability the car is behind Door 2 given the player picks Door 1 and the host opens Door 3 is 2/3) with neither presented as "more correct" than the other, and to include in some later section of the article a discussion of the criticism of the 'simple' solutions.