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false conclusions due to incomplete mathematics

The conclusion in the article that switching is advantageous is due to the incomplete and innacurate mathematical formulations in the calculations leading to that conclusion.

Simply stated the "probability collapse" referred to in the erroneous conclusion that there is a 2/3 advantage to switching doors fails to recognize that the 1/3 value of the first opened door with a goat has to be distributed between the remaing two doors not only on the originally unchosen switch door. The MHP is actually two seperate and mutualy irrelevant sets of conditions, values and outcomes. The first set of probabilities concludes with the outcome where a zero value door is opened. The second set of conditions, values and outcomes must distribute the original 3/3 values with mathematical equality amongst the remaining two doors. There is no mathematical justification for distributing the 1/3 value of the first opened door upon the unchosen of the remaining doors. Both doors remaining doors are equal.

The choice between the final remaining 2 doors is the essence of the MHP. The information derived from outcomes of the original conditions, whether there were three doors, ten doors, or a million doors is has no probabalistic value to the second set of conditions where there are two doors and one car. Since information has no probabalistic value the only values relevant to the essence of the MHP (the choice between two doors) are the value of the prize and the number of doors. 98.164.120.241 (talk) 16:03, 21 March 2013 (UTC)

The Monty Hall problem is probably the most unintuitive simple probability puzzle in the world with most of the population initially believing that there is no advantage in switching. Read the section about the response to vos Savant's correct answer. The fact is, proven and agreed by every reliable source, that switching doubles your chances of winning the car.

Read the article and see if any of the arguments convince you. If not, try one of the simple simulations. You will find, to your surprise, that it really is true. When you have done that and convinced yourself that there is an advantage to switching, come back and help us improve the article in explaining the correct result more clearly. Martin Hogbin (talk) 16:47, 21 March 2013 (UTC)

You know, anon is right: we do have false conclusions due to incomplete mathematics. Who says the contestant doesn't want the goat? Goats are great. Can you milk a car? Can you eat a car?

As for having to distribute the 1⁄3 value of the door Monty opens between the two remaining, anon, you've not shown this to be true. These are not two separate and mutually irrelevant sets of conditions, values or outcomes. Monty has two restrictions placed on him: he has to open a door with a goat and he cannot open the door chosen by the contestant. So, imagine you're Monty; if the contestant initially chooses the door with the car, you can open either of the two remaining doors since they both have goats, but if the contestant initially chooses a door with a goat, you have to choose the other door with a goat; on average about one in three of your contestants will initially choose the door with the car and would loose if they swap but two in three will choose a door with a goat and would win if they swap.

What would happen if we lift either or both of these restrictions? We then have three possibilities.

1. Monty he has to open a door with a goat but he can open the door chosen by the contestant.

   Perhaps the contestant writes his choice down but doesn't tell Monty. In this case there is a fifty-fifty chance of winning but should you switch? If Monty chooses a different door to yours, it doesn't matter whether you switch, but there's a one-in-three chance Monty chooses your door, in which case you have half a chance of winning if you switch and no chance of winning unless you switch.

2. Monty can open either door not chosen by the contestant.

   The contestant chooses which door to keep closed and Monty flips a coin to decide which of the remaining doors to open. There's a 1⁄3 chance that the contestant chooses the right door at first, in which case the door Monty opens will definitely have a goat. There's a 2⁄3 chance that the contestant chooses one of the wrong doors at first, in which case the door Monty opens has a 50% chance of having the other goat. Do you switch? If the door Monty opens is the one with the car, of course you switch. If the door Monty opens has a goat, you've neither got anything to gain or loose by switching.

3. Monty can open any door.

   You choose a door but Monty either doesn't care or doesn't know which and then he opens any of the three doors at random. What do you do? There'll be a one-in-three chance Monty opens the door with the car making the choice easy. If he opens the door with a goat, you have a fifty-fifty chance of winning. Should you switch? It depends on whether Monty opens your door. There'll be a one-in-three chance Monty opens the door you chose; if it's a goat, switch, and if it's the car stick with it. If he opens a door you didn't choose, switch if it's the car but if it's a goat your chances are fifty-fifty whether you switch or not.

Changing how Monty chooses which door to open changes the game entirely. In this problem Monty's choice is restricted. Of the two remaining doors one of them was not available for Monty to open since the contestant initially chose this door. Therefore the two remaining doors are not equal. One of the two remaining doors is the one the contestant chose to have kept closed, the other is the one Monty, who knows where the car is, left closed. Did Monty leave it closed on a whim because the contestant had already picked the winning door (with a one-to-three chance) and it didn't matter which of the other two he opened or was he forced to leave it closed because the contestant had picked the door with the other goat (with a two-to-three chance) and he wasn't about to open the door with the car? JIMp _talk·cont 06:04, 24 March 2013 (UTC)

I think every variation of the MHP has already be thought of, including the farmer who would rather win the goat. Come to think of it, I am not sure we have ever given the goats the choice of which door to open. Martin Hogbin (talk) 23:19, 24 March 2013 (UTC)

Rumiton's observations

I am going to try to address the comments made by Rumiton about the clarity of the article. Please feel free to revert if you think I am doing anything bad. Martin Hogbin (talk) 11:01, 14 February 2013 (UTC)

The lead

Having read through the lead, I cannot see any easy way to shorten it. It is, in fact, four paragraphs with a quotation in the middle of one of them. One section that might be changed is this:

Vos Savant's response was that the contestant should switch to the other door. If the car is initially equally likely to be behind each door, a player who picks door 1 and does not switch has a 1 in 3 chance of winning the car while a player who picks door 1 and does switch has a 2 in 3 chance, because the host has removed an incorrect option from the unchosen doors, so contestants who switch double their chances of winning the car.

I think we might drop the stated 'explanation' by vS as it is not at all clear what it means. In the lead maybe we should just state the right answer, with no attempt at an explanation. I have worded this to avoid the old arguments. So how about:

Vos Savant's response was that the contestant should switch to the other door. Contestants who switch have a 2/3 chance of winning the car, while contestants who stick have only a 1/3 chance Martin Hogbin (talk) 09:45, 15 February 2013 (UTC)

Fine by me. Richard Gill (talk) 07:15, 16 February 2013 (UTC)

Looks good to me, too. Rumiton (talk) 13:44, 17 February 2013 (UTC)

Paul Erdos

I wonder also if we might shorten or remove the bit about PE. It does not seem that clear exactly what did happen. One user, a while back, said that PE did the correct calculation but did not believe his own answer. He then went on to do what, IMO, any good mathematician would do in the circumstances and try to approach the problem from a different angle. Do we have any definitive sources on what exactly did occur?

Yes. There's a reference and a link in the article (it's a great resource!). What exactly did happen is reported at length here: http://www.decisionsciences.org/DecisionLine/Vol30/30_1/vazs30_1.pdf. It's a nice story. But not short.Richard Gill (talk) 07:20, 16 February 2013 (UTC)

That is given as a reference and I did read it. It is not clear to me what happened at the start, when PE was first given the problem. Did he initially give an answer and was it the correct one? Martin Hogbin (talk) 12:15, 16 February 2013 (UTC)

The problem? Which problem? - Goodby!--Albtal (talk) 12:29, 16 February 2013 (UTC)

Answer to Albtal: The Monty Hall problem (the famous "paradox").
Imo in a first glance Erdös did not distinguish clearly enough "the host just opened a door showing a goat" – (1:1, no paradox) – versus: "the host opened a door to intentionally show a goat" – (1:2 paradox!).  Gerhardvalentin (talk) 23:08, 16 February 2013 (UTC)

There is no evidence that Erdos misunderstood the question in this way. Martin Hogbin (talk) 10:40, 17 February 2013 (UTC)

Erdos was a great number theorist but he was not a probabilist. His first reaction to MHP, I'm sure, was exactly the same as thatoif 99.99% of all people "of course it doesn't makea difference. 50-50." That was, BTW, my own intital reaction. I'm a modestly good statistican and moreover I immediately realized the question must be a trick question but still I couldn't immediately overcome my "naieve" instant reaction. Now you can go on and do a complicated calculation and see that th answer must be 2/3-1/3, but this doesn't give intuition. And naturally, Erdos complained that he still didn't "know" why the 50-50 intuition was wrong. A simulation experiment doesn't provide * insight* either, though it can convince you what the right answer must be.

Nobody told Erdos the "combining doors" insight. Nobody told him the insight one gets from Bayes rule, odds form! So he remained perplexed, of course. Richard Gill (talk) 17:47, 21 February 2013 (UTC)

It's a good thing nobody told Erdos about the "combining doors" insight, as there is no such insight. Erdos might have accepted the 2/3 chance, but on false grounds! Nijdam (talk) 11:44, 23 February 2013 (UTC)

Nijdam, I have discussed this subject on the /Arguments page. Martin Hogbin (talk) 13:50, 23 February 2013 (UTC)

Yes, Erdös objected that simulation does not explain why. Vazsonyi recounts that Erdös later received an explanation that satisfied him but, unfortunately, he does not tell us what it was. He only says the same thing that he says of the "combined doors" explanation: that he doesn't understand it. Vazsonyi also says Bayes’ theorem is "an incomprehensible formula that no one could understand, much less use", which (apart from arguing his own decision tree approach is best) underscores the fact that genuinely understanding the "why" of it is indeed elusive. ~ Ningauble (talk) 21:30, 15 March 2013 (UTC)

I agree with Vazsonyi (who also is not a probabilist, by the way). Bayes’ theorem - as it is usually represented in text books - is "an incomprehensible formula that no one could understand, much less use". What people however can use and can understand is Bayes' rule: posterior odds equals prior odds times likelihood ratio aka Bayes' factor. However, you can't use and understand Bayes' rule till you have internalized the notion of odds and studied some examples so that you can internalize the notion of likelihood ratio.

There are no free lunches. If you want to acquire probabilistic intuition you need to internalize probabilistic concepts. Read the book and article by Jeff Rosenthal, or the book by Jason Rosenhouse. These are exactly the kinds of reliable sources (so-called tertiary sources) we need to be following in the article on Monty Hall problem. Richard Gill (talk) 10:47, 17 March 2013 (UTC)

I agree that it's a nice anecdote, and think it should definitely be kept in the article. But this example of stumping the experts should probably be moved from the lead, which should be a summary overview. It really belongs in a section covering widespread incredulity about the answer – the important point being that it defies common sense. At present, that sort of material is spread between sections captioned "Vos Savant and the media furor" and "Sources of confusion", so I am not quite sure how best to restructure it. ~ Ningauble (talk) 21:38, 15 March 2013 (UTC)

Bayes and combining doors

Following discussion with Nijdam and suggestions from Richard I am going to suggest the following intuitive approach to using conditional probability and Bayes' rule to expand the 'Combining doors' solution later on in the article.

We could show the same two pictures but with the posterior probabilities being shown as 1/3? and 2/3? to show that we need to justify that these are the correct probabilities after the host has revealed the goat.

We currently say, '...the 2/3 chance of hiding the car has not been changed by the opening of one of these doors'. This is correct but we provide no justification for it.

If we start with the standard case, where the host must always reveal a goat behind an unchosen door but where we do not know which door the host has opened, the calculation of the posterior odds using Bayes rule becomes very simple. The probability that the host will reveal a goat is 1, regardless of the position of the car thus the posterior odds are equal to the prior odds.

We could then consider the case where the host chooses a door randomly, which just happens to hide a goat. To find the odds, after the host has revealed the goat we need to multiply the original odds by (the probability that the host will reveal a goat, given that the car is behind one of the two unchosen doors) divided by (the probability that the host will reveal a goat, given that the car is behind the originally chosen door), this ratio being 1:2 giving the posterior odds as 2:2.

We could then move on to the case where the host must always reveal a goat behind an unchosen door and reveals a goat behind one specific door (say door 3). We could start with the case where the host is defined to choose evenly when he has a choice (or we take a Bayesian perspective) and show that the odds remain 2:1 in favour of switching.

Finally we could consider the Morgan variants, where the host has a (known) door preference, and give the Morgan results.

This may seem quite long but it covers the standard problem and some variants in an intuitive way that is mathematically sound. Does anyone think this approach is worthwhile? Martin Hogbin (talk) 15:19, 17 February 2013 (UTC)

Let's forget about the idea of 'combining'. The 'combined' probability does not change, but the individual probabilities do. How does this contribute to the understanding? Why does the combined probability not change? The main argument for this is the unchanged probability of the chosen door. How is the combining of any help? Nijdam (talk) 11:51, 23 February 2013 (UTC)

Yes, I believe a simple Bayes is appropriate. Glrx (talk) 01:29, 18 February 2013 (UTC)

Hear, hear. Richard Gill (talk) 17:48, 21 February 2013 (UTC)

Something along the lines I have described above might be considered OR by some. On the other hand it might be considered a routine calculation. What do you think? Martin Hogbin (talk) 19:13, 21 February 2013 (UTC)

Routine calculation. Glrx (talk) 00:23, 22 February 2013 (UTC)

For "professionals" one can give a routine calculation. But for laypersons this is less than useless: they can't follow the calculation, they gain no intuition from it. cf Erdos: the calculation does not explain why things are how they are. For laypersons one must give *ideas* not formula manipulations. The idea is: the actually observed host's action (opened door 3, not 2) is twice as likely as when the car is behind the second door as when it is behind the first door. Before we saw that, the first and second doors were equally likely to hide the car. Afterwards the second door is twice as likely as the first door to hide the car. Richard Gill (talk) 06:36, 22 February 2013 (UTC)

I am not sure you understood what I was asking. I was proposing adding something along the lines I have given above. This is not the argument that you give, which I think most people will find hard to follow, but a different one, based on the 'combining doors' solution but fixed using Bayes' rule. Do you not like that? We could have both, of course. Martin Hogbin (talk) 09:47, 22 February 2013 (UTC)

You are right Martin in saying "hard to follow", and I say: hard to follow without having clearly answered the "why?". Redundancy regarding "that important key" is most welcome. Richard: Yes, you are absolutely right in clearly saying that it is on this "why".

It should be "made obvious" that, as soon as the guest did select his first door, and still before any other action,  a given asymmetry did already pop up within the pair the two unselected host's doors. Now "one" of his two doors became twice as likely to be opened by the host than his "other" door. This asymmetry is a fact, but we still do not (and need not) distinguish which one is which one. Later the host will show us which of his two doors did pop up to be twice as likely to be opened, and not his "other" door, caused by the guest's first decision.

Richard, in order to understand your true argument it could be helpful to say my ceterum censeo: In the standard version, the host is absolutely free to choose which door to open in only 1 out of 3,  but he definitely is slave to the act in 2 out of 3: slave to the the guest's first decision.  In that 2 out of 3 being absolutely bound to open the door that he opens, and never his other door. Consequently, in that 2 out of 3 the door opened (#2 and not #3 resp. #3 and not #2) clearly discloses that the car actually definitely IS behind his second door. – Overall: the door opened by the (part time slave) -host  "always / in any case"   was / is twice as likely to be opened than his second door, so in consequence the car is twice as likely to be behind the door offered, than to be behind the player's first choice: (2:1).

Yes, it is on the "why". And on clearly showing that "why". And on that occasion you can show the difference to some quite aberrant variant of a host who never is (part-time) slave to the act: (1:1). Gerhardvalentin (talk) 11:08, 22 February 2013 (UTC)

I don't think the calculation "is less than useless" for lay persons. I think the formula can be explained, and the significant feature is that dividing by P{Monty reveals a goat}=1 doesn't change the the probability the car is behind the contestant's door. It also plays into if Monty doesn't know where the car is, then P{}=2/3 and the contestant's door now has a 1/2 probability. Glrx (talk) 05:30, 23 February 2013 (UTC)

Bayes' formula is no use for people who can't relate to formulas. 99% of all people. Baye's rule "posterior odds equal prior odds times likelihood ratio", on the other hand, is meaningful, intuitive, easy to apply. Richard Gill (talk) 19:01, 27 February 2013 (UTC)

Which calculation are we talking about?

I am suggesting that we start with a trivially simple Bayes' rule calculation for the case where a (undefined) door is opened by the host to always reveal a goat. This is, I think, what Glrx is suggesting above.

We multiply the prior probability by the probability that host will reveal a goat given the car is behind one of the two unchosen doors divided by the probability the host will reveal a goat given the car is not behind one of the two unchosen doors. This quotient is obviously 1, since the host always reveals a goat, regardless of where the car is.

We can then move on, as Glrk suggests above, to the case where the host chooses an unchosen door randomly and it just happens to reveal a goat. Here we can apply Bayes' rule and explain what it is in one hit.

If the host chooses randomly and the car is behind the originally chosen door it is certain that the host will reveal a goat. On the other hand, if the car is behind one of the two unchosen doors, the host has only a 1/2 chance of revealing a goat. Since we only count cases where a goat is revealed we must multiply our original odds by 1/2, changing 2:1 in favour of switching to 1:1. In fact I wonder if it might be best to have this calculation first.

Finally we can consider the case where the host always reveals a goat and has opened door 3. Now we have covered all the angles. Martin Hogbin (talk) 11:24, 23 February 2013 (UTC)

I don't understand this. If no door numbers are specified we can't use Bayes, and don't need Bayes. There is a chance of 1/3 that the player chooses the door hiding the car. There is a 2/3 chance that he chooses a door hiding a goat. In the first case the host will open a goat door and a player who switches gets a goat too. In the second case the host will open a goat door and the player who switches gets the car.

Bayes is only interesting and useful when we take account of door numbers. Richard Gill (talk) 18:55, 27 February 2013 (UTC)

Why can we not use Bayes' rule when there are no door numbers? We use the rule to calculate the posterior odds that the car is behind the two unchosen doors combined given that the host has revealed a goat. We know the odds of the car being behind the two unchosen doors are initially 2:1 and we use Bayes rule to show that they remain the same after the host has revealed a goat. Martin Hogbin (talk) 23:48, 27 February 2013 (UTC)

The probability the host will open a door and reveal a goat is 1, whether the car is behind the player's door or behind another door. So the Bayes factor equals 1, and the posterior odds equals the prior odds, 1:2. This is not a very interesting application of Bayes' rule. But of course, we already know that everything becomes simpler if we discard door numbers. Some insight is required to know that one can discard door numbers (though some people do it blindly/intuitively). Richard Gill (talk) 16:06, 16 March 2013 (UTC)

That may not be a very interesting application of Bayes' rule but it shows that the odds do not change when the host opens a door. This can be compared with the case where the host chooses an unchosen door randomly that just happens to hide a goat, where the Bayes factor is 2 making the odds evens. This nicely distinguishes between the two cases, which is the thing that puzzles people the most.

Of course, if we are fussed about door numbers we can calculate the Bayes factor given that the host has opened door 3. This is (1/2) / (1/2) = 1 and shows that the posterior odds remain 1:2 after door 3 has been opened and the combining doors solution is fixed. ~~ — Preceding unsigned comment added by Martin Hogbin (talk • contribs)

Yes one can apply Bayes in two steps, thereby fixing the combined doors solution. I have written this solution up in a number of places. Obviously I can't be the one who adds a reference to the article. And probably other people did the same before me, anyway. It's completely elementary. Richard Gill (talk) 13:57, 18 March 2013 (UTC)

I agree that when introducing a new tool (e.g. Bayes' rule) it is useful to show how it works in different problems, different contexts. This helps make people feel at home with the new concepts, and also shows the power of the new tool. It provides a systematic way to attack all kinds of variants to MHP and thereby explains why different variants have different solutions, Richard Gill (talk) 10:04, 17 March 2013 (UTC)

Richard, are there any references in the literature to the 'combining doors' solution failing if the host chooses randomly? Martin Hogbin (talk) 12:51, 17 March 2013 (UTC)

Not as far as I know. It's a flash-of-insight solution unique to the special situation of standard MHP, it is not the result of following a general strategy which would allow you to solve every possible variant of MHP. Richard Gill (talk) 13:52, 18 March 2013 (UTC)

So what should we add to the article?

My suggestion is that we add:
1) Bayes' rule applied to the random-choice host (no door numbers), showing how the odds of the car being behind the original door are changed.
2) Bayes' rule applied to the standard case (no door numbers) showing how the odds do not now change.
3) Bayes' rule applied to the standard case in which the host reveals a goat behind door 3.
Martin Hogbin (talk) 17:43, 18 March 2013 (UTC)

Good plan! Richard Gill (talk) 06:49, 20 March 2013 (UTC)

What sourcing do we need for this? Can it be considered a routine calculation? Does anyone object to this? Martin Hogbin (talk) 09:32, 20 March 2013 (UTC)

Routine WP:CALC: give a sourced expression and then plug in the numbers. An explanation of what Bayes means should be a ref to an appropriate text. Glrx (talk) 19:03, 20 March 2013 (UTC)

Jeff Rosenthal (book chapter; journal article) does some of these calculations. Possibly Jason Rosenhouse (book) too. -Richard Gill (talk) 05:59, 21 March 2013 (UTC)

What I would really like to say is something like this:

Let us consider the variation in which the host chooses at random one of the two doors not chosen by the playerand it just happens to hide a goat. Before the host opens a door, the odds of the car being behind two unchosen doors combined, rather than the door originally chosen by the player are 2:1.

We need to revise these odds to reflect any information that we may obtain when the host reveals a goat behind one of the two unchosen doors. To to this we can multiply the original odds by the proportion of times that the host would reveal a goat if the car is behind one of the two unchosen doors (which is 1/2 as the host was equally likely to have revealed the car) divided by the proportion of times that the host would reveal a goat if the car is behind one of the originally chosen door (which is 1 as the host can only possible reveal a goat).

This changes the odds to 1:1, meaning that there is no advantage in switching.

I suspect that his may be considered OR but I wonder if there is any way that we can apply Bayes' rule and explain what it means at the same time. A bare calculation, in proper notation will be of little help and interest to most people. Martin Hogbin (talk) 10:32, 21 March 2013 (UTC)

I'd mention Bayes and state what it does.

The Monty Hall problem can use some techniques from the theory of probability. Bayes' theorem provides a formula for how the probability of event A (the contestant's door hides the car) is affected by the occurrence of an event B (the host revealing a goat). Bayes' formula is

${\displaystyle P(A|B)={\frac {P(B|A)\,P(A)}{P(B)}}}$

where P(α) is the probability of event α and P(α|β) denotes the conditional probability of event α given that β happened. (Give an explanation of the formula...)

For the MHP, the probability the car is behind the contestant's door, P(A), is 1/3 because each door is equally likely to hide the car. The probability that the host reveals a goat, P(B), takes a little thought. There are two goats, so at least one of the two remaining doors will hide a goat. Monty knows which door hides the car, so Monty will not choose to open that door. Consequently, the probability that Monty reveals a goat behind one of the other two doors, P(B), is 1. Similarly, P(B | A), the probability of event B (Monty reveals a goat) given A (the car is behind the initially selected door) is also 1. Substituting the numbers in Bayes' formula gives

${\displaystyle P(A|B)={\frac {P(B|A)\,P(A)}{P(B)}}={\frac {1\,(1/3)}{1}}=1/3.}$

The formula tells us that the conditional probability that the car is behind the initially selected door is unchanged at 1/3 (i.e., the same probability before Monte revealed the goat). That also means that switching is advantageous because the probability that the remaining door has the car is 2/3.

Bayes' formula can also be used to calculate the probability for a different problem where Monty does not know which door hides the car. In that case, Monty randomly chooses one of the two remaining doors. Monty might reveal a goat or he might reveal the car. We are interested in the situation where Monty reveals a goat (if he reveals a car, the issues of switching is pointless. If the contestant's door hides the car (that is, A), then Monty can only select a goat. Consequently, P(B|A) is a certainty (1.0). Monty's chance of revealing a goat is 2/3. (A footnote could explain two ways of calculating this number.) Therefore

${\displaystyle P(A|B)={\frac {P(B|A)\,P(A)}{P(B)}}={\frac {1\,(1/3)}{2/3}}=1/2.}$

This result, 1/2, corresponds to many people's intuition. If Monty is ignorant and behaves like a second contestant, then the contestant's door and the other unopened door are equally likely to hide the car and switching doors does not improve the chance of winning the car. However, in the original problem Monty knows where the car is and avoids choosing it, so it is beneficial to switch.

Glrx (talk) 16:59, 21 March 2013 (UTC)

That looks good to me but I would prefer to use Bayes' rule which talks in terms of odds and is bit simpler. Martin Hogbin (talk) 20:34, 21 March 2013 (UTC)

And moreover, it has all been done in the literature: Rosenthal's book "Struck by Lightning" (chapter 14 is on MHP), and his published article on MHP http://probability.ca/jeff/writing/montyfall.pdf. Note: in the common situation when prior odds are equal, Bayes' rule is even simpler still: the posterior probabilities of various hypotheses given some particular evidence are proportional to the so-called "likelihood" of these hypotheses given the evidence - by definition the likelihood of each hypothesis is the probability of the evidence under the hypothesis. Rosenthal calls this simplified version of Bayes "the proportionality principle". Richard Gill (talk) 12:30, 22 March 2013 (UTC)

Discretionary sanctions

Notice:  There is an application to remove the authorization for discretionary sanctions from this article at Misplaced Pages:Arbitration/Requests#Amendment request: Monty Hall problem. ~ Ningauble (talk) 15:36, 13 March 2013 (UTC)

Ningauble, thanks for pointing this out. Would you care to clarify your present criticisms on the article, posted there: "Distortions in the current article, such as the inadequately sourced and apparently incorrect narrative under "A second controversy", and the (mis-) interpretation of the context sources refer to under "Criticism of the simple solutions" "? I agree that sources should be added to "A second controversy". That's not difficult to do. I disagree with your qualifications "incrrect" and "misinterpretation". But I'm trying to keep away from this page, so it would be good if new editors would discuss these issues with you here. Richard Gill (talk) 10:10, 17 March 2013 (UTC)

Ninguable, I too am puzzled by your comments. Where is the 'environment of antagonistic browbeating' who are, 'the most pugnacious or masochistic contributors'?

I see no sign of newcomers being driven away, In fact we have had some very useful contributions from them. Martin Hogbin (talk) 12:09, 17 March 2013 (UTC)

@Richard:  I elaborated a little on "A second controversy" in a separate section below. I am generally dubious of things that are not cited, but confess that presuming they are incorrect is a matter of pushing the burden of proof rather than asserting they are wrong. The present section is apparently questionable, or at least ambiguous, in using parenthetical remarks cited as "Later (2011). It would be good to verify and clarify whether the putative source explicitly contrasts "given the situation the player is in" with "averaged over all possible situations" in the manner indicated, or whether the parentheses indicate these are editorial interpretations/clarifications of the source.

@Martin:  I am not going to name names and cite cases because I was not requesting arbitration enforcement, I was only recommending that discretion remain available. I apologize for using some loaded language in commenting on the amendment request. Please feel free to interpret my remark about pugnacity and masochism as a reflection of my own lowly timorousness. If I have repeatedly walked away from discussions here for extended periods when I could not stand it anymore, it was unfair of me to assume anyone else is as pathetically weak-willed as I.

I am not going to delve into the "Criticism" section at this time because I would rather go after some low-hanging fruit before restarting something that has already been filibustered and stonewalled to death, or, if you prefer, because I can't walk and chew gum at the same time. ~ Ningauble (talk) 17:49, 22 March 2013 (UTC)

The remarks "given the situation the player is in" and "averaged over all possible situations" are editorial clarifications - uncontroversial unchallenged interpretations, attempts to convey the meaning of the technical terms unconditional and conditional to the general reader. Richard Gill (talk) 20:06, 23 March 2013 (UTC)

second controversy

Why do we have all the citation needed stuff there? The information can essentially be found in Morgan's original publication and later replies, the letter by Martin & nijdam and Rosenhouse's book.

Also a paragraph based footnotes might be a good choice here.--Kmhkmh (talk) 11:42, 17 March 2013 (UTC)

Kmhkmh, what is this 'second controversy'? Martin Hogbin (talk) 12:11, 17 March 2013 (UTC)

Ok I'm slightly stunned now, of course i was referring to Monty_Hall_problem#A_second_controversy. I would add the sources myself, but I don't have access to them right now with the exception of Rosenhouse's book.--Kmhkmh (talk) 14:05, 17 March 2013 (UTC)

I have copies in a dropbox folder, anyone who is interested send me an email and I'll share them. Richard Gill (talk) 13:42, 18 March 2013 (UTC)

Sorry, Kmhkmh, I understand now. I was thinking of discussions here, where the Morgan issue was the first (and only) controversy. Martin Hogbin (talk) 17:36, 18 March 2013 (UTC)

The fundamental justification, if one is really needed, for my placing tags in the "controversy" section is simply this: any he said / she said narrative about a contentious exchange simply must cite sources.

However, although I would personally find it interesting to peruse the sources, I must say that I think the whole Morgan et al. contretemps is being given undue weight in the article. I agree with Richard Gill's earlier remarks that the "controversy continues" subsection is completely out of place, and that the Morgan affair needs to be downplayed. ~ Ningauble (talk) 18:37, 21 March 2013 (UTC)

What do you suggest? Martin Hogbin (talk) 20:31, 21 March 2013 (UTC)

Ok, let me clarify with three specific suggestions. Some are expressed provisionally, and I indicate my preference.

1. If this material is to be included in the article then I suggest that Misplaced Pages:Verifiability is not optional. It says "Please remove unsourced contentious material about living people immediately." (It also says "Editors might object if you remove material without giving them time to provide references; consider adding a citation needed tag as an interim step" – which is what I did.) The current article reports that vS and M accuse each other of mendacity and evasion: this is contentious material that needs specific citations. This is not really just a suggestion: as policies go, this is a relatively firm one.
2. If this material is to be included in the article then I suggest, as mentioned above, that it is out of place. The initial "media furor" was about widespread naïve 50/50 responses to the riddle, and it may be debatable whether it is best to include this before or after presenting any solutions. A "second controversy" over vos Savant's method of solution and the putative necessity for using conditional probability should not be presented before any solutions are presented. Discussing contention over vos Savant's method of solution before even giving her solution is not just a confusing way to organize the article, it is contrary to both proposals in last year's RfC. If the article is to cover debates about or between vS and M then I suggest placing it in a later section about the merits of different methods of solution, presented after the solutions themselves.
3. The previous two suggestions were contingent on "If this material is to be included in the article". My third suggestion, as mentioned above, which is my personal preference, as should have been clear there, is to downplay the Morgan affair. As much as I like the idea of calling Morgan, et al. on the carpet for their mendacity, the article should focus on the Monty Hall problem and not on the personalities of its discussants. It is one thing to describe the relative merits of different approaches, briefly, to the extent that mathematical pedagogy is relevant for the average Misplaced Pages reader. I suggest doing so, briefly. It is another thing altogether to astonish and confuse our readers with a catfight.

I hope these suggestions clarify what I mean by {{citation needed}} and, perhaps to some extent, by "undue emphasis on contention." ~ Ningauble (talk) 17:21, 22 March 2013 (UTC)

I think this is getting a bit surreal now. Obviously it is appropriate to complain about the lack of citation/sources in that section. However as I wrote above the content is (to my recollection at least) more or less correct and sources are available. So why isn't simply the person who added that content adding the according sources now or alternatively somebody more or less agreeing with that section and having access to all involved sources? Instead we seem to be at the verge of potentially producing much ado about nothing.

@Richard Gill: Since apparently have access to all the related sources couldn't you simply add the citation. I know it is isn't necessarily your responsibility or problem however since you didn't mind to work extensively on the article in the past, I don't quite see what the problem is in doing such a small edit yourself now and why you're offering the sources to others instead. Or is their any content you object toh and hence don't want to source?--Kmhkmh (talk) 21:24, 22 March 2013 (UTC)

P.S.: I see no real reason for "downplaying" the "second controversy" as such, because that controversy was somewhat influential in the academic discussion of the subject and is as such described in (summarizing) secondary sources like Rosenhouse's book. There the subject is treated in 2 separate sections as well (L'Affaire Parade (pp. 22-26), The American Statistician Exchange (pp. 26-31)).--Kmhkmh (talk) 21:33, 22 March 2013 (UTC)

It's not one citation. It's a whole heap of citations (at least, there is a whole list of notices to add references).

Let's Make a Deal: The Player's Dilemma: Comment

Author(s): Richard G. Seymann

Source: The American Statistician, Vol. 45, No. 4 (Nov., 1991), pp. 287-288 Published by: American Statistical Association

Stable URL: http://www.jstor.org/stable/2684454

Let's Make a Deal: The Player's Dilemma: Rejoinder

Author(s): J. P. Morgan, N. R. Chaganty, R. C. Dahiya, M. J. Doviak Source: The American Statistician, Vol. 45, No. 4 (Nov., 1991), p. 289 Published by: American Statistical Association

Stable URL: http://www.jstor.org/stable/2684455

Letters to the Editor

Author(s): William Bell, M. Bhaskara Rao

Source: The American Statistician, Vol. 46, No. 3 (Aug., 1992), pp. 241-242

Published by: American Statistical Association

Stable URL: http://www.jstor.org/stable/2685225

Title: MORGAN, J. P., CHAGANTY, N. R., DAHIJA, R. C., AND DOVIAK, M. J. (1991), "LET'S MAKE A DEAL: THE PLAYER'S DILEMMA," THE AMERICAN STATISTICIAN, 45, 284-287: COMMENTS BY BELL AND RAO

Author(s): Marilyn vos Savant, John P. Morgan, Narasina R. Chaganty, Ram C. Dahiga, Michael J. Doviak, Nicholas R. Farnum, Duncan K. H. Fong

Source: The American Statistician, Vol. 45, No. 4 (Nov., 1991), pp. 347-348 Published by: American Statistical Association

Stable URL: http://www.jstor.org/stable/2684475

Morgan, J. P., Chaganty, N. R., Dahiya, R. C., and Doviak, M. J. (1991), “Let’s Make a Deal: The Player’s Dilemma,” The American Statistician, 45 (4), 284–287: Comment by Hogbin and Nijdam and ResponseRichard Gill (talk) 07:54, 23 March 2013 (UTC)

I have made a couple of deletions to reduce the personal aspect of the text. WE can add things back if we have good sourcing. Martin Hogbin (talk)

(edit conflict, I have not reviewed Martin's latest changes) Thanks Richard. I know you have researched the literature quite extensively, but I am still confused about the correspondence between these sources and statements in the article:

The article refers to "subsequent letters to the editor", but the first two citations here are discussion that ran together with the original Morgan, et al. paper (as sometimes happens when the editors of a journal feel a paper ought not stand on its own), not subsequent letters. Where the article says "In particular, vos Savant defended..." it looks like it refers to a letter by vos Savant. Are we still missing a citation for this, or is one of these a secondary source describing her defense? I assume (?) that where the article says "Later (2011), they did agree...", it refers to the "Comment by Hogbin and Nijdam and Response", but we need a more specific citation for where/when this appears.

I would also like to note that when the article says Morgan, et al. agree that, given random choice of goat, conditional and unconditional probabilities give "the same value", this is hardly news: their original paper makes much ado about the right answer for the wrong reason. They make a stronger statement in their rejoinder to Seymann about legitimate basis for the solution, not just the value. ~ Ningauble (talk) 13:46, 23 March 2013 (UTC)

Yes, sorry, I forgot about the vos Savant contribution. I´ve added it to the list.

PS The fact that Morgan et al´s contribution even generated a really angry response by vos Savant adds, in my opinion, to the noteworthyness of this second controversy.

PPS In Morgan et al´s response to Hogbin and Nijdam´s letter is written "We take this opportunity to address another issue related to our article, one that arose in vos Savant’s (1991) reply and in Bell’s (1992) letter,and has come up many times since. To wit, had we adopted conditions implicit in the problem, the answer is 2/3, period." Richard Gill (talk) 15:16, 23 March 2013 (UTC)

Couldn't you be so kind and simply add those sources and we'd be done with it? Btw. I agree with you regarding the noteworthiness (as outlined above). --Kmhkmh (talk) 15:05, 23 March 2013 (UTC)

Very busy (and I would prefer other editors also studied the sources carefully - one of the problems with MHP is that editors tend to think the problem can be solved by their own common sense and there´s no need to study the literature). But I at least added author (year) citations to make clear who is saying what when. Still to be done: links to proper bibliographic references. All are already in the reference list except for Rao, whose letter is published together with Bell´s. Richard Gill (talk) 15:16, 23 March 2013 (UTC)

Well I agree editors not (carefully) reading the sources has been longstanding problem of this article (in the German version as well). But that's the thing with most evangelists, they tend to stick to reading their own scripture rather than that of others. Be that as it may, thanks for adding the sources.--Kmhkmh (talk) 16:34, 23 March 2013 (UTC)

view from the outside

Administrative goings on elsewhere caught my eye. I'm a long-time fan of Monty Hall's show and old enough to have watched it in the original as well as a student many moons ago (Cooper Union) of statistics, probability, and game theory. The comparison offered from 2005 is straightforward and approachable. Today's version doesn't know if it's focused on the controversies or the mathematics or if it is merely a compendium of everything ever said pro or con (regarding the "2/3rds...") and of all mathematical models which apply in whole or in part.

As the article and the quandary are the "Monty Hall problem", I'm also puzzled as to how and why the article lead metastasized into its current form. There's a lot of stuff in there that should simply be in the body. Also, if we're going to box quote anyone, it should be Monty Hall or no one. Featuring a quote calling the "better odds if you switch" derivation crap is rather giving that position prominence.

Too many cooks stirring the pot?

Some retrospection on how the article got to its current state might assist in improving it. Just saying. VєсrumЬа ►TALK 23:34, 23 March 2013 (UTC)

Vecrumba: the Monty Hall problem was made famous by Marilyn vos Savant and her statement of the problem is repeated at the head of just about every journal article, book, or newspaper article on the problem. That is what we have in the lead. The box quote which you complain about is an illustration of the media controversy. By the way, do I understand that your remark that a derivation of "better odds if you switch" is crap, means that your personal opinion is that the player should not switch doors? Unfortunately, whether you like it or not, the consensus in the literature is that you do have better odds if you switch.

But anyway, if you don't like the lead, why not draft an alternative? Richard Gill (talk) 07:37, 24 March 2013 (UTC)

The following is a copy of something I posted at Misplaced Pages:Arbitration/Requests#Amendment request: Monty Hall problem. I think you will find the series of links in the middle to be of interest (especially the newer ones near the end):

In my considered opinion, we should rethink this issue and consider new solutions.

This is the longest-running content dispute on Misplaced Pages, and is featured at WP:HALLOFLAME.

I have been making periodic efforts to resolve this content dispute for the last two years. Some of my efforts have been:
Misplaced Pages:Arbitration/Requests/Case/Monty Hall problem/Evidence#Evidence presented by Guy Macon (outside observer, uninvolved with editing the page in question)
Talk:Monty Hall problem/Arguments/Archive 8#A Fresh Start
Talk:Monty Hall problem/Archive 23#A Fresh Start
Talk:Monty Hall problem/Archive 24#Consensus
Talk:Monty Hall problem/Archive 24#We Won an Award!
Talk:Monty Hall problem/Archive 25#How far have we come?
Talk:Monty Hall problem/Archive 25#Longstanding Content Dispute Resolution Plan Version II
Talk:Monty Hall problem/Archive 29#The Final Solution
Talk:Monty Hall problem/Archive 29#Ten Years And A Million Words
Talk:Monty Hall problem/Archive 33#Conditional or Simple solutions for the Monty Hall problem?
Talk:Monty Hall problem/Archive 35#The longest-running content dispute on Misplaced Pages
...and those are just the places where I created a new section.

After well over a million words, we have not reached a consensus on article content. To this day Talk:Monty Hall problem is full of spirited debates about what the content of the Monty Hall problem page should be. Another million words are unlikely to change that.

This has reduced the quality of the page, as evidenced by the fact that it is a former featured article. A comparison of the present page with the with the (featured 2005 version) is instructive.

Every avenue of dispute resolution has been tried, some repeatedly. Unlike many articles with unresolved content disputes, this does not appear to be the result of any behavioral problems. Instead, it is an unfortunate interaction between editors, each of whom is doing the right thing when viewed in isolation.

In my opinion, it is time to ignore all rules and start considering new ways to solve this, the longest-running content dispute on Misplaced Pages.

I propose applying a 6-month topic ban -- no editing of the MHP page or MHP talk page -- on every editor who was working on the page two years ago, one year ago, and is still working on the page today (this of course includes me). I predict that within a few months the remaining editors (and perhaps those who have gone away discouraged) will create an article that is far superior to the one we have now, and they will do it without any major conflicts. Giving the boot to a handful of editors who, collectively, have completely failed to figure out what should be in the article will have a positive effect. Of course it should be made clear that this does not imply any wrongdoing on anyone's part, but rather is an attempt to solve the problem with a reboot.

Two years is enough. It is time to step aside and let someone else try. --Guy Macon (talk) 01:39, 24 March 2013 (UTC)

I like this idea, both for this article, and in general for long-running-dispute (or talk-heavy) articles that are effectively owned by a small group of editors. Old revisions aren't deleted; they will still be here in 6 months too :-) – SJ + 07:26, 25 March 2013 (UTC)

The is no long running dispute here, just the normal WP cooperative editing which you are most welcome to join. Martin Hogbin (talk) 10:09, 25 March 2013 (UTC)

I think there is no content dispute going on here, there is no problem to be fixed. Guy: you did resolve the content dispute! Congratulations! People who think the article could be a whole lot better can come in and make proposals, they can draft alternatives and we can discuss them. They can be daring and rewrite whole parts of the article! They can cut out stuff which they think is unnotable and too specialistic. They might however also need to spend some time studying the sources since what makes things tricky with MHP is that everyone has an instinctive feeling that they know the answer and the sources are irrelevant. Yes: the old timers should hold back.

It is indeed interesting to look at the history of the article. Why the article was once "featured", short, coherent. Because it took sides in a dispute which is out there in the literature as to what is a right solution and what is a wrong solution. It is much easier to write an article if you are allowed to pick a particular POV than when you are not allowed to do that.

Guy: why don't you become an involved editor of the page rather than a conflict resolver? Richard Gill (talk) 07:43, 24 March 2013 (UTC)

If you are correct about there not being any disputes to resolve (and I am certainly not arrogant enough to assume that I can't possibly be wrong), that would make a lot of sense. If, however, I am correct, the last thing this page needs is one more voice. --Guy Macon (talk) 08:10, 24 March 2013 (UTC)

Guy if you think there are any real content disputes here please tell us what they are. As Richard says, you played a major part in resolving the long-standing dispute, which is now history.

We do have a couple of constructive discussions in progress. One is on adding a Bayes' rule explanation somewhere. No one has argued against this in principle but we are all looking for a way to produce a mathematically sound and well sourced explanation that is accessible to as wide a range of readers as possible. This is standard WP cooperative editing and anyone is welcome to join in.

There have also been suggestions that we have one or two of the simplest and most convincing solutions before the section on media response. I have personally shied away from pushing this because it might inflame old passions if done in the wrong way. Again, by working together I actually think we can add at least one simple explanation to the start of the article without causing any unnecessary friction.

Your suggestion that all the regular editors walk away from this article is not one of your better ones, it is totally against the ethos of WP and has received no support from anyone else. Far better would be for you to join in the ongoing and civil discussions on how to improve the article. Martin Hogbin (talk) 10:27, 24 March 2013 (UTC)

@Gil, I think you misunderstood me re: "By the way, do I understand that your remark that a derivation of "better odds if you switch" is crap, means that your personal opinion is that the player should not switch doors?", which is that if the article was to feature any spot-quote, a quote from Monty Hall on why the reveal/switch offer works for the show, not a spot quote highlighting the opinion on one side of the equation (no pun). Well, I've rewritten content elsewhere for some contentious topics,... might try the lead.

This does remind me of another threesome, on a three lane highway in traffic the other lane really is moving faster most of the time, statistically speaking. VєсrumЬа ►TALK 21:07, 24 March 2013 (UTC)

Monty has made a comment about this problem and it said two things. Firstly he agreed with vos Savant (and everybody else) that it is better to switch in the circumstances described in the problem and secondly he pointed out that, in the real show, he only offered money and never the opportunity to swap. Martin Hogbin (talk) 21:48, 24 March 2013 (UTC)

Vecrumba, I'm glad I had misunderstood you! Richard Gill (talk) 07:56, 25 March 2013 (UTC)

Question: is the above a disagreement concerning what the content of the Monty Hall problem page should be or is it something else? This talk page gets a lot of words posted to it each week. Surely those words must be about something. I'm just saying. --Guy Macon (talk) 22:10, 24 March 2013 (UTC)

You will have to ask VєсrumЬа that, I am not sure exactly what his/her point is. Martin Hogbin (talk) 23:22, 24 March 2013 (UTC)

The "there is no content dispute" hypothesis

Let us consider the hypothesis that "There is no long running dispute here, just the normal WP cooperative editing" and "there is no content dispute going on here".

An article that has been around for years and which has no content disputes settles into a fairly stable form, with occasional additions of citations or minor rewording. The article talk page has very little activity because there are no content decisions to be made.

Let us consider the amount of activity in a 60 day period for the following pages, chosen because they have "problem" in the title:

Birthday problem:
13 revisions by 10 users
Talk:Birthday problem:
0 revisions by 0 users

Three Prisoners problem:
4 revisions by 3 users
Talk:Three Prisoners problem:
1 revisions by 1 user

Two envelopes problem:
12 revisions by 5 users
Talk:Two envelopes problem:
9 revisions by 6 users

Sleeping Beauty problem:
2 revision by 2 users
Talk:Sleeping Beauty problem:
0 revisions by 0 users

Monty Hall problem:
266 revisions by 29 users
Talk:Monty Hall problem:
498 revisions by 22 users

Is this the activity level of an article with stable content, or is this the activity level of an article which has an ongoing discussion about what the content of the article should be?

Now let us consider selected quotes from this talk page (I have purposely deleted the names and the actual arguments so that this does not rekindle an old argument. The point here is whether there is evidence of a content dispute):

" is highly misleading"

"It is not misleading but there is an argument that it requires additional logical steps to be correct."

"That's your opinion and the opinion of some sources. And of some editors. But not all sources, not all editors. There's no point in discussing this again. The discussion has gone on for five years or so and as far as I know, nobody involved ever changed their minds."

"You are speculating that thinks like you. A way of thinking which is not even discussed in published literature. Pure speculation and highly biased. I am arguing from knowledge of the context in which the article was written, and knowledge of the preceding literature."

"I am not suggesting that we add my interpretation of this solution to the article. Just that we leave our own personal interpretations out of it."

"Do you have a copy of the article that I can read. If it clearly supports your view that then we can, of course, say that in the article."

"I have been bold and made changes to to explain exactly what I mean."

"I've been bold also, and reverted your changes."

"Some people (somewhat perversely) consider there to be . To start half way through the problem with a hand-waving argument about starting where convenient is not acceptable if we want to be thorough."

"This is not perverse, it is eminently sensible. If you want to decide rationally on a course of action you need to know "

"The perverseness is in assuming that "

"It's also not perverse to . is an eminently sensible way to solve the problem in a principled way. That's why all the probability texts do it that way."

"There was no handwaving in my description of the solution. I told you explicitly that . Absolutely sensible, absolutely normal."

"Not exactly clear or simple. Why not start with , just as you do with ?"

"Clear and simple if you've learnt some formal probability theory. Why not? Because it would be a complete waste of time."

Are these the comments one would expect for an article with stable content, or for an article which has an ongoing discussion about what the content of the article should be? Comparing them with the talk pages of the other "problem" articles listed above is quite instructive.

I think that it is pretty clear that there is indeed a long-running dispute about the content of this article. --Guy Macon (talk) 17:07, 25 March 2013 (UTC)

It is interesting to note that the discussion now apparently moves from disputes over content to disputes over disputes (over content). It seems editors here can't exist without disputing something.--Kmhkmh (talk) 17:40, 25 March 2013 (UTC)

"Perhaps when a man has special knowledge and special powers like my own, it rather encourages him to seek a complex explanation when a simpler one is at hand." --Sherlock Holmes

--Guy Macon (talk) 18:22, 25 March 2013 (UTC)

That is an interesting (cherry picked!) collection of quotes. Guy's theory is that there is an ongoing content dispute. There certainly *was* a content dispute, I thought that it was resolved through Guy's patient and hard work, which led to a working "consensus" as to how the article should be structured. Since the new consensus structure differed from the structure the article had before, a lot of work was done by a lot of editors, old and new, to restructure the article according to the new consensus. Naturally this led to a lot of discussion. I don't think it is quite finished yet. My first conclusion is that Guy should wait for at least two years for the dust to settle, before concluding that there is some kind of terrible dispute still going on which needs some draconian intervention to fix. (By the way I think there is much less activity on the talk page than in the hey-days of the dispute, and much more serious editing of the article: so I disputes Guy's interpretation of his statistics)

Now another thing is, do we expect this situation ever to change? Guy proposes that all editors who were fairly active over the last two years should stop editing the article for the next six months. There certainly is some merit to this as the old hands do from time to time still repeat to one another what they have been saying for years. On the other hand, let's suppose all the old hands not only quit editing but also quit talking on the talk page, and also quit talking on the Arguments page. Many of the old hands had, at least, taken the trouble to read a lot of the literature on MHP. You know, the reliable sources on which wikipedia articles are supposed to be based? Preferably ternary sources?

My prediction is that in no time there would be new quarrels going on here among new editors. Possibly the article will get drastically rewritten by adopting just one of the numerous Points of View which exist, out there, on how MHP ought to be solved. If you want a powerful concise clear article on MHP it should be written by one person with a clear and consistent point of view. The old encyclopedias had a single authoritative person write each article. Many on-line encyclopedia's today are still organized in this way. An authoritative editorial board invites authoritative scientists and scholars to each write an article about their own pet subjects.

My prediction is that if Guy's proposal is adopted, we will see no superficial change in the volume and nature of exchanges on this talk page, but the Misplaced Pages-Quality of the article will decline markedly. (Sure, some readers will love the result; but others will hate it. Probably better that everyone hates the article a little. I'm reminded of Democracy - a very bad political system but unfortunately there isn't a better one). Richard Gill (talk) 18:44, 25 March 2013 (UTC)

a minor flaw

Currently the article writes : "In Tierney (1991), the mathemagician and Stanford professor Persi Diaconis stands up for vos Savant, see Diaconis (1988) for his work on symmetry in statistics."

Sadly enough Tierney (1991) doesn't even mention Diaconis nevermind describing him as standing up for vos Savant.--Kmhkmh (talk) 17:52, 25 March 2013 (UTC)

Have you read all of Tierney's article in New York Times? It's three pages long. It does mention Diaconis and Diaconis does support vos Savant (incidentally I also corresponded with Diaconis about this ...). Richard Gill (talk) 18:41, 25 March 2013 (UTC)

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