Wikipedia talk:Requests for mediation/Monty Hall problem/Archive 2

Rick
Although not prompted by Andrevan I'd like to offer my opinion on the question he's asked Glkanter, Martin, Jeff, and Gill. I believe this gets at the crux of the issue that brings us here, and rather than specifically frame this as an issue with the Morgan et al. reference I think the issue is how to handle two specific POVs.

One POV, which I think we can comfortably call "vos Savant's", is that a solution that addresses the overall probability of winning by switching or staying is a complete and correct solution. I think we all agree that this is the POV taken by most popular sources. One common characteristic of solutions presented from this POV is that if we think about 900 instances of the game where the player initially selects a door at random, the solution applies to all 900 instances or the (roughly) 300 instances where the player initially picks a specific door (such as door 1), without differentiating the (roughly) 150 instances where the player picks a specific door (such as door 1) and the host opens another specific door (such as door 3).

The other POV, which I think we can comfortably call "conditionalist", is that the problem asks about the conditional probability given the player has picked a specific door (such as door 1) and the host has opened another specific door (such as door 3) and that this question is mathematically different from the question of the overall probability - i.e. the question is asking specifically about the 150 cases corresponding to a given pair of initial player pick and door the host opens, not all 300 involving a given player pick or all 900 given any player pick. From this POV, answers that do not specifically address the conditional probability are answering a slightly different question, whether or not the numeric answers are the same. To demonstrate the difference between the two questions (and, thus, the two different types of solutions), those holding this POV generally offer a slight variant of the problem where instead of the host choosing between two goats randomly the host is assigned a preference value between two goats. Those holding this POV describe the other solutions variously as "does not quite solve the problem" (Grinstead and Snell), "does not address the problem posed" (Gillman), "shaky" (Rosenthal), "incomplete" (Lucas, Rosenhouse, and Schepler), or (most bluntly) "false" (Morgan et al.).

The question we are faced with is how to represent both of these POVs in an NPOV manner. I've suggested (repeatedly) that we present a single solution section to the "normal" (symmetric) problem that presents both types of solutions in an NPOV manner with enough context to be able to distinguish how they are different. I haven't heard any other suggestion that doesn't seem blatantly POV. For example Martin's suggestion to present the "simple" solutions first and completely, deferring any mention of this issue to an "Academic extensions" section, explicitly makes the article take the first POV.

To keep this from becoming our typical ridiculously endless thread, please don't respond here but simply consider what I've said in your responses to Andrevan's question. -- Rick Block (talk) 20:18, 2 March 2010 (UTC)


 * If anyone else wants to respond to my question or to Rick, please do so in your own section. Rick, thank you for responding; the reason why I didn't ask you this question is because I think it's not very challenging for those who believe Morgan et al. and other conditionalists should be balanced more or less equally with the vos Savant/popular version. I need to think of how to challenge that perspective. Andrevan@ 02:27, 3 March 2010 (UTC)

Can we stipulate that the Monty Hall problem as a historical phenomenon is much greater than the conditional formulation by Morgan et al. and others? Andrevan@ 00:52, 13 March 2010 (UTC)


 * I don't know what you mean by this. The MHP is a probability puzzle for which most people asking intend the answer to be 2/3 and most people answering get wrong (thinking the probability is 1/2).  It is usually stated at least somewhat ambiguously meaning various interpretations are possible of the precise mathematical question that is being asked.  The mathematical literature clarifies two likely questions and the specific assumptions required (for each) to make the answer 2/3.  Many (most) popular sources don't make it clear exactly what question they're answering meaning their answers are just as ambiguous as the question leading to many popular misconceptions.  In addition to the mathematical literature, there's psychological literature exploring why so many people get the answer wrong (and are so attached to their answer) and economics literature exploring game theoretic versions of the situation where the player and host are each active participants.  Is this what you mean? -- Rick Block (talk) 03:20, 13 March 2010 (UTC)


 * Yes, I think that answers my question. So you would agree that the literature encompasses many other aspects of the problem than merely the conditionality? Andrevan@ 17:03, 16 March 2010 (UTC)


 * Yes, although I think the basic problem is fundamentally about the difference between the obvious 1/3:1/3:1/3 distribution in effect before the host opens a door and the resulting ?:?:0 distribution after the host opens, say, door 3. People imagine the situation having picked door 1 and having seen the host open door 3 (35 out of 36 recognizable drawings by 40 participants in a study per Krauss and Wang) and, since the probability of the remaining two closed doors was the same (each 1/3) before the host opens a door, strongly believe the probability of these doors must be equal (each 1/2) after the host opens a door (this is per Falk and others) - which means whether they realize it or not people are at least attempting to solve the conditional problem.  I've said this elsewhere, but I think the "unconditional" solutions are basically ignoring the conditional problem people attempt to solve and instead focus on the overall (average) probability of winning by switching (which, all cases being equal, must match the probability in any specific case).  This is one way to approach it, but (per Krauss and Wang) it conflicts with the mental model most people construct of the problem and the very strong intuition that if there are two unknowns they must be equally likely - which I think is a very reasonable explanation for why people argue with these sorts of solutions.  Martin keeps saying we should "fully" address the "simple" solutions before moving on to a conditional explanation, but I think this completely misses the entire reason the problem is paradoxical - which is that people try to solve it conditionally relying on a deeply intuitive principle (that doesn't hold for this problem).  So, (IMO) not only is omitting a conditional solution from the first solution section horribly POV (doing this implicitly says the "unconditional" approach is easier, or better, or "more" correct) but it fails to address the problem in the way most people are initially looking at it.  My point continues to be that although looking at the problem unconditionally is one way to look at it, this is certainly not the only way and even more certainly not the single "right" way - so for the article to explicitly say or even simply imply either of these is not at all acceptable. -- Rick Block (talk) 19:34, 16 March 2010 (UTC)

Reply to Martin
Martin says my assertion above that "people try to solve it conditionally relying on a deeply intuitive principle" is not supported by any reliable source. I disagree. The references for the "deeply intuitive principle" are Falk, and Fox and Levav. And, per Krauss and Wang:


 * Although, semantically, Door 3 in the standard version is named merely as an example ("Monty Hall opens another door, say, number 3"), most participants take the opening of Door 3 for granted and base their reasoning on this fact. In a pretest we gave participants (N=40) the standard version, asking them to illustrate their view of the situation described by drawing a sketch. After excluding four uninterpretable drawings, we saw that 35 out of the remaining 36 participants (97%) indeed drew an open Door 3, and only a single participant (3%) indicated that other constellations also remain possible according to the wording of the stand version.  The assumption that only Door 3 will open is further reinforced by the question that follows: "Do you want to switch to Door Number 2?" Note that, once formed, this assumption prevents the problem solver from gaining access to the intuitive solution illustrated in Figure 1 [this figure shows three obviously equally probable possibilities where the player has picked door 1 and the car is behind door 3, door 2 and door 1 respectively, showing the player wins by switching if the car is behind door 3 or 2, and loses only if the car is behind door 1].

To summarize - nearly all participants (97%) attempted to solve the specific conditional case (semantically described as an example in the Parade version of the problem statement) where the player picks door 1 and the host opens door 3. -- Rick Block (talk) 23:52, 16 March 2010 (UTC)

New question
Does the article need a "solution" section? Would it suffer if we incorporated the various types of solutions into sections organized, say, chronologically or otherwise topically? Andrevan@ 00:30, 17 March 2010 (UTC)
 * I think a "main" solution section is required, and that incorporating solutions into sections organized chronologically or topically would lead to a confusing mess. In particular, I see no reason to separate the two kinds of solutions into separate sections other than POV pushing.  Selvin presented both (one in his original letter and the other in his second letter), and neither is particularly novel or difficult to understand given only the most rudimentary familiarity with probability.  These solutions are really two sides of the same coin, each contributing to the understanding of the problem in its own way.  As user:Boris Tsirelson puts it "The coexistence of the conditional and the unconditional can be more peaceful." -- Rick Block (talk) 00:09, 18 March 2010 (UTC)
 * Isn't the very title "solution" somewhat POV since it implies that a given way is the answer, or the primary representation of the problem? Why can't we treat each popular solution as part of a greater representation by a certain camp, ie the Game theory representation, the Bayesian representation, the simple/popular/naive representation, the conditional representation... Andrevan@ 23:27, 8 April 2010 (UTC)


 * What I've been suggesting for some time now is that an initial section titled "solution" present multiple solutions (from easiest to somewhat harder to understand), without taking a stance on whether any of the solutions presented are "correct" (per the draft in this thread). The solutions in this section, as well as the formal Bayesian solution, are the predominant mainstream solutions and all address the same basic problem.  The game theory approach is a variant, based on relaxing various rules (like the other variants) and seems clearly appropriate for a later section discussing variations on the basic problem.  I think this is a very NPOV approach.  The only argument I've seen against this approach is Martin's claim that this makes the "simple" solutions somehow harder to understand - I completely disagree with this.


 * I think treating the unconditional solution as representative of a "camp", and confining the conditional analysis to another camp's section is that these "camps" both claim to be addressing the same problem and the interrelationship between these camps (specifically that the conditionalists claim the unconditionalists typically present solutions that don't quite address the problem they say they're addressing) gets lost. In addition, this structure implicitly endorses whatever "camp" is presented first, especially if no criticism is included. -- Rick Block (talk) 03:51, 9 April 2010 (UTC)

Glkanter
What is an appropriate level of coverage for Morgan et al.'s paper? Does it get its own section? How will it be interleaved with the rest of the article? Andrevan@ 16:03, 2 March 2010 (UTC)


 * Andrevan, have you read Morgan's article? Glkanter (talk) 00:57, 3 March 2010 (UTC)
 * Yes, but this is not relevant. For me to form my own conclusions would be WP:OR. Have you read that page? Andrevan@ 02:28, 3 March 2010 (UTC)


 * Yes, I have. Why do you ask such a question of me? Glkanter (talk) 03:47, 3 March 2010 (UTC)


 * If you are suggesting that Morgan has errors or that Morgan is somehow invalid, then indeed, we can write in the article, "Morgan says X, Smith says not-X." Our opinions as editors are irrelevant and to incorporate own's own interpretation is original research. Andrevan@ 04:23, 3 March 2010 (UTC)

How is Morgan's ignorance of Selvin's letters to be addressed? Selvin clearly states the host chooses randomly when faced with 2 goats. Morgan's paper, and others like it, can only exist by virtue of this ignorance. Glkanter (talk) 04:34, 3 March 2010 (UTC)


 * Simple: "Selvin followed up his first with a second clarifying the problem, but this was not widely disseminated... Morgan, in a departure from Selvin's second letter, wrote X..." Andrevan@ 04:45, 3 March 2010 (UTC)


 * That's not bad. How do you reconcile Morgan's claim that all simple solutions are false with the continuous subsequent publishing of simple solutions? Glkanter (talk) 05:06, 3 March 2010 (UTC)


 * "Morgan goes so far as to describe all non-conditional solutions as false, which has not discouraged mathematicians from publishing them..." Andrevan@ 13:40, 3 March 2010 (UTC)

Once again, not bad. Last question: is the contestant being aware of a 'host bias' that is not part of the official rules consistent with "Suppose you're on a game show"? Glkanter (talk) 15:17, 3 March 2010 (UTC)


 * For this one I think you need to find me a source that analyzes "Suppose you're on a game show." To me, that sentence sets up the setting and nothing else. Reading a lot into it is not found in the sources as far as I know. Andrevan@ 05:05, 4 March 2010 (UTC)


 * "Suppose you're on a game show..." is perhaps the most important part of the puzzle. It unambiguously tells us whose State of Knowledge the puzzle is to be answered from, and it tells us that all the rules of game shows apply. As Gill once wrote, and I'm paraphrasing, 'I have no interest in a puzzle where the host and contestant are either acting in collusion or mind reading'. How else can you explain the contestant being 'aware' of some contrived 'host bias'? Glkanter (talk) 19:21, 4 March 2010 (UTC)


 * Show me a source that you can cite to say this. We do not need to explain; we need only to synthesize and rehash existing explanations. Andrevan@ 22:09, 4 March 2010 (UTC)


 * The Morgan paper is based on the contrivance that the contestant is aware of some host bias when faced with 2 goats. This is contrary to the rules of game shows, and thus is not consistent with the opening words of the story problem "Suppose you're on a game show...". But I don't want to include this in the article, it is one of my justifications for saying Morgan is not addressing the Monty Hall problem. Glkanter (talk) 08:48, 5 March 2010 (UTC)


 * "An article on the societal responses to the puzzle and paradox would include Morgan." Wikipedia articles are inclusive overviews; not specific academic studies. Andrevan@ 20:40, 5 March 2010 (UTC)


 * The solution(s) provided should be for the Monty Hall story problem. Not some illogical and unsolvable contrivance. Glkanter (talk) 22:11, 5 March 2010 (UTC)


 * Articles' intended purposes are not to provide solutions but to develop a comprehensive overview of all aspects of a societal phenomenon. Andrevan@ 04:41, 6 March 2010 (UTC)


 * I've been considering that. Maybe the article should not include any solutions. Just a history, supported by sources and links. Glkanter (talk) 04:55, 6 March 2010 (UTC)


 * @Andrevan, there are a load of sources which address "suppose you're on a game show". By the time this mediation is finished, there will be at least two published papers in the mathematics literature by some guy called Gill. As well as that, there is Nalebuff (1987), an extremely influential (and not dumb) mathematical economist, and there is a huge literature in psychology and behavioural research. As well as that, since Nalebuff, it is given as an elementary exercise or merely a side remark in most books on game theory. I hope you realise that mathematical economists are often much more knowledgeable and reliable as mathematicians, than applied statisticians or biostatistians. Unfortunately, people in game theory are more interested in getting Nobel prizes than in publishing in third-rank pedagogical journals, or in wasting time on wikipedia. Gill110951 (talk) 11:40, 4 March 2010 (UTC)


 * Gill, please stay in your own section. This is orthogonal to my line of questioning here. Regardless, if you think Nalebuff has relevant things to say, by all means please create a subsection within your section discussing them. Andrevan@ 22:09, 4 March 2010 (UTC)

I lied, one more question. Morgan claims the problem is only appropriately solved via probability. Using a conditional problem statement and commensurate solution. Because of the arrogance of this position, other professionals, save for the recent book, have ignored this nonsense from Morgan. Since it's all about the sources, how does one refute, in Wikipedia, a statement so wrong that nobody bothers publishing a response correcting it? Glkanter (talk) 19:40, 3 March 2010 (UTC)


 * Morgan's paper has been cited by those who agree with it and those who do not. So I don't think what you're saying can be included in Wikipedia at all. Wikipedia is not a place to refute statements. Andrevan@ 05:05, 4 March 2010 (UTC)


 * Morgan et al. present a point of view on what is the MHP. No one bothers to write papers refuting a point of view. They also prove two theorems which contradict one another so it is a bit silly to take them as great authorities in mathematics. Gill110951 (talk) 11:42, 4 March 2010 (UTC)


 * Again, these are not criteria for notability, inclusion, or reliability. Andrevan@ 21:54, 4 March 2010 (UTC)

Glkanter's response
Despite it's various claims, the Morgan paper does not address The Monty Hall story problem. It serves no purpose in understanding the puzzle or the paradox. An article on the puzzle and paradox need not include Morgan, et al. An article on the societal responses to the puzzle and paradox would include Morgan. Glkanter (talk) 19:28, 4 March 2010 (UTC)
 * And Wikipedia's article is the latter. Andrevan@ 21:53, 4 March 2010 (UTC)
 * Yep: Morgan et al are part of the Monty Hall story! (In my point of view, a small part...) Some people are keen on Morgan et al because they see it as *defining* THE Monty Hall Problem. Gill110951 (talk) —Preceding undated comment added 12:59, 6 March 2010 (UTC).

Selvin
Yes, when looking for a conditional solution, refer to Selvin's 2nd letter. When looking for 'The basis to my solution is that Monty Hall knows which box contains the keys and when he can open either of two boxes without exposing the keys, he chooses between them at random.', Selvin's 2nd letter is conveniently forgotten/ignored, or his letters are outweighed by Morgan's paper. Oh, brother. Glkanter (talk) 09:41, 21 March 2010 (UTC)

Selvin's Conditional Solution
Rick provided a link to a copy of Selvin's 2nd letter some time ago. Here's the relevant part:

An alternative solution to enumerating the mutually exclusive and equally likely outcomes is as follows:

A = event that keys are contained in box B B = event that contestant chooses box B C = event that Monty Hall opens box A

Then

P(keys in box B | contestant selects B and Monty opens A)

= P(A | BC) = P(ABC)/P(BC) = P(C | AB)P(AB)/P(C | B)P(B) = P(C | AB)P(B | A)P(A)/P(C | B)P(B) = (1/2)(1/3)(1/3)(1/2)(1/3)             1/3

If the contestant trades his box B for the unopened box on the table, his probability of winning the card is 2/3.

Note that unlike Morgan, he does not call the simple solution 'false'. Glkanter (talk) 10:15, 21 March 2010 (UTC)

Chronologies And Timelines Have A POV?
I've had a BIG bite of this apple with Rick and some others. Somehow, a dry reporting of who did what, and when, fails to pass Wikipedia's NPOV standards. You figure it out. Then explain it to me. Glkanter (talk) 15:57, 9 April 2010 (UTC)

Martin
What is an appropriate level of coverage for Morgan et al.'s paper? Does it get its own section? How will it be interleaved with the rest of the article? Andrevan@ 16:03, 2 March 2010 (UTC)


 * Morgan's paper, along with other sources which insist on a conditional approach, should be mentioned is a section similar to that which we have now entitled 'Probabilistic solution'.  This section should, in my opinion, be entitled 'Academic extensions' to reflect the fact that the Morgan paper does not address the problem as it is understood by the vast majority of the population, but a more complicated variant in which the host is assumed to open a legal goat door non-uniformly.


 * This section should be immediately after the current 'Popular solutions' and 'Aids to understanding' sections. A clear description of Morgan's argument and why they think other solutions are incomplete should be given in this section along with a statement of the problem that the Morgan paper actually solves.


 * Morgan's criticism of other solutions that are supported by reliable sources should not be included in the section dealing with those solutions (essentially the 'Popular solutions' and 'Aids to understanding' sections) since it only serves to confuse the vast majority of readers and obfuscate the essential paradox. Martin Hogbin (talk) 16:20, 2 March 2010 (UTC)


 * I think what you suggest is quite reasonable. Obviously you and Rick disagree; he believes it should be interleaved with no separation, you believe it should be separate with no interleaving. But I think we are both within the realm of agreement, I can't necessarily say the same for everyone. So permit me to focus on other points of contention for the time being. Andrevan@ 22:11, 4 March 2010 (UTC)


 * I agree with Glkanter and Gill that the Morgan paper is largely irrelevant and tackles the problem from an obscure and essentially perverse academic viewpoint. However I am desperately trying to reach some sort of compromise so that we can get on with improving the article.


 * What I am absolutely against is allowing the Morgan paper to dominate the article to the extent that after any simple solution we have to have a disclaimer which says basically 'this solution is really wrong'. The hardest part for nearly everyone is the fact that the answer is 2/3 and not 1/2.  Our simple solutions and explanations must, above all else, be clear and convincing for the general reader. Interspersing these with things like, 'do not really solve the problem as asked' only serve to make a difficult explanation almost impossible to follow.


 * After the simple solutions, the next most important and notable aspect of the problem is that fact that if the host opens any unchosen door randomly the answer is 1/2. In other words whether the host knows where the goats are makes a difference.  Many people find this hard to believe.


 * After all the important issues above have been fully dealt with we can then go on to discuss what Morgan say about other sources and what other sources say about Morgan. Martin Hogbin (talk) 23:36, 4 March 2010 (UTC)

Comment on Rick's statement
As Rick has mentioned me I will make on comment on what he says. He says, '...people try to solve it conditionally relying on a deeply intuitive principle'. This is Rick's view, which he is entitled to, but it is not on supported by any reliable source.

New question
Can we think of a less pejorative name than "academic extensions"? What is wrong with giving the game theoretical and probabilistic explanations names along those lines? Can't we explain the more complex treatments of the problem in a way understandable by non-experts? Andrevan@ 23:29, 8 April 2010 (UTC)


 * A section on game theory is fine with me, called whatever is appropriate, I have no objection to heading that section  'Game theoretical solution' or 'Game theory'.


 * I do not think that the term 'Probabilistic solution' is appropriate for the case in which the host has a known or assumed door preference (what is often referred to as the conditional case) because the term applies equally to the case where the host chooses randomly or is taken to do so because we have no information about his door preference. Probability theory can still be applied to this latter case to give the answer 2/3, thus it is equally a probabilistic solution.


 * It is not my desire to use a pejorative term for the 'conditional' case but it is hard to think of a term which better describes the situation than 'academic extension'. The problem originally defined the host to choose randomly and it was not until a decade later that the academics Morgan et al. decided to consider the case where the host might have a known door preference.  This is therefore an academic extension to the original problem as defined by Selvin and understood by vos Savant.  I see no reason to regard this term as pejorative.


 * It is hard to think of neutral terms which accurately describe what is essentially Morgan's solution (there was no mention of conditional probability relating to the MHP before the Morgan paper). We could have the long winded heading, 'Solution where the host has a known or assumed door preference' but I guess that some would not like this.  There is 'Morgan's solution', as they were the first to propose it so it might be named in their honour. In the interests of compromise I would accept 'Conditional solution'.  Martin Hogbin (talk) 18:59, 9 April 2010 (UTC)


 * I'm sorry, but "there was no mention of conditional probability relating to the MHP before the Morgan paper" is such utter nonsense that I have to interject. In Selvin's second letter he uses conditional probability to better demonstrate that his original unconditional solution is actually correct (which, of course, it is assuming the host picks randomly if given the chance).  This letter amply demonstrates both 1) Selvin meant the problem to be asking about the situation where the player originally had 3 obviously equal choices and, after the host reveals one, is now faced with one specific conditional case involving only two choices, 2) Selvin considered a solution using conditional probability more convincing than the unconditional solution.  Martin's claim here is absolutely ridiculous.  What Martin considers "Morgan's solution" (the probability of winning by switching is 1/(1+q) treating q, the host's preference, as a variable) is merely a handy device to show that conditional and unconditional solutions address different stages of the problem.  Unconditional and conditional solutions happen to produce the same answer if q is 1/2, and one can reasonably argue that an unconditional solution is "correct" if q is given to be 1/2, but one can also reasonably argue that these solutions address the problem at different stages (e.g., as Gillman puts it, before and after the host opens a door).  Selvin clearly meant the situation after the host eliminates a choice, which is far and away the predominant interpretation.  It is by phrasing the problem to essentially force people to consider a specific situation after the host eliminates one of the choices that leads most people to the conclusion that it doesn't matter whether you switch (two unknowns must mean they are equally probable).  Considering the situation after the host opens a door is (and always has been) fundamentally a conditional probability problem.  -- Rick Block (talk) 01:44, 10 April 2010 (UTC)
 * Rick, I was referring to specific mention of the term 'conditional probability' but even so I accept that I might be mistaken. It is not that important, I was only trying to make some suggestions for a section heading.  If you do not like "Morgan's solution" that is fine with me, let us not use it. I really would like a neutral, factual, section title, the problem is I cannot think of one. Martin Hogbin (talk) 23:12, 12 April 2010 (UTC)


 * I think the main question here is what is your problem with presenting both unconditional and conditional solutions (to the symmetric problem - Morgan's [and Gillman's] 1/1+q answer has already been moved to the variants section) in a single section, with neither being presented as "more correct"? Is it your stance that we can't do this without confusing our poor ignorant readers?  If so, what is your response to my suggestion that presenting a fully explicated unconditional solution without mentioning anything about the conditional approach, let alone the criticisms of the unconditional approach, would be POV?  Do you understand that the article needs to reflect what reliable sources say, in relation to the preponderance of each view, whether or not you think a particular viewpoint is simpler?  If the conditional approach is deferred to an "academic extensions" section the article is taking the POV that the unconditional approach is correct and complete, and essentially saying that there are no sources that dispute this.  Do you actually think this is the case?  -- Rick Block (talk) 04:02, 16 April 2010 (UTC)


 * I do believe that we must first present a solution in which the host's door choice, when the player has initially chosen the car, is ignored. We should do this in a section on it's own, and immediately follow it with an appropriate 'Aids to understanding' for the same case. We need to do this because the problem is recognised to be one of the most unintuitive in the world and thus we should start with the simplest version of the problem.  Remember that many very competent mathematicians and statisticians got the answer wrong. After the simple version, we should add in the various complications.  I do not see this as a right solution vs wrong solution fight, I see it as a discussion on how best to present all the information, as supported by reliable sources, on the subject, thus there is no PoV issue involved.  There is no argument about what is the correct solution to any unambiguous formulation of the problem.  The question we have to address here is how best to present all the variations and solutions to the reader.  Reliable sources do not tell us how to do that.


 * This is an encyclopedia article about the Monty Hall problem it is not a literature survey, thus we should present the subject in the way that best helps our readers to understand the problem, this is the fundamental purpose of Wikipedia. The method that is used in almost every mathematics text book is to start with the simplest version of the problem then, once the reader has understood the basics, add in the complications.  There is nothing wrong with glossing over some of the subtleties of a problem initially, so long as these are fully covered later.  Martin Hogbin (talk) 16:44, 16 April 2010 (UTC)


 * The point is that by doing what you suggest we're making the article take a stance against the significant body of literature that unequivocally says approaching the problem unconditionally does not address the problem (in the interests of explaining the solution in a more understandable way). This is precisely a POV issue.  You agree that an unconditional solution is sufficient - but this is not the consensus of the sources.  If the article presents this solution as the primary solution, the article is saying this is the consensus of the sources.  But it's not.  It's really that simple.  You've tried to argue that Morgan et al. is a flawed source and can therefore be ignored.  Not only is it not a flawed source, but it represents a mainstream interpretation of the problem echoed by many sources.  By "glossing over the subtleties of the problem" you're making the article take the side of the "anti-conditionalists" -  i.e. you're making the article endorse their POV.


 * The primary purpose of the article is not to help our readers understand the problem. The primary purpose is much closer to a literature survey.  It needs to convey what reliable sources say, in proportion to the prevalence of opinions expressed by reliable sources.  Saying "the solution to the MHP is that there are three equally likely cases, car-goat-goat, and in 2 out of three of these cases switching wins the car" does not reflect the consensus of sources.  This is only one solution, presented by only some sources.  Other sources say that this solution is inadequate, and that a better solution is to examine the specific case in which the player initially picks door 1 and the host opens door 3.  For the article to gloss over this at the point the simpler solutions are presented makes the article POV.  I really don't understand how you're not seeing this.  -- Rick Block (talk) 02:29, 17 April 2010 (UTC)
 * I notice a repetition of the old discussion. I want to make clear that right from the start of the article it has to be explained to the reader that there may be a simple version of the problem, with its simple solution, but that the normal version of the problem is the one in which the door has been chosen, which is normally solved by calculating the appropriate (=conditional) probability! Nijdam (talk) 07:34, 17 April 2010 (UTC)
 * You are quite right Nijdam we are going over old ground. The purpose of this page is to allow Andrevan to mediate with us individually so let us leave to him to so that.  Martin Hogbin (talk) 23:42, 17 April 2010 (UTC)

Nijdam
Can we stipulate that the Monty Hall problem as a historical phenomenon is much greater than the conditional formulation by Morgan et al. and others? Andrevan@ 00:53, 13 March 2010 (UTC)
 * No, we can't. The Monty Hall problem is a probability problem, from which the most accepted version is the conditional formulation. Nijdam (talk) 12:50, 13 March 2010 (UTC)
 * Morgan's paper came out in 1991. Prior to 1991, what was the most accepted version? Andrevan@ 17:01, 16 March 2010 (UTC)
 * I will only speak for myself and my colleaques. We considered the MHP to be a the conditional formulation. Morgan made known the "simple solution" is no solution to the most accepted conditional formulation.Nijdam (talk) 23:01, 16 March 2010 (UTC)
 * But I'm talking about history, as Wikipedia is also a work of history as well as mathematics. In fact, it is more a work of history than it is one of mathematics, unlike say Wolfram Mathworld which doesn't mention the conditional formulation, but I digress. Are you saying that prior to Morgan's paper, you formulated the problem conditionally? Is there an earlier paper that you can reference to support this? Andrevan@ 00:29, 17 March 2010 (UTC)
 * Well, at least Steve Selvin himself formulated the answer as the conditional probability in: The American Statistician, August 1975, Vol. 29, No. 3. Nijdam (talk) 07:24, 21 March 2010 (UTC)

How can you back up a claim that the conditional version is the 'most accepted'? What about the Bayesian, game theory, etc? Andrevan@ 23:32, 8 April 2010 (UTC)
 * Let me first make clear that what you perhaps call something like the Bayesian analysis, which is the common approach, like in your "freshman's course", has nothing to do with Bayesian probability theory. The "conditional problem", i.e. the standard problem, is commonly solved using Bayes' theorem. That's all. It would be much less confusing if this simple basic theorem would not carry Bayes' name. The simple MHP has attracted the attention of people who like to use it in applying more advanced (?) theories, like game theory and Bayesian' probability theory. So be it. They have their own audience, and I don't think the common Wiki visitor is one of them.Nijdam (talk) 11:50, 9 April 2010 (UTC)

Kmhkmh
Can Morgan's paper go in a separate section? Andrevan@ 05:06, 4 March 2010 (UTC)
 * Principally yes. More generally speaking what matters is that the article treats all aspects of the problem and summarizes the sources properly. In which orders that happens or how all that is organized within the article is mostly a marginal matter. In fact as far as I'm concerned the article might even refrain from directly citing Morgan's paper at all, provided the general caveat to vos Savants solution is described through other sources (examples are in Rick's posting above). Having said that however I'm very wary of the direction in which Martin seems to push the article and in particular his last posting has raised many red flags for me (again). To be rather frank here: Looking at this posting and observing much of the discussion over the last year his approach seems to be "make vos Savant appear correct at all cost no matter what the (academic) sources say, anything else will just confuse lay people" and that's no a no-go for an encyclopedia. I'm sure he sees that differently, nevertheless that's impression I always get away with when reviewing the various discussions. This means while I'm fine with confining Morgan to the a "math section" or even dropping him altogether, I won't be fine with not mentioning the ambiguity of the problem in the beginning and with not mentioning how vos Savant has resolved the ambiguity (by computing the total probability that switching wins) in the section describing her solution.--Kmhkmh (talk) 00:56, 5 March 2010 (UTC)
 * I think you have more common ground with Martin than you think, but give me some time to work with it. Andrevan@ 02:44, 5 March 2010 (UTC)

Can we stipulate that the Monty Hall problem as a historical phenomenon is much greater than the conditional formulation by Morgan et al. and others? Andrevan@ 00:53, 13 March 2010 (UTC)
 * yes, but it is important that each aspect that is covered describes exactly and accurately what it does, i.e. how it resolves the ambiguity. Generally speaking the MHP is the sum of the reputable or notable literature/papers/articles published on it, obviously not all of those do bother with a Morgan like approach.--Kmhkmh (talk) 10:07, 13 March 2010 (UTC)

Must we "solve" the problem and "aid understanding?" Wikipedia isn't a textbook. Can a chronological, history-grounded treatment of the problem cover all bases sufficiently? Andrevan@ 23:31, 8 April 2010 (UTC)

Gill
What is an appropriate level of coverage for Morgan et al.'s paper? Does it get its own section? How will it be interleaved with the rest of the article? Andrevan@ 16:03, 2 March 2010 (UTC)


 * I think that the Morgan et al paper is a pedantic and boring article by mediocre authors published in a mediocre journal which is used as a reference simply "because it's there" and because it autocratically says "*this* is the problem, everyone who solved a different problem is stupid, now we'll show you how *we* solve it". It is a rather small part of the long long long complex history. We have a long evolution from a probability puzzle (early 1900's) via Martin Gardner (three prisoners) via Steve Selvin (popular statistics journal) which suddenly burst out of its original domain with Marilyn vos Savant. This was the point at which the focus moved from an elementary Probability 101 exercise, which should be solved by computing a conditional probability (and for which various supplementary assumptions need to be made), into a famous problem "in the public domain" as it were, to which also psychology and game-theory have all made contributions. The problem is partly so famous and so popular because it is what we mathematicians call "ill-posed". The question is not "what is the probability?" The question is "should you switch?". The wording of vos Savant/Whitaker is semantically ambiguous (though this is often not picked up by non-native speakers). The problem is not presented as a probability problem, let alone as a conditional probability problem. Craig Whitaker doesn't know anything about probability and hasn't encoded the problem into the language used by teachers of Probability 101, whose students know the intended meaning of various code words. But *this* is the problem which fascinates ordinary people. *This* is the problem which brings people to look and see what wikipedia has to say about it. *This* is the problem which fooled Paul Erdos. *This* is the problem which made it to the NY Times. *This* is the problem which keeps being reinvented and modified and living its own life in all kinds of different domains.


 * The Monty Hall problem in all kinds of versions is an exercise in most elementary probability and statistics texts, and no citation is given to any "mathematical" paper on the problem. Occasionally reference is made to Parade and to vos Savant. Probability text books want to show how conditional probability can solve conditional probability problems.


 * Game theory books show how game theory solves game theoretic problems. Nalebuff (1987) mentions the Monty Hall problem with no citation of any source at all. He is a famous and influential economist and game theorist. Everyone in economics thinks of Monty Hall as Nalebuff's problem and thinks of it as a problem in elementary game theory. Nalebuff gives what people here call the unconditional solution, and he mentions how amusing it is that ordinary people always give the wrong answer "no need to switch" when von Neumann - Morgenstern game theory tells you that you should switch. He is referring here to the fact which I wrote about, that according to von Neumann's minimax theorem "choosing your door uniformly at random and then always switching" is an optimal strategy. He doesn't even bother to spell this out since everyone who has done Game Theory 101 could already easily figure it out for themselves.


 * So to answer your questions:

Q: Appropriate level of coverage?


 * A: Minor.

Q: Own section?


 * A: no.

Q: How to be interleaved with rest?


 * A: In the natural way; it's a tiny part of the big history and it gets mentioned in that history and it is given its due there


 * Morgan et al. introduce some amusing new Monty Hall variations, they do a lot of calculations, they get an important result wrong; nobody who does serious work in probability reads their paper, a few people refer to it simply because it is often referred to... Most people are too busy to find out the whole history, to learn about the enormous ecosystem. Most people hear about the problem in a narrow context and want to add their little bit, in that same context.


 * I learnt today that there is a paper in empirical behavourial research which shows that pigeons are cleverer than people because pigeons make mistakes and learn from mistakes and don't waste too much time thinking. Pigeons rapidly learn that you should always switch. People think, decide they shouldn't switch, and never switch. This is an important part of the Monty Hall problem and it is part of the *correctness* of the so-called quick-easy unconditional problem solution, and it illustrates the total irrelevance of the so-called "conditional problem". Those pigeons aren't interested in a conditional probability. They're interested in getting twice as many free lunches. I will add the reference later.


 * I think that Nalebuf and the pigeons are much much more important and reliable source than Morgan et al. I think we should not be talking about Morgan et al. at all, but what to take as starting point in the article. If we start with vos Savant then from there on, we can branch out in all directions. That will make people who cling to Morgan's authority unhappy, and that is why these people try to put Morgan on a special pedestal. Forget them! Get a life! Start with the big picture, and then see what fits in, what makes sense, what is interesting, what is boring. Gill110951 (talk) 11:44, 4 March 2010 (UTC)

I think you have common ground with Rick Block et al. in that it should be interleaved naturally and not in a separate section, whereas Martin believes it should be kept separate but nonetheless minor. However, I don't think your discussion has addressed the issues from a Wikipedia policy standpoint, which is necessary. Your opinion of the paper's mediocrity is irrelevant if it is clearly influential and oft-cited; it is not for us to speculate as to why this is. Andrevan@ 22:07, 4 March 2010 (UTC)


 * I am not speculating. The paper is not influential. It is merely often cited in some circles, totally ignored in others. By looking at how it is cited and by whom, one can objectively see why. I do agree that My Personal Opinion is irrelevant. I trust that everyone here is smart enough to separate factual information from personal opinions/feelings in what I write. Don't use one as an excuse to ignore the other. Morgan et al is widely cited because it is a convenient reference to a clear Math 101 Problem which people like to cite, and because it gives an aura of authority to a particular point of view, and because of the fact that widely cited papers rapidly become even more widely cited [that is not the same a widely read]. The point of view of Morgan et al, and of some of the folks here, is just that: merely a point of view. There are other points of view, some of them held by some of the other folks here, and they are just as widely held, they are supported by just as reliable authorities. The mathematical economist Nalebuff is a much much much greater authority under anyone's criteria than Morgan of Morgan et al. A world top mathematical economist is as good as an authority on elementary probability as an applied statistician from an obscure teaching university. Please let's be serious. We shouldn't be wasting time on this minor minor issue which is only been pulled out front by those who want their own narrow/dogmatic POV supported by claiming that they are following the Nobel prize-winning thinkers Morgan et al. The latter just want their POV to take precendence over any other, to such an extent, that any other POV is branded as WRONG or INCOMPLETE. That's utter BS and it's either dumb or arrogant (he said arrogantly). [Please take my exaggeration here as poetic licence... I'm trying to get a point across. It's not as extreme or as black-white as I make out, but it seems a lot of people don't want to catch the message, so I have to turn up the volume and switch on some attention-catching flashing lights]Gill110951 (talk) 10:24, 6 March 2010 (UTC)


 * One can't objectively see why the paper was widely cited, merely that it was. Nalebuff should definitely be in there, but Morgan can't be thrown out on the strength of our interpretation. Andrevan@ 19:45, 6 March 2010 (UTC)


 * What wikipedia policy says about a subsidiary issue can be easily figured out after we have settled some more fundamental questions, of course applying wikipedia policy wherever necessary, relevant, or helpful. Honestly, I am rather annoyed that we are having wikipedia policy discussions about a subsidiary issue which has however been used on the Monty Hall talk pages as a not-so-secret lever to force the much bigger issue in an underhand way. That's why I heap more and more scorn on that particular paper. It just doesn't deserve all the attention.


 * Please let's not forget the bigger question. The question which the Morgan et al supporters really want to fix, by leverage from Morgan et al's own point of view: is the wikipedia page on MHP to be primarily about a particular and completely specific Math 101 exercise (which many people already saw and solved in high school), or is it to be about vos Savant's question and the Monty Hall Story.


 * Elsewhere on wikipedia, http://en.wikipedia.org/wiki/Talk:Monty_Hall_problem/Arguments#Discussion_of_some_literature_references, I have written out some extracts from highly reputable sources from mathematical economics (Nalebuff), mathematics (Barbeau), and behavioural research (the pigeon Columba Livia). These are all agreed that you should switch, and that the switcher wins the car with (unconditional) probability 2/3. Nalebuff moreover shows that he (and his readers) know that this is what game theory says you ought to do.


 * I also wrote out, http://en.wikipedia.org/wiki/Talk:Monty_Hall_problem/Arguments#Shorter_proof_of_conditional_result, a short way to do the Bayesian probability calculation, using Bayes law in the posterior odds equals prior odds times likelihood. And I just got an enthusiastic letter of acceptance from the editor of Statistica Neerlandica (now at version 2 of submission: http://arxiv.org/abs/1002.0651), and from the editor of Springer's Lexicon of Statistics (now at version 2 of submission: http://arxiv.org/abs/1002.3878). The former helped me to some more game theory references, and told me about the pigeons too. Gill110951 (talk) 13:25, 6 March 2010 (UTC)


 * You are not objective with respect to your own work and it falls under Wikipedia vanity guidelines to push that as a reference or a jumping-off point. Andrevan@ 19:45, 6 March 2010 (UTC)


 * @Andrevan, I am not pushing those works as a reference or a jumping-off point. I have written up what I learnt from the discussions on wikipedia in order to share it with other scientists and with wikipedia editors. Don't you have a sense of humour? Gill110951 (talk) 13:33, 19 March 2010 (UTC)

Nalebuff
Andrevan wrote above "Articles' intended purposes are not to provide solutions but to develop a comprehensive overview of all aspects of a societal phenomenon". He also asked me to open a subsection of my section on Nalebuff. So I hereby do that. Gill110951 (talk) 13:40, 19 March 2010 (UTC)

Nalebuff is a distinguished mathematical economist and his paper is highly cited in the mathematics economics literature. He sees the Monty Hall problem as a problem of game theory and refers to Morgernstern-von Neumann and the unconditional solution: "always switch gives you probability 2/3 of winning". Gill110951 (talk) 13:42, 19 March 2010 (UTC)


 * The Wikipedia article calls it a "probability puzzle". Which is just one way of seeing it. How about the solution that uses 'you always get the opposite' if you switch'? No probability, just logic. Since it's 'always', that includes 'contestant chooses door 1 and host reveals door 3'. But, no matter. Morgan, et, al in their sweeping 'everyone is wrong but us' took care of that nonsense. Glkanter (talk) 16:39, 19 March 2010 (UTC)


 * That right, @Glkanter. Logic together with "you had the car first with probability 1/3" gives you "switching gives you the car with probability 2/3". IMHO that is the most useful conclusion anyone can make, since no-one knows the way the car is hidden and the way Monty Hall chooses a door. The player must start off choosing a door uniformly at random then always switch. According to von Neumann-Morgernstern this is the best you can do. It is a short swift and decisive answer to a legitate mathematization of Whitaker's problem. Anyone who claims otherwise is obfuscating. Morgan et al give a correct answer to other questions which it is interesting but not obligatory to ask. Gill110951 (talk) 07:02, 20 March 2010 (UTC)


 * Is the contestant's door selection method meaningful? Glkanter


 * The contestant has to choose a door. Choosing it uniformly at random and then switching guarantees himself or herself of a 2/3 chance of winning the car. The contestant's door selection method is vital since we don't know anything about the method used by the quiz team to hide the car. Gill110951 (talk) 15:08, 28 March 2010 (UTC)

Given that I am no expert, I remain unconvinced. I see no difference in the results if the contestant chooses the same door each time. Glkanter (talk) 01:03, 29 March 2010 (UTC)


 * Gill is talking about game theory. Here we assume that the quiz team do all they can to prevent the player from winning the prize and the player does all they can to win the prize.  If, for example, the player (or players) most often initially choose door 1, then the quiz team could reduce the player's chances of winning by switching by placing the car behind door 1 more often.  The player, however, can defeat this strategy by choosing a door initially uniformly at random.  They then win 2/3 of the time if they always switch.  There is nothing the quiz team can do to prevent this.


 * The point here is that we do not need to make any assumptions about the way the host chooses a door, we only need to assume that the players want to win the car (fairly obvious) and the producer and host want to stop the players winning (plausible but not necessarily realistic). In that case, if they both adopt the best strategy to achieve their aims, the player will win 2/3 of the time by switching, without any further assumptions about the host's door choice, thus Morgan's argument is circumvented. Martin Hogbin (talk) 21:48, 29 March 2010 (UTC)

Dude! You there?
Glkanter Glkanter (talk) 01:12, 25 March 2010 (UTC)

I guess you are wondering where our esteemed mediator Andrevan has got to. I was wondering the same thing. Martin Hogbin (talk) 22:15, 24 March 2010 (UTC)


 * I'm still here. I work 40 hours a week and have personal obligations as well. I hope you weren't in a rush! Andrevan@ 23:32, 24 March 2010 (UTC)


 * Im not sure I would define 8 days of respectful patience as being in a rush. Glkanter (talk) 01:12, 25 March 2010 (UTC)


 * As I'm sure you know, this is a thorny problem and it's not immediately clear to me how to approach the mediation or what to propose. So it may be more than 8 days until we make any meaningful progress. Andrevan@ 19:53, 25 March 2010 (UTC)


 * I didn't expect Straw Man arguments from the mediator. Live and learn. Glkanter


 * I think the mediator should actually exercise his brain and try to appreciate the maths (high school level) and content and history. Of course this takes time. I have been exposed to Monty Hall for years and am still learning new insights (many from here, where people come to the problem with a fresh point of view, without preconceived notions). Gill110951 (talk) 10:18, 4 April 2010 (UTC)


 * I'm a computer science major at CMU and we studied the Bayesian analysis in freshman math. Andrevan@ 01:25, 5 April 2010 (UTC)


 * Excellent, @Andrevan! Gill110951 (talk) 13:39, 10 April 2010 (UTC)

Unacceptable slowness of response by the mediator
It is now 12 days since the mediator made a significant contribution to this discussion. Many of us are waiting to get on with improving the article. Does anyone else think things are moving too slowly? Please sign below. — Preceding unsigned comment added by Martin Hogbin (talk • contribs) 21:54, 29 March 2010
 * I am going to remove Colin, Jeff, and Heptalogos as parties since they never answered my questions. Andrevan@ 22:43, 29 March 2010 (UTC)
 * Anyway, in response to your complaint, I am a volunteer like yourself and I work full-time as I mentioned. If this formal discussion proceeds slowly it does not in any way stop you from contributing to the article or its talk page. Formal dispute resolution in real life can take years, not months. We will progress as quickly as we can. Andrevan@ 22:50, 29 March 2010 (UTC)


 * I have no problem with the supposedly lack of "speed". The ongoing arguing may well have been for more than a year, no need to rush now. And I really much appreciate the effort you want to make, helping in this messy and tricky situation. Nijdam (talk) 23:05, 29 March 2010 (UTC)


 * I was not aware you were waiting for a response from me. I added my thoughts to the discussion before and have not changed my mind significantly since then. I would be more than happy to summarize my feelings again if anyone thinks that would be helpful. Also I was out of "Wikiworld" for a bit due to traveling to the states for a wedding. Colincbn (talk) 03:15, 1 April 2010 (UTC)


 * I think we are slowly making some progress. In the meantime life goes on. The problems with achieving some kind of concensus about how this page shouuld look, raise the complex issue of where the demarcation line between common sense and specialized knowledge lies. In real life there is a smooth transition. But on wikipedia we ahve to agree to draw a line between the area where editors can use common sense and the area where they have to defer to so-called "reliable sources". Since so-called reliable sources might also differ, we have the problem of how an amateur can decide who is reliable, who is not. This is a fascinating issue in the sociology of science. How it is resolved here on wikipedia is very similar to how it is resolved in court-room fights. It's a fact of life that "might is right". Yet the pen is mightier than the sword. So we have to struggle with our pens and hope that we sway opinion. In the end wikipedia is both democratically run, and also owned by those who provide the bandwidth and storage. Gill110951 (talk) 10:16, 4 April 2010 (UTC)

Humor me, please.
Tell me that there's all kinds of high-level-behind-the-scenes discussions going on that I can't be privy to. Thanks. GKanter


 * A Cabal? What Cabal? hydnjo (talk) 13:27, 17 April 2010 (UTC)

Question for the mediator
Why is this anything other than a simple POV issue? Isn't the fundamental issue that some sources say X, other sources say X or Y, yet other sources say Y and that sources that say X aren't quite right - where:

X is the solution is to enumerate all outcomes where the player has picked (say) door 1 (per, for example, vos Savant).

Y is the solution is to compute the conditional probability given the player has picked (say) door 1 and the host has opened door 3 (per, for example, Grinstead and Snell).

Sources of the last sort (that say X isn't quite right) include Morgan et al., Gillman, and others.

I don't understand why this is so difficult to resolve according to Wikipedia policies. There is no policy that editors must AGREE with what sources say. -- Rick Block (talk) 18:40, 10 May 2010 (UTC)


 * How about chronologically? That method is used in many, many areas of reporting. Glkanter (talk) 18:52, 10 May 2010 (UTC)

Next steps
Copied from on my talk page:


 * What exactly is the objection to putting the conditional, Morgan, and Bayesian stuff in a separate section and simply linking it with a text anchor from the "simple" explanation? Andrevan@ 18:27, 27 May 2010 (UTC)


 * This is not what Martin wants. He wants the conditional and Bayesian stuff presented in a subservient fashion, i.e. he wants the article to endorse the POV (his POV) that the "simple" solutions are complete and correct.  There is clearly dispute about this, so to be NPOV the article MUST NOT take a stand on this.  Martin is demanding that the article take a stand - and not just any stand, but a stand in opposition to a widely held expert, "academic" POV.  This would be more clear if he were to draft actual text (which he refuses to do).   -- Rick Block (talk) 18:41, 27 May 2010 (UTC)


 * BTW - you can tell separate section is not what he's talking about since the stuff he objects to is already in a separate section. It's not just separate he's after, but separate and subservient. -- Rick Block (talk) 19:07, 27 May 2010 (UTC)

Multiple reliable sources say the MHP is conditional (full stop) and that the simple solutions are therefore inadequate. This POV is not directly contested by any reliable source Martin has yet offered, so it is entirely within NPOV guidelines to take this as a fact for the purposes of editing this article. This would mean that the article could (perhaps should) say, in the lead and in the very first section, something very similar to what these sources say. Perhaps something like "Many popular sources present solutions to the Monty Hall problem that end up with the correct numeric answer, 2/3 chance of winning by switching, without fully addressing the problem." Taking this uncontested (by sources) POV as fact, it would be fine to include the simple solutions in an "aid to understanding" section, or start with one and immediately point out the deficiency and proceed to a full conditional solution. This is what taking the POV of these sources would mean in an editing sense. Given that there are multiple sources that take this POV and no sources that directly contradict it (by which I mean a source that references this criticism and says anything remotely like "sources insisting on a conditional approach overcomplicate the problem because ..."), this would be a perfectly reasonable stance to take. I believe it is, in fact, Nijdam's stance.

The compromise I (and I believe Kmhkmh) have been suggesting, even with no counterbalancing sources, is to treat this as a POV issue meaning the article won't take a stance on this issue but will instead present simple solutions as an equally valid approach to conditional solutions and present the direct criticism of the simple solutions in a much later section of the article not as fact but as opinion. What I hear Martin (and Glkanter) saying is that they are completely unwilling to compromise in this way, and will continue arguing on the talk page about this until the article is changed so that it fully endorses the opposite POV (i.e. that the simple solutions are what are correct, and any conditional solution is merely an academic diversion).

Martin has resisted Andrevan's attempts to engage in a real-time mediation.

Question for Andrevan - now what? -- Rick Block (talk) 15:31, 28 May 2010 (UTC)


 * Your conclusion, "...so it is entirely within NPOV guidelines to take this as a fact..." is not valid:


 * "Multiple reliable sources say the MHP is conditional (full stop) and that the simple solutions are therefore inadequate. This POV is not directly contested by any reliable source Martin has yet offered, so it is entirely within NPOV guidelines to take this as a fact for the purposes of editing this article."


 * This position, and how Rick has historically applied it in the article, is a major source of the extended arguments. Glkanter (talk) 15:47, 28 May 2010 (UTC)


 * Not valid? How so?  There are clearly numerous reliable sources that say the MHP is conditional and that the simple solutions are inadequate (there's a list with direct quotes on the talk page).  Are there sources that directly contest this?  If so, please cite one.  If not, then it's simply like any other fact, i.e. something that can be attributed to a reliable source (numerous reliable sources in this case) that is not contradicted by some other (any other) reliable source.  It's verifiable, while the converse is not.  This makes it a fact as far as Wikipedia is concerned and whether you think it's true or not doesn't matter in the least.


 * Even though I think it's a completely defensible stance (in accordance with Wikipedia policies) please note that I'm NOT demanding the article take this POV as a fact. I bring it up only to remind you (and Martin) how far I'm willing to go to achieve a compromise.  The article arguably should take this POV as fact.  You and Martin insist that the article endorse the opposite POV, contrary to what these reliable sources say but without sources directly supporting your stance.  OK.  My compromise (between Nijdam's stance and your stance) is we treat this as a POV issue and endorse neither POV.  Are you really saying this is not enough?  Seriously? -- Rick Block (talk) 16:54, 28 May 2010 (UTC)


 * 'Not valid' as there are other good reasons that no one has directly called out Morgan's paper. Instead, as has happened, they simply continue publishing simple solutions. One would have to be a professional mathematician, *and* willing to get into a pissing contest with Morgan, et al. It's easy to understand that no professional mathematician would care to risk his good name over such a trivial, inconsequential issue. For example, they could look as petty as Morgan, et al do when they criticize vos Savant. Glkanter (talk) 00:35, 29 May 2010 (UTC)


 * Don't forget, Rick, there *is* a well known paper that does not support Morgan's assertions:
 * Richard G. Seymann is Professor of Statistics and Business Administration, School of Business, Lynchburg College, Lynchburg, VA 24501, who wrote a commentary in the 1991 American Statistical Association The American Statistician, November 1991, Vol. 45, No. 4 287 (the same issue as Morgan's paper) that immediately follows Morgan's paper.
 * It looks to me like that is the style one uses to disagree with a fellow mathematics professional's paper. Which is very different than the technique used by Morgan, et al when they attacked vos Savant. Glkanter (talk) 11:59, 29 May 2010 (UTC)


 * With your first comment you're saying we should assume from the fact that sources continue to publish simple sources that they are implicitly disagreeing with the explicit criticisms levied against these approaches. Maybe they're aware of these criticisms and are disagreeing and maybe they're not - but since they don't explicitly say we can't assume so on their behalf.  If some sources were to say the earth is flat, and other sources said the people saying the earth is flat are wrong it is actually round, and then subsequent sources said the earth is flat without mentioning anything about the "round" theory - what are we to believe?  And again, I'm NOT saying the article must take it as fact that the simple solutions are wrong.  I'm saying this is a defensible stance.


 * Regarding Seymann's comment - he's not saying the problem isn't inherently conditional, he's defending vos Savant's solution on the basis of an additional assumption that the "host is to be viewed as nothing more than an agent of chance". In their rejoinder to Seymann's comment (on yet the next page of the same issue of this journal, for folks following along at home) Morgan et al. grant that this assumption makes the numeric answer for the unconditional and conditional problems the same, but since vos Savant's experimental procedure includes explicitly randomizing the initial placement and the player's initial pick but NOT the host's choice they also say "From this and her previous solutions, one is tempted to conclude that vos Savant does not understand that the conditional problem (of interest to the player) and the unconditional problem (of interest to the host) are not the same, and that 2/3 is the answer to the relevant conditional problem only if p = q = 1/2.  Certainly the condition p = q = 1/2 should have been put on via a randomization device at this point.  It could also have been mentioned that this means that which of the unchosen doors is shown is irrelevant, which is the basis for solving the unconditional problem as a response to the conditional one."


 * My contention is still that there is explicit support for the view that the simple solutions are (at least typically) incomplete or address a slightly different problem (unconditional vs. conditional), but no explicit support for the converse. In spite of this, I'm willing to compromise and treat this as a POV issue meaning the article must not endorse either view.  Are you saying this is not enough? -- Rick Block (talk) 18:51, 30 May 2010 (UTC)

The question here is actually for Andrevan. Now what? -- Rick Block (talk) 16:54, 28 May 2010 (UTC)

What's left to argue about?
Rick used to insist, using the exact logic above, that Morgan's claim that all simple solutions are false was the 'prevailing' science. Every aspect of the Wikipedia MHP article was soaked in Morgan. Even through the second FAR. Today's version still contains far too many weasel words, caveats, cautions and blather from this. Yeah, Rick and another Wikipedia Admin used to tell me how stupid I was because I couldn't grasp why the conditional solution was required. Some of it is on my talk page. Regardless that there are countless simple solutions published every day.

Then Rick argued endlessly that the host may have a bias when faced with 2 goats. Ignoring, as Morgan do, Selvin's 2nd letter where he states clearly that the host will choose randomly and always offer the switch. And that the puzzle begins, "Suppose you're on a game show..." Hosts don't tell contestant's where the car is.

Now Morgan has agreed it's always 2/3.

And we know the various simple solutions apply to any and all conditional scenarios, including the contestant chooses door 1 and the host opens door 3, revealing a goat.

And since it's a game show, we are only concerned with the contestant's State of Knowledge.

The simple solutions celebrate the paradox, the conditional solution doesn't recognize the paradox's existence.

The only thing left to discuss is the wording of the article. Rick and Nijdam, with nothing else going for them, cry 'POV VIOLATION' whenever a chronological or easy-to-complex order is suggested.

They have nothing left to exchange in a compromise except failed arguments, reverting valid edits, and the repeated written threats of an edit war. Glkanter Glkanter (talk) 21:45, 30 May 2010 (UTC)


 * Now this is realllly encyclopedic, right? Is this more in keeping with what you would like the en article to be? hydnjo (talk) 21:09, 30 May 2010 (UTC)


 * Well, I certainly appreciate the brevity of the whole thing. Especially in comparison to the English version. There's an awful lot to like in the 'Simplified explanation'. I'm afraid the translation was just a little too choppy for me to make an authoritative judgment, but I presume it's much closer to my preference than what we have now. They didn't mention Morgan. Why such a glaring oversight/ommission? Glkanter (talk) 21:55, 30 May 2010 (UTC)


 * Sorry about the G-translate, it was for illustration only. How about this (also sans-Morgan) version. hydnjo (talk) 19:17, 31 May 2010 (UTC)

No problem with the G-translate. It worked well, how else could I have understood the German article at all?

I have written that 90 - 95% of the English article is unnecessary at best, confusing at worst. And that Morgan's paper is roughly equivalent to 'the Earth is flat', and in my first posting on these talk pages, I proposed an OR Seinfeld-like solution (not unlike the German 3 line table), because 'nothing happens'.

If what you just proposed had been the article I read when I came to Wikipedia for an understanding of the MHP, I wouldn't have batted an eye. You all would have never heard from me. But, it didn't happen that way. Go back and read the October 25, 2008 version of the article that I first encountered.

Really though, you need to engage Nijdam. His last comment a couple of weeks ago was along the lines of "I will not accept the conditional solution being presented subserviently to the simple solutions in the article." And he readily reverts changes not to his standards. Which, unfortunately, are not equivalent to Wikipedia's standards. Thanks! Glkanter (talk) 19:51, 31 May 2010 (UTC)

Heresy
I sense that one of the major stumbling blocks here is not the validity but perhaps the emphasis of some of the sources (Morgan?) which is thought by some to add confusion rather than illumination for some of the visitors. This may indeed be true however, this is after all an encyclopedia and not a newspaper supplement. So, what to to about this dichotomy of opinion?

So, a possible compromise path could be a separate article which might exclude some of the more academic (and perhaps confusing) aspects of the complete encyclopedic article and of course would not be the "Full Monty". This article might be called Monty Hall problem (simplified). It would of course be PROMINENTLY LINKED (or showcased) in the main article as well as in the simplified version. Thus if a viewer starts to feel that the article is "above his/her head" they could default to the simpler "switching is better" article without its sometimes complex alternatives.

I really think that most of the criticism of the current article has to do with its completeness which is perceived to be confounding to the "average" reader. An easy sidetrack to a (fill in your own adjectives) article might provide an escape from this never ending debate. hydnjo (talk) 20:15, 31 May 2010 (UTC)


 * Well, I'll be honest. Based on our preceding postings, I didn't see *that* coming. Is that German article you linked to a 'separate article'? Glkanter (talk) 20:26, 31 May 2010 (UTC)


 * In my opinion NO. What I'm proposing would be a separate (or alternative) article within the en-pedia which by its descriptive pagename would be easily accessed from the "main" article. It would also include a back-link to the "main" article. hydnjo (talk) 20:34, 31 May 2010 (UTC)


 * Why not just have the two sections in one article? What is the actual objection to this.  Even if it were the case that the simple solution was technically incorrect, there would still be a logic for doing this.  Look at the article on Coulomb's_law.  The law is stated and explained in detail and only after that in the section 'Electrostatic approximation' is it explained that the law is in fact only valid for (strictly speaking non-existent) stationary objects.  This is just the normal way of doing things, start simple then explain the details. Martin Hogbin (talk) 21:22, 31 May 2010 (UTC)


 * Because, a visitor to Coulomb's law is most likely already scientifically inclined. The principle arguments going on here have to do with the perception that the casual visitor is just that - a casual (non-scientist) visitor and as such will be turned off by the "full monty" and further doesn't give a crap. He just wants to know why his/her intuitive 50/50 is wrong. The "Too Long; Didn't Read" is at work here by some of the articles critics. So, why not accommodate that perception by providing an escape, Learn the virtue of "switching" without the complexity provided in the full encyclopedic article. hydnjo (talk) 21:54, 31 May 2010 (UTC)
 * Hydnjo, that is exactly what I am trying to do. Nobody minds stopping when it gets too complicated.  The current article gets too complicated too quickly.
 * I don't have/never had any objections against 2 parts. And it is kinda ridiculous that in the end just a question of ordering otherwise identical content is at the core of a year long editing conflict. Unless the order is proxy for something else, but then it is probably not even clear what the actual disagreement is.--Kmhkmh (talk) 22:17, 31 May 2010 (UTC)
 * Kmhkmh, just have a look at the Coulomb's law article. It has a description of the law followed by a long discussion of it (with no warnings saying, 'this is really wrong', or 'there are two ways of looking at this', then after all that it gives the limitations of the law with full details.  That is what I once suggested here. Martin Hogbin (talk) 22:28, 31 May 2010 (UTC)
 * I don't have any objections there and never had (if you carefully review the discussions of the last year). What I take/took issue with are the various other arguments you have started, which were imho smokescreens and misrepresentations. If an article structure like Coulomb's law or Newtonian mechanics was really your only or at least primary concern then why the heck did you start all these other threads which are ultimately just distractions? The main effect all those other threads had, was that the discussion became rather convoluted and hard to follow. Other editors (at least me) lastly had no idea, what kind of changes or modifications of the article you actually really want.--Kmhkmh (talk) 00:04, 1 June 2010 (UTC)

Hydnjo - I think an 'intellectually satisfied' reader would be able to gauge for him/herself when (if) to stop reading the article, as Kmhkmh points out. For many, including me, that would be somewhere in the simple solution. One could equally suggest a link to 'more extrapolation...' for those interested, which would seemingly avoid redundancy.

Kmhkmh - A one year battle over ordering? When the article repeatedly emphasized that "all simple solutions are false", and it takes 18 months (for me, anyways) to disprove that (to everyone except Nijdam, I believe), and there are STILL countless Morgan-inspired weasel words, etc. in the article, there's still a LOT more going on than an argument over order. Glkanter (talk) 22:30, 31 May 2010 (UTC)
 * The final article will still contain the information that most simple solutions can be considered as "incomplete", simpy because that's a correct (and sourced) assessment. The only thing that really changes here, that it is mentioned only in one place rather than several times all over the article.--Kmhkmh (talk) 00:04, 1 June 2010 (UTC)
 * I might add that there are some crazy people who think that Newton's laws are absolutely correct and Einstein was wrong but no on has suggested that they are trying to push their POV in the Newton's laws of motion article which mentions nothing about any problems with Newton's laws until the 'Importance and range of validity'. No weasel words no warnings or diversions, and most people have far less problem accepting Newton's laws that accepting the solution to the MHP. Martin Hogbin (talk) 22:39, 31 May 2010 (UTC)
 * Yes there is nothing wrong with that approach, but on the other hand there is nothing wrong with hinting limits of the Newtonian model in the lead either. Both option are fine and there's really no good reason to endlessly quarrel about this. Personally I really don't care which version is used since both are ok. The only thing that really matters is, that the restrictions are mentioned somewhere in the article.--Kmhkmh (talk) 00:04, 1 June 2010 (UTC)
 * Martin, Coulomb's law is a flawed comparison. A discussion amongst colleagues as to whether to switch or not has little to do with science but instead with a flawed interpretation (you get one, he gets two) which doesn't change no matter what. Pounding that realization (you get one, he gets two) into non-science/non-math reader is what the at the article should do. The article should also present all of the diversions and complexities that have standing and there lies the main argument.


 * Once the reader has become convinced then he/she may well be inspired to delve into the many intricacies provided. I don't think that is the business of an encyclopedia to delete information because it may confuse the casual reader. I'm covering old ground here but the main article needs to be comprehensive. That comprehensiveness bothers some and I understand but, the article should not be aimed at the lowest level of comprehension - this is an encyclopedia. hydnjo (talk) 23:12, 31 May 2010 (UTC)
 * I agree--Kmhkmh (talk) 00:04, 1 June 2010 (UTC)

Anyhow at this point it might be a good idea to involve the mediator to assess, who actually is still having real issues with separate chapters. Is it only Rick or somebody else? Also it should be assessed whether some editors have additional issues which are not fixed by having separate chapters.--Kmhkmh (talk) 00:04, 1 June 2010 (UTC)


 * Since the article already has split the "Popular solution" section from the "Probabilistic solution" section (and has for quite some time) it seems clear to me Martin and Glkanter are saying something else. Martin in particular has recently claimed it is his opinion that ANY conditional solution is not a reasonable approach (see ).  The structure he keeps proposing is essentially "complete article based on simple solutions, then anything you insist must be added (as long as the initial sections are presented as a complete article and anything else is treated as an "academic" appendix)".  Glkanter's main point seems to be that anything that criticizes unconditional solutions in any way is "Morgan-inspired weasel words".  IMO, neither of them have any interest whatsoever in what SOURCES have to say and simply want the article to reflect their own personal opinions about the topic. -- Rick Block (talk) 00:49, 1 June 2010 (UTC)
 * The articles still mixes the conditional solution with the popular one as the sections "the problem", "aids to understand", "sources of confusion" still mix both approaches and as I understand Martin wants to separate as well, which would be ok from my perspective. However that's something you don't want so far as I understand it. Still all these differences are mere matter of ordering the content, which is not really worth to endlessly argue about imho. I'm aware that Martin has said different things at different times, but judging by his last postings he seems to be ok with 2 separate parts and I thnink we can come up with a better title for the 2nd parts than "academic solution". So why not take him by his word and give that a try. As far as Glkanter's "Morgan-inspired weasel words" are concerned, I don't think that's worth any serious discussion.--Kmhkmh (talk) 01:42, 1 June 2010 (UTC)


 * Glkanter is quite capable of expressing his concerns, Rick. My main point is that the article always has been horrible, and remains so today. Readers come away unnecessarily confused and uninformed. Period. I understand that until Morgan's paper has been completely discredited it is 'entitled' to some sort of inclusion in the Wikipedia article. But not the emphasis it once had and still has, as per your unending cheerleading. Kmhkmh, the primary reason we're having these mediated discussions is because of my advocacy (you might read that as 'agitation') for improvements to the article. I've taken many shots on these pages, and like with your's above, I just consider the source. Glkanter (talk) 03:24, 1 June 2010 (UTC)


 * Martin has never proposed actual text so I frankly have no idea what he's actually suggesting (and I don't think anyone else does either). I've suggested numerous times he draft actual text so we can all see what he's really talking about - I even tried this on his behalf a while ago (by rearranging sections) but even this was not he meant.  What I do know is he keeps resisting drafts I've written that explicitly attempt to show no preference to conditional vs unconditional solutions.  My conclusion is that he does not want this, which would seem to imply he wants the article to show a preference (which is pretty much a no-go from my point of view).  I'm perfectly willing to give anything a "try".  But to try it, somebody is going to have to write it.  Asking me to "pre-agree" to something I've never seen seems a little silly.  -- Rick Block (talk) 04:05, 1 June 2010 (UTC)
 * I agree somewhat however it is equally silly to expect somebody to write a draft (based on a complete separation), if you are highly likely to reject such an attempt in the first place. What's the point in investing time there? The point of such a "pre-agreement" is to determine whether you could principally live with such an approach or not. So far you seem you to consider the latter and in that case writing any draft is just a (pointless) waste of time.--Kmhkmh (talk) 09:11, 1 June 2010 (UTC)
 * Rick, you now seem to have been reduced to hurling general insults. I have given a clear outline of the compromise that I am proposing, I am not going to rewrite the whole article just to see if you like it. I have moved the 'Aids to understanding' section again to show what I mean. This addresses 80% of my concerns, I cannot speak for Glkanter.
 * If a complete separation covers 80% of your concern then what's with the other 20%? Imho if Rick (or others) compromises on that they should be able to expect that this essentially settles the issue. But if this is likely to turn into a pitstop to another endless discussion about something else with no clear vision of the final article, that everybody can agree on, then the compromise may look rather pointless. If you want Rick, Nijdam, me or others to agree or compromise to something, then the very least you need to do, is providing a clear and concrete idea of what you actually want and what the end result is supposed to look like. So far that's apparently not the case, i.e. neither Rick nor me are really clear on what you ultimately want.--Kmhkmh (talk) 09:31, 1 June 2010 (UTC)
 * Firstly, let me say that although this change covers most of my concerns, the same may not be true for the many other editors who want major change here. Some of these may feel that far more needs to be done.


 * My main reason for making this change, however, is that I strongly believe that it will defuse the current situation and let all editors work together. Many of the changes I would like to see in the future are relatively non-contentions.  For example I would like to see a pretty picture for the vos Savant solution and I would like to add one more simple solution.  The section titles 'Popular solution' and 'Probabilistic solution' are not ideal for me but I am not going to fight to the death over it.  Personally I would like to see 'Sources of confusion' move up as well, with the claim that 'conditional probability' has anything to do with why people are confused being removed; in my opinion this view is not supported by the sources.  There is some tidying up of collateral damage from the minor editing skirmishes to be done.


 * Let me repeat my main point again though. With this change I think we can all be a little more relaxed about the article, and work together to improve it.  The only think there would be strong objection to from many editors would be the addition of weasel words and health warnings to the simple section.  Martin Hogbin (talk) 09:53, 1 June 2010 (UTC)


 * Just have a look at the article as it is now. Does it not look more welcoming and less oppressive to the ordinary reader?  What exactly has be lost from a strict and formal probability viewpoint?  Martin Hogbin (talk) 09:56, 1 June 2010 (UTC)
 * I have no objection against this different order nor do I need any caveats at the simple solution. However when I read this "weasel word" nonsense again, I'm getting rather wary. There are/were never any "weasel words" but sourced objections, so I'd appreciate if we can cut the crap here since such remarks only cause distractions and spawn off pintless discussion, which convolute the issue and potential progress with article. If you remove stuff from the "sources of confusions" or "aids to understanding sections" because it might distract from the simple solution that is fine with me as long as it get moved somewhere else in the article rather than being deleted. Personally I still prefer chapter titles like "(simple solution" and "detailed analysis"/"scientic analysis"/"mathematical analysis". The latter can contain (sourced) information on how conditional problems can cause confusion or difficulties for understand, i.e. what you remove from the other sections should be moved there.--Kmhkmh (talk) 11:37, 1 June 2010 (UTC)


 * "Weasel words" is a direct quote from the Wikipedia Policy on NPOV. As offensive as you find the term "weasel words", that's how offensive I find being accused of violating NPOV, especially before it's happened. Interesting that despite your comment above, '...nor do I need any caveats at the simple solution.', Nijdam felt he had a consensus to add a caveat to the simple solution. Using exactly the terminology you say the article does not contain, and that Wikipedia says to avoid . Glkanter (talk) 09:44, 2 June 2010 (UTC)
 * Neither the term on its own was appropriate nor the referenced guideline, since it was not violated here. As far as Nijdam's edits are concerned talk to him and not to me.--Kmhkmh (talk) 15:07, 2 June 2010 (UTC)
 * Firstly, I have not yet removed anything from the 'Simple' section. Maybe you would want to move the K&W statement to the 'detailed section'.   What I am referring to is potential future off-putting remarks in the simple solution section which say things like, 'this does not address the question as asked' or 'this solution is incomplete'. Perhaps 'disclaimers' is a more neutral word to use. Obviously when we get to the "detailed analysis"/"scientic analysis"/"mathematical analysis" section we can say exactly what the sources say about the simple solutions.  This is exactly how it is now. Martin Hogbin (talk) 11:56, 1 June 2010 (UTC)
 * Please can we leave the article in its new state for detailed discussion rather than reverting it immediately. Martin Hogbin (talk) 08:54, 1 June 2010 (UTC)


 * I have added a section on the article talk page about the move. Please all comment there and state any objections you may have to the change. The mediator is, of course, welcome to comment too. Martin Hogbin (talk) 09:16, 1 June 2010 (UTC)