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At day's end, it will be 7 days since Rick requested comments from all the editors we could think of who had shown an interest in the MHP, plus a general request to the WikiProject Mathematics page. Three days ago, Rick requested mediation assistance. To date there have been no volunteers.
How and when do we keep moving forward toward a consensus? Glkanter ( talk) 13:56, 9 December 2009 (UTC)
Rick, based on the following, I don't see this procedure as being any help whatsoever to this particular group of editors. Is there some other benefit to this that I do not understand? What other path can the clear consensus take toward gaining 'permission' from the minority view to move forward with editing the article?
You made some claim a couple of days ago about this legitimately created good faith consensus violating NPOV, which I'm sure each member of the consensus would dispute strongly. Is this the issue you want mediated? The claim seems far fetched, certainly, to me. Or is this still an issue from your point of view? Glkanter ( talk) 13:01, 10 December 2009 (UTC)
I don't think the informal mediation is going to be of any value. It requires a volunteer mediator, of which none have come forward yet. It could takes weeks before one comes forward, it could be never. Whatever the mediator comes up with is non-binding. It has no teeth. In the meantime, all sorts of edits are being made to the article without any discussions whatsoever.
I suggest we request Mediation immediately, recognize the consensus for the proposed changes, and stop being hostages to this 6 year long filibuster. Glkanter ( talk) 14:40, 14 December 2009 (UTC)
The first section I created after my return is called 'Is the Contestant Aware'. http://en.wikipedia.org/wiki/Talk:Monty_Hall_problem#Is_The_Contestant_Aware.3F
All I ask is this:
It's a pretty simple, straightforward, and incredibly relevant question.
But neither Rick or Nijdam have given me a straight 'yes' or 'no'.
So, we're asking for mediation, but we haven't even stated our underlying reasons for disagreement. Because without their responses, any logical argument I might make to a mediator can be refuted, for most any reason.
And, as the section name indicates, using your noggin is not the same as OR. But that seems to be the reason for not replying.
So, enough of the 'well, I didn't say that per se', and let's get to the bottom of this. No mediator can help us if we're not being forthright. Glkanter ( talk) 05:11, 11 December 2009 (UTC)
JeffJor, oh, yeah, you've made the right decision. We have clearly demonstrated a consensus. Rick is going to use every method he can devise to extend his filibuster. There have been a lot of folks prior to us who ultimately made the same decision, to quit arguing with Rick. But we have proven the argument unlike anyone before us. "Suppose you're on a game show..." End of discussion on who's POV for the doors, and no more host behaviour. They used to argue 'little green men from space's' POV as being the MHP. I kid you not. And, no more host behaviour means no more Morgan. Of course, kmhkmh is still arguing the definition of a game show, but won't answer the 'Is The Contestant Aware?' question.
As far as the details, Morgan and his ilk get mentioned, they're published. But no more bad mouthing the Devlin solutions. Did you read my Huckleberry section? Please re-read my modified proposal. So, we just have to navigate Wikipedia's consensus processes. Rick is the king of that crap, so we'll learn as we go up the chain, whatever it is. Do you have any experience with that? So, a few of us will continue working together the straight path to improving the article. Glkanter ( talk) 22:53, 12 December 2009 (UTC)
I think this is at least one of the changes that has been argued for, and I haven't seen anyone argue against it (and those of you who think this is what I have been arguing against are simply incorrect), so I've moved the paragraph about the Morgan/Gillman generalization introducing the host preference as a variable q to the Variants section. If anyone is arguing about this, feel free to revert. -- Rick Block ( talk) 00:51, 13 December 2009 (UTC)
Here's a proposal for a unified solution section that I suggest replace the current two solution subsections. I offer this partly as an example of what I mean by a specific suggestion, and partly to show what I think would be a sufficient, NPOV, solution section.
According to the problem statement above, a car and two goats are arranged behind three doors and then the player initially picks a door. Assuming the player's initial pick is Door 1 ( vos Savant 1990):
Players who choose to switch win if the car is behind either of the two unchosen doors rather than the one that was originally picked. In two cases with 1/3 probability switching wins, so the probability of winning by switching is 2/3 as shown in the diagram below. In other words, there is a 2/3 chance of being wrong initially, and thus a 2/3 chance of being right when changing to the other door. This result has been verified experimentally using computer and other simulation techniques (see
Simulation below).
Another way to understand the solution is to consider the two original unchosen doors together. Instead of one door being opened and shown to be a losing door, an equivalent action is to combine the two unchosen doors into one since the player cannot choose the opened door ( Adams 1990; Devlin 2003; Williams 2004; Stibel et al., 2008).
As Cecil Adams puts it ( Adams 1990), "Monty is saying in effect: you can keep your one door or you can have the other two doors." The player therefore has the choice of either sticking with the original choice of door, or choosing the sum of the contents of the two other doors, as the 2/3 chance of hiding the car hasn't been changed by the opening of one of these doors.
As Keith Devlin says ( Devlin 2003), "By opening his door, Monty is saying to the contestant 'There are two doors you did not choose, and the probability that the prize is behind one of them is 2/3. I'll help you by using my knowledge of where the prize is to open one of those two doors to show you that it does not hide the prize. You can now take advantage of this additional information. Your choice of door A has a chance of 1 in 3 of being the winner. I have not changed that. But by eliminating door C, I have shown you that the probability that door B hides the prize is 2 in 3.'"
Another way to analyze the problem is to determine the probability in a specific case such as that of a player who has picked Door 1 and has then seen the host open Door 3, as opposed to the approach above which addresses the average probability across all possible combinations of initial player choice and door the host opens ( Morgan et al. 1991). This difference can also be expressed as whether the player must decide to switch before the host opens a door or is allowed to decide after seeing which door the host opens ( Gillman 1992). The probability in a specific case can be determined by referring to the expanded figure below (note the case where the car is behind Door 1 is now the middle column) or to an equivalent decision tree as shown to the right ( Chun 1991; Grinstead and Snell 2006:137-138). Considering only the possibilities where the host opens Door 3, switching loses with probability 1/6 when the player initially picked the car and otherwise wins with probability 1/3. Switching wins twice as often as staying, so the conditional probability of winning by switching for players who pick Door 1 and see the host open Door 3 is 2/3—the same as the overall probability of winning by switching. Although these two probabilities are both 2/3 for the unambiguous problem statement as presented above, depending on the exact formulation of the problem the conditional probability may differ from the overall probability and either or both may not be able to be determined ( Gill 2009b), see Variants below.
A formal proof that the conditional probability of winning by switching is 2/3 using Bayes' theorem is presented below, see Bayesian analysis.
I have tried to remove any POV-ish statements in the above. If there's anything left that does not sound NPOV please either just fix it or discuss here. The idea is to present both a plainly correct unconditional solution (it's basically vos Savant's from her second column) as well as a plainly correct conditional solution, without expressing a preference for either treatment. -- Rick Block ( talk) 19:12, 14 December 2009 (UTC)
1/3 | 1/3 | 1/3 | |||
You choose a goat | You choose a goat | You choose a car | |||
The host opens a door to reveal a goat | The host opens a door to reveal a goat | The host opens a door to reveal a goat | |||
You Stick | You Swap | You Stick | You Swap | You Stick | You Swap |
You get a Goat | You get a Car | You get a Goat | You get a Car | You get a Car | You get a Goat |
Any other comments? I'm particularly interested in comments from the folks Glkanter is considering part of the "consensus", i.e. JeffJor, Colincbn, Boris, and Melchoir. -- Rick Block ( talk) 14:29, 15 December 2009 (UTC)
But Rick, you are not part of the consensus. You are against the proposals. Or has that changed, and mediation is no longer required? Glkanter ( talk) 21:30, 15 December 2009 (UTC)
Holy cow. I went camping this weekend and I woke up in the tent in 33 degree F. cold trembling in a cold sweat, having a nightmare about goats and shiny cars and numbered doors and a genetic-cross monster whose body was that of a water buffalo and the head was that of Thomas Bayes, and everyone was throwing food about and nobody knew whether everything or anything is random or predetermined and people were capriciously changing their minds in the middle of the game conditionally and unconditionally, and I decided that I would just run off and try to re-read "Kant's Critique of Pure Reason", and then maybe shoot myself. That might be easier. :o) Worldrimroamer ( talk) 02:04, 15 December 2009 (UTC)
There's plenty of editing of the article currently taking place, including by Rick Block, who is not part of the consensus.
Why couldn't the consensus just go ahead and begin fixing the article, so that it is in line with the proposals? Glkanter ( talk) 11:51, 15 December 2009 (UTC)
How do we resolve the inconsistency between the Contestant's POV in the MHP, and the "unknowns'" POV in all the host variant stuff? Especially that large table. The whole thing makes no sense to me. Glkanter ( talk) 15:08, 15 December 2009 (UTC)
I suggest we quit waiting around for the informal mediation. There may never be a volunteer.
Formal Mediation is the next step, then arbitration.
Is there a second to my motion? Glkanter ( talk) 15:26, 16 December 2009 (UTC)
Is Rick's diff out of control consistent with our efforts to find an unbiased informal mediator? Or has he made that impossible?
Glkanter ( talk) 20:22, 16 December 2009 (UTC)
I can see why someone who has a great deal of time, effort and pride invested in Wikipedia would be protective of his work. Especially if the only Featured Article which he personally 'sheparded' through the review process was at risk of being dramatically revised. Revised so much, that the FA designation would likely be at risk.
But there is a difference between understanding and condoning. In addition to all the filibustering that takes place on the talk pages, these phrases were used when requesting (supposedly) un-biased assistance as per Wikipedia policy:
So, I can see why an owner of an article would reject all good faith efforts at improved clarity. I just don't agree with the continual passive-aggressive intellectual dishonesty that I have witnessed throughout the 14 months I've been active on this article. I've got a lot of time, effort and pride invested in this article, too. And I'm part of a legitimate consensus for making the proposed changes. That's why I point out, without hesitation, when I think another editor is not behaving in good faith. These aren't personal attacks. They are a recognition of why the article has been so wrong, for so long, despite the efforts of so many 'agitating' editors who disagree with the "shepard's" POV.
Some people will argue that this discussion is out of line. But everything I wrote is supported by diffs. Why fear the truth? I would reply that the criticisms would come from those who favor the status quo for the article. Glkanter ( talk) 13:05, 17 December 2009 (UTC)
The article states (without citation) that Kanov stated that in the "Ignorant Monty" case, swapping still yields a 2/3 chance of winning - but a quick simulation of all cases reveals this to be wrong: suppose I pick door 1, and Monty opens door 2 without knowing what is there but reveals a goat (all other permutations are equivalent to this): the car will now be behind either door 1 or door 3 with a 1/2 probability. -- New Thought ( talk) 09:44, 19 December 2009 (UTC)
Even though this problem is always described as "counter-intuitive", I find it interesting that EVERYONE on Earth understands the problem intuitively if you look at it another way: When you watch Deal or No Deal, the only reason it's suspenseful is because the person opening a case does NOT know if there's a big number inside that case. If you were on a Monty Hall Problem game show, and picked door #1, and the host said "I'm going to open a door now... hmmm... number 2" (ignorant monty - or at least from the player's POV, you must assume ignorant monty), you would be worried and suspense-filled that he might open the door with the car. When he doesn't, you feel relief. However, if Monty said, "Now, let me open a door with a goat in it... number 2" you would feel no suspense. He has told you the door has a goat, you know it's a goat, and it has no suspense. This is because there is no risk in him opening a door. He will always open a goat door. If your odds of having a goat behind your original selection improved, you'd be excited after he revealed a goat, but because he knows it's a goat, you feel no more excited about your first choice than before he opened the good. This is an example of how people DO intuitively understand this, but then don't recognize the ramifications of this feeling when offered the choice to switch observe below:
Here is an analysis of all cases when the car is behind Door number 3 (logic dictates that there are tables for the car behind behind doors 1 and 2 that have identical probabilities (for the appropriate doors). The number at left is the door you choose; the number at the top is the door Ignorant Monty opens. The result is whether you should switch ("y" or "n"). "c" represents Monty revealing the car.
1 | 2 | 3 | |
---|---|---|---|
1 | y | c | |
2 | y | c | |
3 | n | n |
1,1 2,2 and 3,3 are greyed out, because he can't open the door you chose. As you can see, there are two cases where switching nets you a car, and two cases when it does not. There are also two cases where he reveals the car ("c") and you are (presumably) not offered a choice, as the car location is now known. Ignorant Monty has a 1/3 chance of revealing a car and ending the game. ONCE that does not happen, there are four possible cases left, 1/2 of which require switching to win, 1/2 of which require keeping to win. This is the conditional probability of "What is the probablity that switching will win GIVEN that Montry did not reveal the car?" The absolute probability is absolutely true - even with ignorant Monty, switching will win you the car 1/3 of the time - 1/3 of the time staying will win, and 1/3 of the time Monty will reveal the car, and you will not get the option.
Regular Monty has 0 chance of revealing a car. While regular monty has a decision to make SOMETIMES (if you select the car, he must pick which goat to reveal), as long as his pick is random, the result of his pick are both the same: you should still not switch, (so the conditional probability of winning by switch IF monty randomly selects one door or the other is 0 in both cases - you can't win by switching). Thus, if you picked right the first time, don't switch. If you picked wrong the first time, DO switch. Therefore, 1/3 of the time, don't switch, 2/3 of the time, switch.
This is true in the ignorany monty case also: If you picked wrong (2/3), do switch. If you picked right (1/3) don't switch. However, half of the time when you pick wrong (half of 2/3 = 1/3), Monty reveals the car, and you don't get to make a choice. Therefore, IF you get the option to switch (only 2/3 of the time will you get this far), then the odds are even between keeping (1/3) and switching (1/3) (the other third is monty reveals the car). TheHYPO ( talk) 19:47, 19 December 2009 (UTC)
I believe I correctly summarized vos Savant.
Let's re-apply some things we've learned: 'Suppose you're on a game show...' Still true? Contestant's SoK? 'Random' would equal Deal or No Deal. 'He's drunk' or 'forgetful' might not be communicated to the contestant. Then it's still the MHP from the contestant's SoK.
What exactly is the revised problem statement? —Preceding unsigned comment added by Glkanter ( talk • contribs) 20:04, 19 December 2009 (UTC)
By 'random' I mean 'car or goat revealed by Monty'.
I don't thìnk your summary or Rick's summary reflect my thoughts on this puzzle. Have I been obtuse? Why summarize me at all? —Preceding unsigned comment added by Glkanter ( talk • contribs) 21:03, 19 December 2009 (UTC)
I have added names to the sections below based on comments above. If I have got it wrong please move yourself.
Please do not make comments in this section.
Editors are invited to sign against their names to confirm that they are in the right section.
Martin Hogbin (
talk)
11:29, 5 December 2009 (UTC)
Colincbn
Martin Hogbin
Martin Hogbin (
talk)
11:29, 5 December 2009 (UTC)
Glkanter
Glkanter (
talk)
12:16, 5 December 2009 (UTC)
JeffJor
Melchoir
Dicklyon
Boris Tsirelson
Boris Tsirelson (
talk)
15:27, 5 December 2009 (UTC)
Gill110951 (
talk)
13:28, 20 December 2009 (UTC)
Rick Block
Nijdam
kmhkmh
Glopk
Please move your name to the correct section if appropriate.
Martin Hogbin (
talk)
11:24, 5 December 2009 (UTC)
Henning Makholm
Chardish (I object to summary classification of my comments. -
Chardish (
talk)
00:59, 11 December 2009 (UTC))
Why does the entire Krauss and Wang text appear twice in the first bit of the article? Isn't the article long enough without this repetition? RomaC ( talk) 14:48, 10 December 2009 (UTC)
Thanks, Rick, for finding a solution that resolves my concern (an overly long intro) Butwhatdoiknow ( talk) 00:02, 21 December 2009 (UTC)
Way back in junior high, we did some proofs or problems or something to do with absolute values. That's all I can remember.
But the thing I do remember is that after you 'solved' the problem, you had to go back and check each of the results to make sure it didn't violate the original problem statement in some way.
That's all I'm saying about Morgan and the rest. When you check your work with some 'host behaviour' variant, it no longer meets the original problem statement, "Suppose you're on a game show..." Go ahead and argue. Better you should save your breath. Hosts don't tell contestants where the car is.
So, as an encyclopedia, Wikipedia will properly refer to reliably published sources like Morgan. And Devlin. No problem.
But, as a self-appointed 'explainer' of all things MHP, I think the article improperly gives the conditional solutions way too much emphasis. Because it doesn't match the original problem statement any longer. Glkanter ( talk) 21:47, 6 December 2009 (UTC)
Selvin poses the MHp. He solves it unconditionally at 2/3 vs 1/3 if you switch. The problem is hailed as a great paradox.
vos Savant prints a letter inspired by Selvin in a general interest USA Sunday newspaper supplement. She solves it unconditionally at 2/3 vs 1/3 both when you made your choice, and when the switch is offered. Because Monty's actions don't impart usable knowledge to the contestant. It's a sleight of hand. Nothing happened.
All heck breaks out. Tens of thousands of letters, including over 1,000 from PhDs tell her she's wrong. And they are certain!
vos Savant soothes the savage beasts with logic and smarts. The unconditional solution carries the day. The problem is, again, hailed as a great paradox.
This group, "J. P. Morgan, N. R. Chaganty, and M. J. Doviak are Associate Professors and R. C. Dahiya is Professor, all in the Department of Mathematics and Statistics, Old Dominion University, Norfolk, Virginia" (284 The American Statistician, November 1991, Vol. 45, No. 4 (C 1991 American Statistical Association) develops the argument that the problem is only properly solved using a conditional problem statement. Their criticisms, etc. rest on this: That when faced with 2 goats, the host must decide which goat to reveal. This rests on the assumption (presumption, invention) that the contestant might somehow gain usable information as to the location of the car in this particular instance of the game by Monty's actions. It's left unstated whether Monty's actions would be shared with the contestant. And if they are shared, what method is used. But it's clear: in this instance of game play they claim, the subject contestant could be armed with more useful information that the average contestant.
Others come out with papers supporting Morgans criticisms, including Gillman in 1992 and Grinstead and Snell 2006.
Others continue publishing unconditional papers. (It seems likely that if 3 Wikipedia editors plus Seymann find fault with the paper, so too would members of the Professional Mathematics Community. And as professionals, they don't make a big stink about it. They just ignore the paper and continue publishing articles that rely solely on the unconditional problem statement.)
So, has the Professional Mathematics Community decided that Morgan is right, and Selvin was a hack? I don't think so. Before, during and after Morgan's paper, respected, credentialed reliable Mathematics professionals continued to publish articles solving the MHP unconditionally. I don't know that any of these professionals in either camp have attacked or counter-attacked anyone else's paper. It looks to me, that in the Professional Mathematics Community nothing happened. No usable information was gained. Perhaps Morgan's paper, like Monty revealing a goat is just sleight of hand, imparting no usable knowledge? It's possible. Most published MHP articles say nothing of Morgan or conditionality.
Which brings us, finally, to the Meta Paradox. The Wikipedia editors are arguing, essentially, over whether or not solving the unconditional problem is 'enough'.
Suppose you are given a story problem about a game show. The Professional Mathematics Community agrees heartily that this is a delightful paradox which can be 'proved' or 'solved' using an unconditional problem statement. Maybe not even requiring formal probability notation. Symbolic notation is often used. Then "J. P. Morgan, N. R. Chaganty, and M. J. Doviak are Associate Professors and R. C. Dahiya is Professor, all in the Department of Mathematics and Statistics, Old Dominion University, Norfolk, Virginia" come forth and say it must be solved conditionally, based on the arguments set forth in their paper. You are then offered to stay with the unconditional solution being complete, or you may switch to the conditional solution.
Many people are fooled by this paradox, and accept the switch. Because they don't realize that like Monty revealing the goat, no new usable information has been revealed by this paper. Nothing happened. Glkanter ( talk) 18:27, 8 December 2009 (UTC)
Wow, this thread is long! And I haven't even looked at the archive(s?). I thought it might be worthwhile to make a comment as a person who has not been following this thread before now. I just, in the last couple of days, read the article and a big portion of the discussion.
My comment is simple: Please, I am not attacking anyone; I am just making a general, honest, respectful IMO comment. (And yes, I am schooled in mathematics.) I agree with those that say the article is too long, very unwieldy, and often downright confusing. I think the article as it now stands is almost worthless. I agree with those who say: Just state the "standard" problem as most people assume it is stated, and give a simple explanation as to why it is correct. Then meander off into the conditional and unconditional ponderings, the Bayesian statistics, etc.
I started out reading the article, with expectation of fun. I was already familiar what the "Monty Hall problem", and I understood it, at least in its more obviously stated form (based on the generally accepted assumptions). As I read on I thought, "Whaaa???" Much of the -- sorry, but most -- of the article is a murky mess, and even those who are somewhat probabilistically astute I think would have difficulty making sense of some of it. I'll cite just one example: The section titled "Popular Solution" is, IMHO, poorly written and confusing. Frankly, it's not clear what the author is meaning to get across in several places (even though I understand exactly what it is that he/she is intending to say). It needs to be rewritten, as does much of the rest of the article. Not tweaked, but rewritten. This sort of muddled presentation is just not necessary, and it is not worthy of the standards of Wikipedia. This stuff is not string theory or Gödel's incompleteness theorems in ZFC. This is introductory-level probability, albeit a very subtly tricky example of it.
I never seen an article on Wikipedia that has created such a WikeWar as this article has. It apparently has no resolution in sight. Anyway, I'm all out of suggestions -- if I have even made any.
Finally, just for fun, I wanted to mention a somewhat similar conditional-probability problem which I haven't seen anyone else mention. (It is not relevant to this article, nor should it appear in it; it's just related.) You play a "flip three coins game". The person I am gambling with shakes up three fair coins in a canister and spills them onto the table top. I am not allowed to see the coins initially before I make my choice; the canister shaker (my opponent) hides the coins from me. The rules are, the shaker peeks at the coins on the table and he has to tell me what the "majority" coin is. There will be either a majority of heads (3 heads or 2 heads) or a majority of tails (3 tails or 2 tails). Then, having been told what the majority is, I must guess what the third coin is -- heads or tails. If I get it right I get paid a dollar by the shaker; if I get it wrong, I pay him two dollars. Most people would think this a stupid gamble on my part; they will assume that the guess as to the heads-tails of the third coin has a 50-50 chance of being right. But it's easy to see (though it is initially counter-intuitive to many people) that if you always guess the opposite of the majority, you will win 3/4 of the time. Just write down all combinations: HHH, HHT, HTH, THH, HTT, THT, TTH, TTT, and it's obvious. That would make a cool bar game. Even offering your opponent the 2-to-1 payoff, you would still win, on average, in the long run 25 cents per play:
1/4*(-2) + 3/4*(1) = 1/4 of a dollar per coin-shake, in the long-run average.
Good luck with your little war. Worldrimroamer ( talk) 23:53, 8 December 2009 (UTC)
Sorry for being so cryptic. 'The editor' is you. As we try to bring this discussion to a close, we are attempting to build a Wikipedia Consensus to make changes very much as you described. So, I was asking the other editors if there is any reason your opinion should not be considered as part of the 'let's change the article' consensus, of which I am a part. It's all good. I think you'll find the discussion of the last few weeks most meaningful. Some extra Wikipedia Mathematics Project people have begun contributing, by request, and it's helped move things forward a great deal. Again, sorry for being unclear. Glkanter ( talk) 03:27, 9 December 2009 (UTC)
__________________________________________________ —Preceding unsigned comment added by Worldrimroamer ( talk • contribs) 17:51, 9 December 2009 (UTC)
I very much like this question to be answered first. (BTW several sources mention the MHP to be equivalent to the three prisoners problem.) Nijdam ( talk) 22:35, 15 December 2009 (UTC)
Until now only Boris has shown the derivation of a solution in formulas, using symmetry. This leads to the conclusion - as I BTW showed a million comments ago - that the conditional probability we are interested in is equal to the unconditional and hence may be easily calculated. It doesn't show the conditional probability is not needed. All others come with words, words, .... Nijdam ( talk) 17:25, 20 December 2009 (UTC)
I don't understand why all this article editing is taking place without being discussed.
While we 'old guys' are working towards a formal WP solution, newer people are editing at will.
This seems unproductive, not good for the article or readers, and distracting.
Any support for a temporary freeze? Is this even plausible? Thanks. Glkanter ( talk) 12:25, 21 December 2009 (UTC)
He's expecting Dicklyon to 2nd it. I see a lot of unintended irony here. I had just created a new section on the talk page with 3 edits. Then, here's what I call Dicklyons's unprovoked vandalism on my talk page edits:
It's all right here: Is This Chronology Correct?
So, if anybody wants to put in a good word for me, I'd be much obliged. Please note, I'm pretty sure I will get this promptly dismissed, but any support is appreciated. Glkanter ( talk) 04:25, 22 December 2009 (UTC)
On this RfC/U, Rick Block and Dicklyon are trying to make a case that I am disruptive, don't edit the article often enough(?),incivil, interrupt consensus building, chase other editors away, contribute nothing of value, too aggressive with my POV, have bad breath, etc. I'm holding my own on the RfC. It's gotten pretty ugly. So, if anybody would like to drop a supportive word about good ol' Glkanter, now would be a good time. By reading the RfC, you will also learn a lot about the inner thought processes of some well known editors. Thanks. Glkanter ( talk) 22:22, 26 December 2009 (UTC)
Thank you. Glkanter ( talk) 15:10, 23 December 2009 (UTC)
I think there are 2 POVs regarding how to 'cherish' the MHP paradox.
Some of us, including myself, love the simplicity. Nothing happens. Heated Arguments over 1/2 vs 2/3 ensue. More than once, even.
Other people like the complexity, and 'what ifs' that the MHP could be with just a little tweaking. The permutations can approach Game Theory scenarios.
Since it was a great paradox before Morgan and conditional, I consider the 'simplicity' people the ones who accurately support how Selvin's MHP paradox should be presented in the Wikipedia Article. Glkanter ( talk) 15:35, 23 December 2009 (UTC)
1. The simple solutions are not solving the correct problem.
2. Morgan's paper, published in 1991, can claim to recognize and describe the Monty Hall Problem Paradox, first published by Selvin in 1975, equally as well (and equally importantly) as Selvin's original paper, which relied only on simple solutions.
I'd like to see the people arguing in support of those 2 arguments come out and directly say it. Once you clearly state your positions, the other editors, using reliably published sources can then address your objections to the proposed changes. Glkanter ( talk) 18:32, 23 December 2009 (UTC)
In the RfC that Rick Block and Dicklyon filed on me RfC Glkanter one of the 'complaints' was that I argue on the MHP talk pages too much, at the expense of actually editing the MHP article. The associated 'remedy' was that I modify the MHP article more frequently and discuss my reasons for doing so less often.
Now, that's no reason to slap me with an RfC, but the point is well taken. I've asked for a 'freeze' on the article of some sort at least twice in the last couple of weeks. Meanwhile, some editors just make edits without discussing them first.
So, consistent with my stated understanding of the various literature on the MHP, and in accordance with Rick's criticism/suggestion as conveyed via Wikipedia's formal RfC procedure, I will begin to thoughtfully edit the article as I understand the consensus has approved. Glkanter ( talk) 15:51, 24 December 2009 (UTC)
How about I start with the FAQs on the talk page? That looks like pure Morgan POV, a clear violation of NPOV. Anybody want to clean it up, or should I just delete it?
Glkanter (
talk)
16:47, 24 December 2009 (UTC)
Here's another one. Id like to change the 'Simple solution' heading to something like 'Original Paradox explanation' or 'Selvin's Proof' or 'vos Savant's Popular Solution'? I'd like to get the point across concisely that it was this level of understand from which all the excitement about the paradox came. Not to be confused with the 'conditional solution' or, non-solution without the equal goat door constraint being equal to exactly 1/2, that came out some 15 years later.
Glkanter (
talk)
16:03, 25 December 2009 (UTC)
Then a transition section that says 'For many people, this is all the understanding they need, and was Selvins and vos Savant's point. Others may want to continue further into this article...' And as long as there's no bad-mouthing the 'original' solutions, you 'conditional' guys can pretty much do what you want with the article from there. Glkanter ( talk) 16:10, 25 December 2009 (UTC)
Rick, the current text includes this:
I still disagree that using a different problem is a means of challenging a particular problem. Originalists would argue that all you've demonstrated is the difference between puzzles with different premises. I would further argue that with the contestant being aware of Monty's left door bias, this is no longer the MHP about a game show that Selvin and vos Sovant made so famous. Glkanter ( talk) 06:38, 27 December 2009 (UTC)
When asked how he was able to sculpt the venerated 'David', Michelangelo replied, 'It was easy really. I removed everything that didn't look like David'. —Preceding unsigned comment added by Glkanter ( talk • contribs) 23:51, 8 December 2009 (UTC)
This is most of the 'greeting' to the talk page of the FAQs. Probably only seen by other editors.
I think this can be improved. Anybody mind if I take a shot at it? Glkanter ( talk) 23:32, 26 December 2009 (UTC)
I appreciate your help with this, Rick. I'm suggesting we would edit this. What then? Glkanter ( talk) 19:27, 27 December 2009 (UTC)
<noinclude>{{FAQ page}}</noinclude>
<noinclude>blah blah blah</noinclude>
Variants - Slightly Modified Problems section.
Since the MHP is from the contestant's POV, there should be some narrative about what the POV's in this whole section represent. Are they the contestant's? Is it a premise in each different problem that it's no longer the contestant's POV? What about addressing the Monty Hall problem from 'not-the-contestant's POV' for comparison purposes? This would be beneficial to the readers, I believe. Glkanter ( talk) 16:55, 27 December 2009 (UTC)
Selvin's - simple: 2/3 & 1/3, always switching doubles your likelihood of getting the car
Morgan's - conditional, no symmetry: between 1/2 and 1 (?), never to your disadvantage to switch
Morgan's - conditional, with symmetry: 2/3 & 1/3, always switching doubles your likelihood of getting the car
Have I summarized the above properly? Glkanter ( talk) 11:03, 27 December 2009 (UTC)
If so, maybe the article could transition from:
Simple, to conditional - with symmetry (they are equivalent), to conditional - no symmetry (leftmost door variant). Glkanter ( talk) 11:30, 27 December 2009 (UTC)
I disagree with your recent reverts to the article, Rick.
I just checked the Morgan paper, and they do not use the word 'variant' or any derivative of it when describing the problems.
I think this is an uncommon usage, and does not clearly indicate to the reader exactly what is being described. I don't think adding 'Slightly Modified Problem' to a heading, and replacing 1 instance of 'variant' in the article also with 'slightly modified problem' is 'pointy'. Different than your POV, perhaps, but that does not necessarily make it, or any other edits I may make in good faith, 'pointy'. Glkanter ( talk) 19:45, 27 December 2009 (UTC)
In an attempt to see exactly who thinks what I have set up some questions on User:Martin_Hogbin/Monty_Hall_problem/dissenters. Everyone is welcome to add their answers. Please comment briefly only in the comment section and have discussions about the questions on the associated talk page.
Whether we have external mediation or not I am sure it will help if everyone answers the questions on this page. I am trying to determine of we have two distinct camps, a single axis of opinion, or just randomly scattered views on the subject. Are there any other questions that editors feel will help sort out the differences of opinion here? I have just added a few extra ones. Martin Hogbin ( talk) 11:36, 28 December 2009 (UTC)
Explain the problem to me please. Glkanter ( talk) 01:45, 28 December 2009 (UTC)
If you're here because you've been invited to comment, there are ,two,. three (related) suggestions.
Please indicate in subsections below whether you favor or oppose each of these suggested changes.
The intent is to try to determine whether there is community consensus for any of these changes. I would suggest one subsection per user who is commenting, and to avoid endless arguments, restricting your comments to your own section (this is modeled after the process used at Wikipedia:Arbitration Committee). I've precreated sections for everyone I've explicitly invited to comment. -- Rick Block ( talk) 15:31, 2 December 2009 (UTC)
In this section please summarize the changes you're suggesting. I'll be asking the set of folks I mentioned to Glkanter above to come here and offer their opinions, so please keep it as brief as possible. Please let me know when you think this section is ready for others to comment on. -- Rick Block ( talk) 01:07, 1 December 2009 (UTC)
We should take the current K & W statement as our starting definition of the MHP.
The primary solution and explanation should not use conditional probability
The Morgan paper clearly does not answer the question as stated in the article and thus should not be regarded as our ultimate reliable source.
The Morgan solution should be introduced in a later section of the article that deals with variations of the problem.
(referring to JeffJor's suggestion)
(referring to Glkanter's suggestion)
I really don't know jack about probability and whatnot, but I still tend to agree with Glkanter's points. I came to this article through looking up various paradoxes and this was a really neat one that I got to try out in the real world (see simulation question above). As I understand it the "Monty Hall problem" states that the host chooses randomly, so any other discussion about host behavior should be limited to the "Variants" section under "Other host behaviors". Just my 2 cents, Colincbn ( talk) 02:41, 1 December 2009 (UTC)
By my count, that's 4 in favor of the proposed changes, and 0 against. I've been championing these changes since October, 2008, Martin prior to that, and countless other editors for about 5 years. When can we declare an end to the pointless filibustering, acknowledge a consensus, and move on? Rick, will you be offering your comments? Have you contacted the others? Glkanter ( talk) 22:29, 1 December 2009 (UTC)
About Martin Hogbin's suggestion - :I agree 100% with your proposed changes. I would like to add my 2 cents to the rationale, however. Morgan is criticizing and solving something other than the Monty Hall game show problem in the article. The introduction of the contestant being aware of any 'host behaviour' when selecting from 2 remaining goats changes the Problem Statement of both vos Savant/Whitaker and Karauss & Wang from "Suppose you are on a game show" to the converse, "Suppose you are not on a game show". Individual contestants on game shows are never provided more information than the 'average' contestant will have. There can be no 'condition'. It's illogical. Glkanter ( talk) 15:33, 2 December 2009 (UTC)
[Repeated in part from comments below]
The point of separating the articles is not to eliminate any POVs. It is to emphasize them. To not let one facet of the MHP (simple solution w nonintuitive result) become overpowered by the other (good teaching tool for conditional probabilites). If we don't physically separate them, we need to more clearly divide the article. The first part should be about the classic (unconditional) MHP, as stated by MvS (not K&W), and listing the set of assumptions she has said (and 99.9% of readers agree) are implied: interchangable doors, and any kind bias becomes irrelevant because of interchangeable doors. Then a section about game protocals (part of what some call host stratgies) such as always opening a door or revealing a goat, WITHOUT mention of bias or conditional problems. This mostly exists. Finally, you can cite Gillman (not Morgan) as a reference that introduces the possibility that the conditional problem is intended, but matters only if there is a bias. Use the K&W statement here, not Gillman's misquote. Gillman is better than Morgan because it is clearer, includes placement bias, and does not launch into possibilities that we are never told how to use. I think this is pretty consistent with Martin's suggestion. JeffJor ( talk) 17:44, 4 December 2009 (UTC)
As a matter of fundamental Wikipedia policy, articles MUST be written from a neutral point of view. What the proponents of these changes are essentially suggesting is that this article take the POV that the interpretation of the problem described by a significant number of reliable sources (the Morgan et al. reference and others) is invalid. Even if this were a stance taken by reliable sources (which, as far as I know, is not the case), by relegating the "Morgan" interpretation to a "variant" subsection or splitting it into a POV fork this article would then be taking the "anti-Morgan" POV. I've made this point to these editors numerous times before, but yet they keep tendentiously arguing that the "Morgan" POV is wrong, or the Morgan et al. reference has errors, or (most recently) that the Morgan POV is NOT about the "real" Monty Hall problem (as if by convincing me that their POV is "correct" I would then agree with the changes they're suggesting).
I sincerely hope the "consensus" from this process is against making these changes, because even if there is a consensus for these changes they cannot be implemented - doing so would violate Wikipedia policy. -- Rick Block ( talk) 04:01, 3 December 2009 (UTC)
You all realize Martin's proposal implies the article will not even mention conditional probability except in a "variant" section, don't you? How anyone can think this is not a blatant POV issue escapes me. -- Rick Block ( talk) 20:19, 3 December 2009 (UTC)
I have to state the opposite view, which is that you have taken a ridiculously pro-Morgan POV. There are many reliable sources that relate to the MHP and not all of them have a host door choice parameter. Those that do generally quote Morgan as the source for this.
The article already takes a problem statement from a reliable source (K & W) and that same source confirms that this is how most people view the problem. In that statement, the host is defined to choose a legal goat door randomly. It is thus a simple matter of fact that the Morgan paper does not address that problem in so far as it allows a door choice parameter where none is permitted by the problem statement.
The Morgan paper clearly addresses a scenario where where the player is somehow aware of the host's policy for choosing a legal goat door. This rather bizarre scenario is not the one described by our problem statement and thus it should be viewed as a variant of the MHP as it is most commonly understood. Martin Hogbin ( talk) 21:30, 3 December 2009 (UTC)
I thought I made it clear we were to use arbcom style rules here, which are that you only comment in your own section (it really does help keep the threads from getting absurdly long). However, since you've been rude enough to post here I'll respond to each of you, BUT please do not continue this as a thread here.
Glkanter asks why so dramatic? The argument has shifted from "present an unconditional analysis first (and don't criticize it)" to "exclude the conditional analysis completely (except as a variant)". This is a huge difference.
Glkanter asks why I haven't responded about his "Is The Contestant Aware?" question. Why should I? Glkanter has repeatedly demonstrated a complete lack of comprehension of nearly everything I've ever said. It's like trying to explain something to a cat. At some point you just have to give up. However, I'll give it another go. Meow, meeeow, meow, meowww. I'm not sure I have that quite right since I don't speak cat, but it's probably about as comprehensible to him as anything else I could say.
Martin (incorrectly) claims again that the Morgan et al. paper does not address the K&W version of the problem. Quote from the paper: "Incidentally, Pr(Ws | D3) = 2/3 iff p = q = 1/2". This is the solution to the K&R version of the problem statement. The Morgan et al. paper (and the Gillman paper and many, many others who approach the problem conditionally) absolutely address the K&R version. Because they also address other versions doesn't mean they don't address the K&R version.
Martin and Glkanter are both apparently completely incapable of understanding the main point of the Morgan et al. paper (and the Gillman paper, and what Grinstead and Snell have to say) which is that the MHP is fundamentally a conditional probability problem and that there's a difference between an unconditional and conditional solution. What these sources are saying is that a conditional solution clearly addresses the MHP (as they view the problem), but an unconditional solution doesn't unless it's accompanied by some argument for why it applies to the conditional case as well (and there are many valid arguments, but no argument at all which is what is generally provided with most unconditional solutions is not one of them). The fact that the problem can be (and typically is meant to be) defined in such a way that unconditional and conditional solutions have the same numeric answer in no way invalidates what these sources say. To have the article take the stance that the conditional solution is invalid (which would be truly absurd), or that the criticism these sources make of unconditional solutions is incorrect, or that a conditional solution applies only to a "variant" is making the article take a POV. This would be a direct violation of a FUNDAMENTAL Wikipedia policy. -- Rick Block ( talk) 01:53, 4 December 2009 (UTC)
Delayed response (am not a very active editor at all these days), but here it is.
Statement
Motivation. The purpose of an encyclopedia is to present a "best" selection from the body of knowledge about each topic, being POV neutral as well as reader-neutral. -- glopk ( talk) 18:53, 29 December 2009 (UTC)
Thanks for the invitation to comment. In my opinion, Martin Hogbin's suggestion seems the post prudent. The Monty Hall problem as popularly explained doesn't rely on conditional probability, and the Whitman explanation seems sufficient for anyone who is not a mathematician. Wikipedia is a general-purpose encyclopedia, and as such main articles should focus on explaining topics as they are popularly understood, with specific scientific analysis relegated to separate articles.
And, to be honest, the article as it stands is much harder to read and understand (as a layperson) than it was several years ago. NPOV isn't "pleasing everyone equally"; don't let efforts towards neutrality wind up hurting the article. - Chardish ( talk) 02:53, 6 December 2009 (UTC)
Just from reading the present Wikipedia article, I agree with Martin Hogbin's suggestion, because I don't see why allowing the host to prefer one goat over the other is a more relevant generalization than allowing the host other behaviors. Melchoir ( talk) 06:47, 3 December 2009 (UTC)
I fully support Rick's view. Nijdam ( talk) 10:34, 3 December 2009 (UTC)
To make my position crystal clear: there is no such as an unconditional solution. There are different problems: an unconditional problem and a conditional one. The latter generally being called the MHP. Nijdam ( talk) 22:24, 3 December 2009 (UTC)
I haven't been watching this article for a while; glad to see the K&W treatment up front; that looks like the most sensible article I've seen on it. As for the Morgan conditional approach, I think it's an unnecessary distraction, but it's out there in mainstream reliable sources about the topic, so we ought to cover it in the article. I think Martin Hogbin's proposal sounds best. Dicklyon ( talk) 05:01, 3 December 2009 (UTC)
I agree with Rick Block that the other two proposals essentially violate WP:NPOV; but I disagree that moving the conditional stuff to a more minor position is a problem; his heavy promotion of the conditional approach violates WP:UNDUE in my opinion. Dicklyon ( talk) 16:29, 3 December 2009 (UTC)
I have long since given up on following these discussions, and am not even a very active editor these days. However, since somebody went to the length of creating a heading for me, here are my general recommendations -- for whatever they are worth:
– Henning Makholm ( talk) 07:13, 3 December 2009 (UTC)
I summarize my position in two points:
Boris Tsirelson ( talk) 06:44, 9 December 2009 (UTC)
Being invited by Glkanter, I quote here some paragraphs of a discussion that happened on my talk page on February 2009. As far as I understand, my position is close to that of JeffJor. Boris Tsirelson ( talk) 17:20, 2 December 2009 (UTC)
Why split? Because of different importance. The "conditional" article will be, say, of middle importance, while the "unconditional" article – of high importance. We surely have our point of view about importance (rather than content). Boris Tsirelson ( talk) 05:54, 4 December 2009 (UTC)
The quotes follow.
Each time giving the course "Introduction to probability" for our first-year students (math+stat+cs) I spend 20-30 min on the Monty Hall paradox. I compare two cases: (a) the given case: the host knows what's behind the doors, and (b) the alternative case: he does not know, and it is his good luck that he opens a door which has a goat. Im addition I treat the case of 100 (rather than 3) doors (just like Monty Hall problem#Increasing the number of doors). And, I believe, students understand it.
I have no idea, why some people spend much more time on the Monty Hall paradox (and even publish papers). (Boris Tsirelson)
This simple little problem is deeper than it might appear, and likely well worth more than 20-30 mins of lecture time. Perhaps even worth revisiting once or twice during a term to explore its more subtle aspects. (Rick Block)
Deeper than it might appear? OK, why not; but still, for now I am not enthusiastic to deep into it. Tastes differ. I find it more instructive, to restrict myself to the simpler, symmetric case, and compare the two cases mentioned above.
If an article leaves many readers puzzled, why it is unnecessarily complicated, it is a drawback. (Boris Tsirelson)
If a problem that appears so simple to me, like the Monty Hall problem, is not sufficiently solved using my unconditional proof, in what circumstances is the unconditional proof appropriate? Thank you. (Glkanter)
The unconditional argument shows that "always switch" is better than "never switch". This is what it can do. Let me add: if you (that is, the player) are not informed about possible asymmetry then you cannot do better than these two strategies, either "always switch" or "never switch". (Boris Tsirelson)
I'll start with a clear statement and give some more detailed information afterwards:
If one surveys the available literature literature/publications on the topic, you pretty much get an relatively obvious outline for the article: original problem (in vos savant's column), unconditional solution (basically vos savant and/or various math sources), conditional solution (Morgan and almost in any math source), various problem variation and caveats, history of the problem, application of the problem outside the math domain. Which is essentially for the most part, what we already had and what Rick managed to maintain. In that context I fully agree with Henning Makholm's comments above, who puts it fairly well. The article wouldn't have such problems if all participants would follow that rationale.
The fuzz over quality or minor mistakes in Morgan's paper is a somewhat ridiculous distraction, since Morgan's paper is not needed to argue the conditional solution or caveats to the unconditional solution at all. There is plenty of other math literature dealing with the problem in more or less the same manner.
My personal advice would be to pass the article for final thorough review and modification to the math or a science portal. During that review neither of the 4 disagreeing authors (JeffJor, Glkanter, Martin Hogbin, Rick Block) are allowed to participate/edit. After that review the article should be fully protected for good.
I've seen what happened to the German version, that had similar problems (without a Rick Block around to constantly remain some standard). So we had a lot of people with a somewhat fanatic approach constantly pushing for their favoured explanation and constantly ignoring wiki standards, common sense and more important the available literature on the subject. As result mathematicians and scientists basically dumped the article and gave up on improving it.An effect this article has partially seen as well.-- Kmhkmh ( talk) 16:45, 4 December 2009 (UTC)
No comment right now. But a lot of Christmas break reading to do here, to catch up. Happy Wikipedia Christmas, everyone! Gill110951 ( talk) 13:27, 20 December 2009 (UTC)
(I welcome you all back to my screen. This article has improved a lot over the last year.)
Morgan et al. (1991) seem to assume that the doors are statically numbered, having the same numbers through repeated experiment. Vos Savant however writes in her column: "You pick a door, say #1, and the host opens another door, say #3". This may mean that after a door is picked, we (always) call it #1, while the opened door is (always) called #3. Such dynamic numbering can make it easier to discuss and calculate the given options. The consequences of the assumption of Morgan et al. are further explained in this article under "Probabilistic solution - 1991".
The Morgan paper classifies solution F5 as "incorrect because it does not use the information in the number of the door shown". This is only true assuming statical numbering. In this context it is questionable why Morgan et al. quote vos Savant wrongly, writing "You pick door No. 1, and the host opens No. 3". Heptalogos ( talk) 14:11, 30 December 2009 (UTC)
The Morgan paper is not about Monty Hall, but about a question in a column of vos Savant, starting with "Suppose you're on a game show". All exact information is, of course, in the paper, so no other sources are relevant. Heptalogos ( talk) 19:44, 30 December 2009 (UTC)
The source I mention, "Morgan et al. (1991)", is probably the most argued source in this article. It is in the article reference list mentioned as: "Morgan, J. P., Chaganty, N. R., Dahiya, R. C., & Doviak, M. J. (1991). "Let's make a deal: The player's dilemma," American Statistician 45: 284-287." Heptalogos ( talk) 20:11, 30 December 2009 (UTC)
If you're suggesting to move or continue discussion about the specific arguments used in the Morgan source, to or on the arguments subpage, then that's fine with me. But I'm doing more than that, namely introducing a new element to the global dilemma, which is the method of numbering doors. Heptalogos ( talk) 20:43, 30 December 2009 (UTC)
The Morgan paper is quite clear about the disctinction between conditional and unconditional. I quote: the unconditional problem, which may be stated as follows: "You will be offered the choice of three doors, and after you choose the host will open a different door, revealing a goat. What is the probability that you win if your strategy is to switch?" The distinction is made by opening a specific door, instead of "a different door". This is mentioned elsewhere in the paper several times. I agree that No. 3 is an example and might be No. 2 as well, but the paper assumes that there is an essential difference between "the open door" and "door No. x, which is open". To my opinion these are only labels which don't make any difference, unless of course one assumes that a specific door is labelled the same through repeated experiment. Heptalogos ( talk) 21:40, 30 December 2009 (UTC)
I want this article to explain how the conditional probability could actually differ from the overall probability (I refer to chapter "Probabilistic solution - 1991"), when the distinction between both is made by information (a door number) which seems to have no statistic dependency or influence on the requested probability. To my opinion, the average intelligent reader of this paradox, who has no mathematical skills, still doesn't understand the necessicity of using the relatively complex method of conditional solution. I agree that the discussion about the necessicity itself should preferably be held elsewhere, but an elementary explanation key in the article should be, I guess, in the idea of a static door position through repeated experiment, whatever it means. The meaning of that I would like to be explained. Heptalogos ( talk) 23:45, 30 December 2009 (UTC)
I propose adding an external link to http://www.opentradingsystem.com/quantNotes/Monty_Hall_problem_.html
The link in question contains derivation of solution in a general context developed on other examples. —Preceding unsigned comment added by Kaslanidi ( talk • contribs) 20:27, 30 December 2009 (UTC)
I object, per WP:ELNO points 1, 4, and 11. - MrOllie ( talk) 20:32, 30 December 2009 (UTC)
My 'POV' is that this paradox twists peoples' brains a lot, just the way it is. Whatever 'is' means.
So a sequenced roll out of how the problem became published, then controversial twice would help the interested reader. What could make more sense then to describe the events roughly as they occurred, and beliefs/understandings changed, or maybe they didn't.
Let the reader decide for himself, or herself.
Yes, 'sequenced roll out' really means 'chronological'. Forgive me.
Pretty radical, eh? Just tell the story as the sources do, and let the reader draw his own conclusions. Whoda thunk it? Glkanter ( talk) 20:35, 30 December 2009 (UTC)
Simple solution is not a solution at all
"This is the same topic discussed in more detail three sections down (about the subtly different question), and indeed Morgan et al. argue the "simple" solution is not a solution at all." -- Rick Block ( talk) 16:28, 26 October 2008 (UTC) —Preceding unsigned comment added by Glkanter ( talk • contribs)
@Rick, you seem to be putting up an Aunt Sally (Strawman argument). You seem to be implying that I want to remove the POV of Morgan and others who agree with them from the article. That is not the case. I have always suggested that the article should start with the simple non-conditional solutions and then, after discussing these thoroughly, move on to the conditional case discussed by Morgan and others. It is clear, from your reposted quote above (I had not noticed that it had been reposted) that you believe that the Morgan paper should somehow veto or overrule all other sources no matter what they say. Martin Hogbin ( talk) 22:54, 26 December 2009 (UTC)
I think Rick Block and Nijdam are fillibustering and ownershipping against beneficial changes to this article.
I see no point in waiting for either form of mediation unless Nijdam indicates he will accept the findings.
Rick filed an RfC against me last week, the first item of which is 'only edited the article 1 time.' Now, as you've seen yesterday, every edit I make, he or Nijdam at his request, reverts.
If at least 2 people are with me, I'll proceed. Glkanter ( talk) 17:31, 28 December 2009 (UTC)
Case link
I've re-opened the case at MedCab and volunteered to assume the role of mediator in a discussion aimed at resolving an on-going dispute here. Additionally, I've issued invitations to participate in the discussion to all involved parties listed in the mediation request. While anyone is welcome to offer input, I ask that those who participate do their best to be concise and refrain from assumption/presumption regarding other's perspectives.
As mediator, my primary goal is to step in as an uninvolved party and help find some common ground from which to proceed. It is not my task to pass judgment on anyone's opinion in the discussion and there is no 'right' or 'wrong' beyond that which is dictated by Wikipedia policy.
I have read the article and understand its subject matter and all it details. As I begin delving through the talk page archives, I'll open the discussion with a call for opening statements. If you feel any archived passages are significant in summarizing the situation, it would help to include links, but please conclude your first post with a Summary of Position (your opinion as it relates to the matter). And remember...concise ;-)
--
(
talk)
05:28, 29 December 2009 (UTC)
I want the article clearly mention the remark made by some sources that the so called "simple solution" is not complete. It doesn't need initially mentioning the technical term "conditional probability". To make my point clear: the following resoning:
is not complete and better should read:
Something alike holds for the so called "combined doors solution" and most of the other simple ways of understanding. That's all. Nijdam ( talk) 08:36, 29 December 2009 (UTC)
I'd like to add that the (a) MHP always involves enumerated doors and a decision to switch offered to the player after a door is opened, seen by the player who has to decide. This is in my opinion and of many (most) sources the only relevant problem. Nijdam ( talk) 11:48, 31 December 2009 (UTC)
The MHP is essentially a simple mathematical puzzle that most people get wrong. At least the first part of the article should concentrate on giving a simple, clear, and convincing solution that does not involve conditional probability. All diagrams and explanations in this section should not show or discuss the possible difference that the door opened by the host might make, although I would be happy to include, 'this action does not give the player any new information about what is behind the door she has chosen' as in Nijdam's second statement above. The first section should give aids to understanding and discuss why many people get the solution wrong, without the use of conditional probability. The first section should be supported by sources which do not mention conditional probability
The simple solution section should be followed by an explanation of why some formulations of the problem require the use of conditional probability, with reference to the paper by Morgan et al. and other sources. It should also include the various variations of the basic problem and other, more complex, issues. Martin Hogbin ( talk) 10:19, 29 December 2009 (UTC)
I want the article to clearly mention that the remarks made by some sources, that the so called "simple solution" is not complete, is not shared by all sources. It need not mention "conditional probability" beyond saying that due to the symmetry forced by being a game show, the simple solution is equivalent to the symmetric 'conditional solution'.
I think I agree with Nijdam on the text, although they are both OR. It's consistent with my 1st talk page edit, using an IP address in October, 2008:
I'd like to see 3 solution sections: Selvin's simple solution of 1975, transitions to Selvin's symmetrically equivalent conditional solution of 1975 (where the discussion of the simple solution's criticisms occurs), transitioning to Morgan's conditional non-solution of 1991.
I'd like to see the word 'variant' either stricken, or augmented by 'slightly different problem'.
I'd like to see a lot of 'blather' removed from the article. Too much time and effort is spent in the various remaining sections explaining the conditional solution, for no real reader benefit. Glkanter ( talk) 10:39, 29 December 2009 (UTC)
And the 'Variants - Slightly Modified Problems' section needs work. The MHP is from the contestant's state of knowledge (SoK). The versions in this section are not. This needs to be normalized for the reader in a few possible ways: An explicit statement that the contestant is aware of these new conditions (in which case these are no longer game show problems), or the explicit statement these problems are not from the contestant's SoK, and a comparison of the MHP from a non-contestant's SoK. Glkanter ( talk) 13:14, 29 December 2009 (UTC)
First, I think the basic issue is an NPOV issue. The primary question is whether the article currently expresses a "pro-Morgan" POV, i.e. takes the POV of the Morgan et al. source that "unconditional" solutions are unresponsive to the question and are therefore "false" solutions - and, if so, what should the remedy be.
There are a variety of sub-issues we need to discuss but I think the main event is how the solution section is presented. I strongly object to splitting the solution section into separate sections (this was done some time ago, well after the last FARC), which inherently favors whatever solution is presented in the first such section. I mildly object to including the "combining doors" explanation in the solution section rather than in a subsequent "aid to understanding" section.
What I would like is for the article to represent in an NPOV fashion both a well-sourced "unconditional" simple solution (e.g. vos Savant's or Selvin's) and a well-sourced conditional solution of the symmetric case (e.g. Chun's, or Morgan et al.'s, or Gillman's, or Grinstead and Snell's) in a single "Solution" section, more or less like the suggestion above (see #Proposed unified solution section - somewhat modified just now). This follows the guidelines at Wikipedia:Make technical articles accessible, specifically most accessible parts up front, add a concrete example, add a picture, and do not "dumb-down".
Once we address this basic issue I think the other issues will be easier. -- Rick Block ( talk) 19:43, 29 December 2009 (UTC)
-- K10wnsta ( talk) 22:01, 1 January 2010 (UTC):Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, "Do you want to pick door No. 2?" Is it to your advantage to switch your choice?
Hello K10wnsta. There are several editors here keen to get on with improving this article. Are you still intending to mediate? Martin Hogbin ( talk) 10:08, 4 January 2010 (UTC)
And a fruitful start (continuation) in 2010! Nijdam ( talk) 11:45, 31 December 2009 (UTC)
Say, the 'forgetful' Monty?
Marilyn vos Savant says this is really a 'random' Monty, who might reveal a car.
I expand this to say, if it's random, then anyone, including the contestant could open the doors.
And if it's the contestant, then we're really talking about 'Deal Or No Deal'.
Does it makes sense to criticize the original solutions to the MHP based on an analysis of Deal or No Deal? Not in my book. Glkanter ( talk) 17:21, 1 January 2010 (UTC)
Another Straw Man from Rick. Both sides go in the article. Why not chronologically? I've been saying this for a week. Your's and Morgan's POV not dominating the current article? Don't make me laugh. Now, why not answer for yourself, as a sentient being, what does "Suppose you're on a game show...' mean? Without hiding behind Wikipedia's policies. It's OK, we're on a talk page. Glkanter ( talk) 01:16, 4 January 2010 (UTC)
So, by watching, you realize he nods his head at where the car is. Now the female contestant has a 100% likelihood of selecting the car.
This is equivalent to Morgan's argument about a left-most door bias. It's published, but pretty darn stupid.
There is no contestant, or viewer, awareness of a host bias on a game show. And the puzzle begins, 'Suppose you're on a game show...' Glkanter ( talk) 17:20, 5 January 2010 (UTC)
I have now shown that in order to get an answer (probability of winning by switching) of anything other than 2/3, Morgan have had to assume that we know that the producer places the car randomly, but we do not know that the host opens a legal door randomly. Is there anyone here who can justify that odd POV.? Martin Hogbin ( talk) 10:12, 4 January 2010 (UTC)
I disagree on 1 point, Martin. "Suppose you're on a game show..." means the car placement and host choice, as far as the contestant is concerned, are random. This is true whether it's a hypothetical game show, or a mathematical puzzle. Because that is the host/contestant relationship on a game show. And it's every bit as much a premise of this math puzzle as '1 car and 2 goats' which is clearly stated. Because 'Suppose you're on a game show...' has also been clearly stated. Glkanter ( talk) 18:44, 4 January 2010 (UTC)
JeffJor, I'm with you on this 100%. So, living with the requirement that since they're published, Morgan and its ilk must be included in the article, how would you apply your argument to the article? Bear in mind, imho, the conclusion that 'Morgan's paper does not address the MHP' is, unfortunately, OR. Unless you have a source? Seymann just couldn't quite say it. Glkanter ( talk) 18:03, 7 January 2010 (UTC)
![]() | This is an archive of past discussions. Do not edit the contents of this page. If you wish to start a new discussion or revive an old one, please do so on the current talk page. |
Archive 10 | Archive 11 | Archive 12 | Archive 13 | Archive 14 | Archive 15 | → | Archive 20 |
At day's end, it will be 7 days since Rick requested comments from all the editors we could think of who had shown an interest in the MHP, plus a general request to the WikiProject Mathematics page. Three days ago, Rick requested mediation assistance. To date there have been no volunteers.
How and when do we keep moving forward toward a consensus? Glkanter ( talk) 13:56, 9 December 2009 (UTC)
Rick, based on the following, I don't see this procedure as being any help whatsoever to this particular group of editors. Is there some other benefit to this that I do not understand? What other path can the clear consensus take toward gaining 'permission' from the minority view to move forward with editing the article?
You made some claim a couple of days ago about this legitimately created good faith consensus violating NPOV, which I'm sure each member of the consensus would dispute strongly. Is this the issue you want mediated? The claim seems far fetched, certainly, to me. Or is this still an issue from your point of view? Glkanter ( talk) 13:01, 10 December 2009 (UTC)
I don't think the informal mediation is going to be of any value. It requires a volunteer mediator, of which none have come forward yet. It could takes weeks before one comes forward, it could be never. Whatever the mediator comes up with is non-binding. It has no teeth. In the meantime, all sorts of edits are being made to the article without any discussions whatsoever.
I suggest we request Mediation immediately, recognize the consensus for the proposed changes, and stop being hostages to this 6 year long filibuster. Glkanter ( talk) 14:40, 14 December 2009 (UTC)
The first section I created after my return is called 'Is the Contestant Aware'. http://en.wikipedia.org/wiki/Talk:Monty_Hall_problem#Is_The_Contestant_Aware.3F
All I ask is this:
It's a pretty simple, straightforward, and incredibly relevant question.
But neither Rick or Nijdam have given me a straight 'yes' or 'no'.
So, we're asking for mediation, but we haven't even stated our underlying reasons for disagreement. Because without their responses, any logical argument I might make to a mediator can be refuted, for most any reason.
And, as the section name indicates, using your noggin is not the same as OR. But that seems to be the reason for not replying.
So, enough of the 'well, I didn't say that per se', and let's get to the bottom of this. No mediator can help us if we're not being forthright. Glkanter ( talk) 05:11, 11 December 2009 (UTC)
JeffJor, oh, yeah, you've made the right decision. We have clearly demonstrated a consensus. Rick is going to use every method he can devise to extend his filibuster. There have been a lot of folks prior to us who ultimately made the same decision, to quit arguing with Rick. But we have proven the argument unlike anyone before us. "Suppose you're on a game show..." End of discussion on who's POV for the doors, and no more host behaviour. They used to argue 'little green men from space's' POV as being the MHP. I kid you not. And, no more host behaviour means no more Morgan. Of course, kmhkmh is still arguing the definition of a game show, but won't answer the 'Is The Contestant Aware?' question.
As far as the details, Morgan and his ilk get mentioned, they're published. But no more bad mouthing the Devlin solutions. Did you read my Huckleberry section? Please re-read my modified proposal. So, we just have to navigate Wikipedia's consensus processes. Rick is the king of that crap, so we'll learn as we go up the chain, whatever it is. Do you have any experience with that? So, a few of us will continue working together the straight path to improving the article. Glkanter ( talk) 22:53, 12 December 2009 (UTC)
I think this is at least one of the changes that has been argued for, and I haven't seen anyone argue against it (and those of you who think this is what I have been arguing against are simply incorrect), so I've moved the paragraph about the Morgan/Gillman generalization introducing the host preference as a variable q to the Variants section. If anyone is arguing about this, feel free to revert. -- Rick Block ( talk) 00:51, 13 December 2009 (UTC)
Here's a proposal for a unified solution section that I suggest replace the current two solution subsections. I offer this partly as an example of what I mean by a specific suggestion, and partly to show what I think would be a sufficient, NPOV, solution section.
According to the problem statement above, a car and two goats are arranged behind three doors and then the player initially picks a door. Assuming the player's initial pick is Door 1 ( vos Savant 1990):
Players who choose to switch win if the car is behind either of the two unchosen doors rather than the one that was originally picked. In two cases with 1/3 probability switching wins, so the probability of winning by switching is 2/3 as shown in the diagram below. In other words, there is a 2/3 chance of being wrong initially, and thus a 2/3 chance of being right when changing to the other door. This result has been verified experimentally using computer and other simulation techniques (see
Simulation below).
Another way to understand the solution is to consider the two original unchosen doors together. Instead of one door being opened and shown to be a losing door, an equivalent action is to combine the two unchosen doors into one since the player cannot choose the opened door ( Adams 1990; Devlin 2003; Williams 2004; Stibel et al., 2008).
As Cecil Adams puts it ( Adams 1990), "Monty is saying in effect: you can keep your one door or you can have the other two doors." The player therefore has the choice of either sticking with the original choice of door, or choosing the sum of the contents of the two other doors, as the 2/3 chance of hiding the car hasn't been changed by the opening of one of these doors.
As Keith Devlin says ( Devlin 2003), "By opening his door, Monty is saying to the contestant 'There are two doors you did not choose, and the probability that the prize is behind one of them is 2/3. I'll help you by using my knowledge of where the prize is to open one of those two doors to show you that it does not hide the prize. You can now take advantage of this additional information. Your choice of door A has a chance of 1 in 3 of being the winner. I have not changed that. But by eliminating door C, I have shown you that the probability that door B hides the prize is 2 in 3.'"
Another way to analyze the problem is to determine the probability in a specific case such as that of a player who has picked Door 1 and has then seen the host open Door 3, as opposed to the approach above which addresses the average probability across all possible combinations of initial player choice and door the host opens ( Morgan et al. 1991). This difference can also be expressed as whether the player must decide to switch before the host opens a door or is allowed to decide after seeing which door the host opens ( Gillman 1992). The probability in a specific case can be determined by referring to the expanded figure below (note the case where the car is behind Door 1 is now the middle column) or to an equivalent decision tree as shown to the right ( Chun 1991; Grinstead and Snell 2006:137-138). Considering only the possibilities where the host opens Door 3, switching loses with probability 1/6 when the player initially picked the car and otherwise wins with probability 1/3. Switching wins twice as often as staying, so the conditional probability of winning by switching for players who pick Door 1 and see the host open Door 3 is 2/3—the same as the overall probability of winning by switching. Although these two probabilities are both 2/3 for the unambiguous problem statement as presented above, depending on the exact formulation of the problem the conditional probability may differ from the overall probability and either or both may not be able to be determined ( Gill 2009b), see Variants below.
A formal proof that the conditional probability of winning by switching is 2/3 using Bayes' theorem is presented below, see Bayesian analysis.
I have tried to remove any POV-ish statements in the above. If there's anything left that does not sound NPOV please either just fix it or discuss here. The idea is to present both a plainly correct unconditional solution (it's basically vos Savant's from her second column) as well as a plainly correct conditional solution, without expressing a preference for either treatment. -- Rick Block ( talk) 19:12, 14 December 2009 (UTC)
1/3 | 1/3 | 1/3 | |||
You choose a goat | You choose a goat | You choose a car | |||
The host opens a door to reveal a goat | The host opens a door to reveal a goat | The host opens a door to reveal a goat | |||
You Stick | You Swap | You Stick | You Swap | You Stick | You Swap |
You get a Goat | You get a Car | You get a Goat | You get a Car | You get a Car | You get a Goat |
Any other comments? I'm particularly interested in comments from the folks Glkanter is considering part of the "consensus", i.e. JeffJor, Colincbn, Boris, and Melchoir. -- Rick Block ( talk) 14:29, 15 December 2009 (UTC)
But Rick, you are not part of the consensus. You are against the proposals. Or has that changed, and mediation is no longer required? Glkanter ( talk) 21:30, 15 December 2009 (UTC)
Holy cow. I went camping this weekend and I woke up in the tent in 33 degree F. cold trembling in a cold sweat, having a nightmare about goats and shiny cars and numbered doors and a genetic-cross monster whose body was that of a water buffalo and the head was that of Thomas Bayes, and everyone was throwing food about and nobody knew whether everything or anything is random or predetermined and people were capriciously changing their minds in the middle of the game conditionally and unconditionally, and I decided that I would just run off and try to re-read "Kant's Critique of Pure Reason", and then maybe shoot myself. That might be easier. :o) Worldrimroamer ( talk) 02:04, 15 December 2009 (UTC)
There's plenty of editing of the article currently taking place, including by Rick Block, who is not part of the consensus.
Why couldn't the consensus just go ahead and begin fixing the article, so that it is in line with the proposals? Glkanter ( talk) 11:51, 15 December 2009 (UTC)
How do we resolve the inconsistency between the Contestant's POV in the MHP, and the "unknowns'" POV in all the host variant stuff? Especially that large table. The whole thing makes no sense to me. Glkanter ( talk) 15:08, 15 December 2009 (UTC)
I suggest we quit waiting around for the informal mediation. There may never be a volunteer.
Formal Mediation is the next step, then arbitration.
Is there a second to my motion? Glkanter ( talk) 15:26, 16 December 2009 (UTC)
Is Rick's diff out of control consistent with our efforts to find an unbiased informal mediator? Or has he made that impossible?
Glkanter ( talk) 20:22, 16 December 2009 (UTC)
I can see why someone who has a great deal of time, effort and pride invested in Wikipedia would be protective of his work. Especially if the only Featured Article which he personally 'sheparded' through the review process was at risk of being dramatically revised. Revised so much, that the FA designation would likely be at risk.
But there is a difference between understanding and condoning. In addition to all the filibustering that takes place on the talk pages, these phrases were used when requesting (supposedly) un-biased assistance as per Wikipedia policy:
So, I can see why an owner of an article would reject all good faith efforts at improved clarity. I just don't agree with the continual passive-aggressive intellectual dishonesty that I have witnessed throughout the 14 months I've been active on this article. I've got a lot of time, effort and pride invested in this article, too. And I'm part of a legitimate consensus for making the proposed changes. That's why I point out, without hesitation, when I think another editor is not behaving in good faith. These aren't personal attacks. They are a recognition of why the article has been so wrong, for so long, despite the efforts of so many 'agitating' editors who disagree with the "shepard's" POV.
Some people will argue that this discussion is out of line. But everything I wrote is supported by diffs. Why fear the truth? I would reply that the criticisms would come from those who favor the status quo for the article. Glkanter ( talk) 13:05, 17 December 2009 (UTC)
The article states (without citation) that Kanov stated that in the "Ignorant Monty" case, swapping still yields a 2/3 chance of winning - but a quick simulation of all cases reveals this to be wrong: suppose I pick door 1, and Monty opens door 2 without knowing what is there but reveals a goat (all other permutations are equivalent to this): the car will now be behind either door 1 or door 3 with a 1/2 probability. -- New Thought ( talk) 09:44, 19 December 2009 (UTC)
Even though this problem is always described as "counter-intuitive", I find it interesting that EVERYONE on Earth understands the problem intuitively if you look at it another way: When you watch Deal or No Deal, the only reason it's suspenseful is because the person opening a case does NOT know if there's a big number inside that case. If you were on a Monty Hall Problem game show, and picked door #1, and the host said "I'm going to open a door now... hmmm... number 2" (ignorant monty - or at least from the player's POV, you must assume ignorant monty), you would be worried and suspense-filled that he might open the door with the car. When he doesn't, you feel relief. However, if Monty said, "Now, let me open a door with a goat in it... number 2" you would feel no suspense. He has told you the door has a goat, you know it's a goat, and it has no suspense. This is because there is no risk in him opening a door. He will always open a goat door. If your odds of having a goat behind your original selection improved, you'd be excited after he revealed a goat, but because he knows it's a goat, you feel no more excited about your first choice than before he opened the good. This is an example of how people DO intuitively understand this, but then don't recognize the ramifications of this feeling when offered the choice to switch observe below:
Here is an analysis of all cases when the car is behind Door number 3 (logic dictates that there are tables for the car behind behind doors 1 and 2 that have identical probabilities (for the appropriate doors). The number at left is the door you choose; the number at the top is the door Ignorant Monty opens. The result is whether you should switch ("y" or "n"). "c" represents Monty revealing the car.
1 | 2 | 3 | |
---|---|---|---|
1 | y | c | |
2 | y | c | |
3 | n | n |
1,1 2,2 and 3,3 are greyed out, because he can't open the door you chose. As you can see, there are two cases where switching nets you a car, and two cases when it does not. There are also two cases where he reveals the car ("c") and you are (presumably) not offered a choice, as the car location is now known. Ignorant Monty has a 1/3 chance of revealing a car and ending the game. ONCE that does not happen, there are four possible cases left, 1/2 of which require switching to win, 1/2 of which require keeping to win. This is the conditional probability of "What is the probablity that switching will win GIVEN that Montry did not reveal the car?" The absolute probability is absolutely true - even with ignorant Monty, switching will win you the car 1/3 of the time - 1/3 of the time staying will win, and 1/3 of the time Monty will reveal the car, and you will not get the option.
Regular Monty has 0 chance of revealing a car. While regular monty has a decision to make SOMETIMES (if you select the car, he must pick which goat to reveal), as long as his pick is random, the result of his pick are both the same: you should still not switch, (so the conditional probability of winning by switch IF monty randomly selects one door or the other is 0 in both cases - you can't win by switching). Thus, if you picked right the first time, don't switch. If you picked wrong the first time, DO switch. Therefore, 1/3 of the time, don't switch, 2/3 of the time, switch.
This is true in the ignorany monty case also: If you picked wrong (2/3), do switch. If you picked right (1/3) don't switch. However, half of the time when you pick wrong (half of 2/3 = 1/3), Monty reveals the car, and you don't get to make a choice. Therefore, IF you get the option to switch (only 2/3 of the time will you get this far), then the odds are even between keeping (1/3) and switching (1/3) (the other third is monty reveals the car). TheHYPO ( talk) 19:47, 19 December 2009 (UTC)
I believe I correctly summarized vos Savant.
Let's re-apply some things we've learned: 'Suppose you're on a game show...' Still true? Contestant's SoK? 'Random' would equal Deal or No Deal. 'He's drunk' or 'forgetful' might not be communicated to the contestant. Then it's still the MHP from the contestant's SoK.
What exactly is the revised problem statement? —Preceding unsigned comment added by Glkanter ( talk • contribs) 20:04, 19 December 2009 (UTC)
By 'random' I mean 'car or goat revealed by Monty'.
I don't thìnk your summary or Rick's summary reflect my thoughts on this puzzle. Have I been obtuse? Why summarize me at all? —Preceding unsigned comment added by Glkanter ( talk • contribs) 21:03, 19 December 2009 (UTC)
I have added names to the sections below based on comments above. If I have got it wrong please move yourself.
Please do not make comments in this section.
Editors are invited to sign against their names to confirm that they are in the right section.
Martin Hogbin (
talk)
11:29, 5 December 2009 (UTC)
Colincbn
Martin Hogbin
Martin Hogbin (
talk)
11:29, 5 December 2009 (UTC)
Glkanter
Glkanter (
talk)
12:16, 5 December 2009 (UTC)
JeffJor
Melchoir
Dicklyon
Boris Tsirelson
Boris Tsirelson (
talk)
15:27, 5 December 2009 (UTC)
Gill110951 (
talk)
13:28, 20 December 2009 (UTC)
Rick Block
Nijdam
kmhkmh
Glopk
Please move your name to the correct section if appropriate.
Martin Hogbin (
talk)
11:24, 5 December 2009 (UTC)
Henning Makholm
Chardish (I object to summary classification of my comments. -
Chardish (
talk)
00:59, 11 December 2009 (UTC))
Why does the entire Krauss and Wang text appear twice in the first bit of the article? Isn't the article long enough without this repetition? RomaC ( talk) 14:48, 10 December 2009 (UTC)
Thanks, Rick, for finding a solution that resolves my concern (an overly long intro) Butwhatdoiknow ( talk) 00:02, 21 December 2009 (UTC)
Way back in junior high, we did some proofs or problems or something to do with absolute values. That's all I can remember.
But the thing I do remember is that after you 'solved' the problem, you had to go back and check each of the results to make sure it didn't violate the original problem statement in some way.
That's all I'm saying about Morgan and the rest. When you check your work with some 'host behaviour' variant, it no longer meets the original problem statement, "Suppose you're on a game show..." Go ahead and argue. Better you should save your breath. Hosts don't tell contestants where the car is.
So, as an encyclopedia, Wikipedia will properly refer to reliably published sources like Morgan. And Devlin. No problem.
But, as a self-appointed 'explainer' of all things MHP, I think the article improperly gives the conditional solutions way too much emphasis. Because it doesn't match the original problem statement any longer. Glkanter ( talk) 21:47, 6 December 2009 (UTC)
Selvin poses the MHp. He solves it unconditionally at 2/3 vs 1/3 if you switch. The problem is hailed as a great paradox.
vos Savant prints a letter inspired by Selvin in a general interest USA Sunday newspaper supplement. She solves it unconditionally at 2/3 vs 1/3 both when you made your choice, and when the switch is offered. Because Monty's actions don't impart usable knowledge to the contestant. It's a sleight of hand. Nothing happened.
All heck breaks out. Tens of thousands of letters, including over 1,000 from PhDs tell her she's wrong. And they are certain!
vos Savant soothes the savage beasts with logic and smarts. The unconditional solution carries the day. The problem is, again, hailed as a great paradox.
This group, "J. P. Morgan, N. R. Chaganty, and M. J. Doviak are Associate Professors and R. C. Dahiya is Professor, all in the Department of Mathematics and Statistics, Old Dominion University, Norfolk, Virginia" (284 The American Statistician, November 1991, Vol. 45, No. 4 (C 1991 American Statistical Association) develops the argument that the problem is only properly solved using a conditional problem statement. Their criticisms, etc. rest on this: That when faced with 2 goats, the host must decide which goat to reveal. This rests on the assumption (presumption, invention) that the contestant might somehow gain usable information as to the location of the car in this particular instance of the game by Monty's actions. It's left unstated whether Monty's actions would be shared with the contestant. And if they are shared, what method is used. But it's clear: in this instance of game play they claim, the subject contestant could be armed with more useful information that the average contestant.
Others come out with papers supporting Morgans criticisms, including Gillman in 1992 and Grinstead and Snell 2006.
Others continue publishing unconditional papers. (It seems likely that if 3 Wikipedia editors plus Seymann find fault with the paper, so too would members of the Professional Mathematics Community. And as professionals, they don't make a big stink about it. They just ignore the paper and continue publishing articles that rely solely on the unconditional problem statement.)
So, has the Professional Mathematics Community decided that Morgan is right, and Selvin was a hack? I don't think so. Before, during and after Morgan's paper, respected, credentialed reliable Mathematics professionals continued to publish articles solving the MHP unconditionally. I don't know that any of these professionals in either camp have attacked or counter-attacked anyone else's paper. It looks to me, that in the Professional Mathematics Community nothing happened. No usable information was gained. Perhaps Morgan's paper, like Monty revealing a goat is just sleight of hand, imparting no usable knowledge? It's possible. Most published MHP articles say nothing of Morgan or conditionality.
Which brings us, finally, to the Meta Paradox. The Wikipedia editors are arguing, essentially, over whether or not solving the unconditional problem is 'enough'.
Suppose you are given a story problem about a game show. The Professional Mathematics Community agrees heartily that this is a delightful paradox which can be 'proved' or 'solved' using an unconditional problem statement. Maybe not even requiring formal probability notation. Symbolic notation is often used. Then "J. P. Morgan, N. R. Chaganty, and M. J. Doviak are Associate Professors and R. C. Dahiya is Professor, all in the Department of Mathematics and Statistics, Old Dominion University, Norfolk, Virginia" come forth and say it must be solved conditionally, based on the arguments set forth in their paper. You are then offered to stay with the unconditional solution being complete, or you may switch to the conditional solution.
Many people are fooled by this paradox, and accept the switch. Because they don't realize that like Monty revealing the goat, no new usable information has been revealed by this paper. Nothing happened. Glkanter ( talk) 18:27, 8 December 2009 (UTC)
Wow, this thread is long! And I haven't even looked at the archive(s?). I thought it might be worthwhile to make a comment as a person who has not been following this thread before now. I just, in the last couple of days, read the article and a big portion of the discussion.
My comment is simple: Please, I am not attacking anyone; I am just making a general, honest, respectful IMO comment. (And yes, I am schooled in mathematics.) I agree with those that say the article is too long, very unwieldy, and often downright confusing. I think the article as it now stands is almost worthless. I agree with those who say: Just state the "standard" problem as most people assume it is stated, and give a simple explanation as to why it is correct. Then meander off into the conditional and unconditional ponderings, the Bayesian statistics, etc.
I started out reading the article, with expectation of fun. I was already familiar what the "Monty Hall problem", and I understood it, at least in its more obviously stated form (based on the generally accepted assumptions). As I read on I thought, "Whaaa???" Much of the -- sorry, but most -- of the article is a murky mess, and even those who are somewhat probabilistically astute I think would have difficulty making sense of some of it. I'll cite just one example: The section titled "Popular Solution" is, IMHO, poorly written and confusing. Frankly, it's not clear what the author is meaning to get across in several places (even though I understand exactly what it is that he/she is intending to say). It needs to be rewritten, as does much of the rest of the article. Not tweaked, but rewritten. This sort of muddled presentation is just not necessary, and it is not worthy of the standards of Wikipedia. This stuff is not string theory or Gödel's incompleteness theorems in ZFC. This is introductory-level probability, albeit a very subtly tricky example of it.
I never seen an article on Wikipedia that has created such a WikeWar as this article has. It apparently has no resolution in sight. Anyway, I'm all out of suggestions -- if I have even made any.
Finally, just for fun, I wanted to mention a somewhat similar conditional-probability problem which I haven't seen anyone else mention. (It is not relevant to this article, nor should it appear in it; it's just related.) You play a "flip three coins game". The person I am gambling with shakes up three fair coins in a canister and spills them onto the table top. I am not allowed to see the coins initially before I make my choice; the canister shaker (my opponent) hides the coins from me. The rules are, the shaker peeks at the coins on the table and he has to tell me what the "majority" coin is. There will be either a majority of heads (3 heads or 2 heads) or a majority of tails (3 tails or 2 tails). Then, having been told what the majority is, I must guess what the third coin is -- heads or tails. If I get it right I get paid a dollar by the shaker; if I get it wrong, I pay him two dollars. Most people would think this a stupid gamble on my part; they will assume that the guess as to the heads-tails of the third coin has a 50-50 chance of being right. But it's easy to see (though it is initially counter-intuitive to many people) that if you always guess the opposite of the majority, you will win 3/4 of the time. Just write down all combinations: HHH, HHT, HTH, THH, HTT, THT, TTH, TTT, and it's obvious. That would make a cool bar game. Even offering your opponent the 2-to-1 payoff, you would still win, on average, in the long run 25 cents per play:
1/4*(-2) + 3/4*(1) = 1/4 of a dollar per coin-shake, in the long-run average.
Good luck with your little war. Worldrimroamer ( talk) 23:53, 8 December 2009 (UTC)
Sorry for being so cryptic. 'The editor' is you. As we try to bring this discussion to a close, we are attempting to build a Wikipedia Consensus to make changes very much as you described. So, I was asking the other editors if there is any reason your opinion should not be considered as part of the 'let's change the article' consensus, of which I am a part. It's all good. I think you'll find the discussion of the last few weeks most meaningful. Some extra Wikipedia Mathematics Project people have begun contributing, by request, and it's helped move things forward a great deal. Again, sorry for being unclear. Glkanter ( talk) 03:27, 9 December 2009 (UTC)
__________________________________________________ —Preceding unsigned comment added by Worldrimroamer ( talk • contribs) 17:51, 9 December 2009 (UTC)
I very much like this question to be answered first. (BTW several sources mention the MHP to be equivalent to the three prisoners problem.) Nijdam ( talk) 22:35, 15 December 2009 (UTC)
Until now only Boris has shown the derivation of a solution in formulas, using symmetry. This leads to the conclusion - as I BTW showed a million comments ago - that the conditional probability we are interested in is equal to the unconditional and hence may be easily calculated. It doesn't show the conditional probability is not needed. All others come with words, words, .... Nijdam ( talk) 17:25, 20 December 2009 (UTC)
I don't understand why all this article editing is taking place without being discussed.
While we 'old guys' are working towards a formal WP solution, newer people are editing at will.
This seems unproductive, not good for the article or readers, and distracting.
Any support for a temporary freeze? Is this even plausible? Thanks. Glkanter ( talk) 12:25, 21 December 2009 (UTC)
He's expecting Dicklyon to 2nd it. I see a lot of unintended irony here. I had just created a new section on the talk page with 3 edits. Then, here's what I call Dicklyons's unprovoked vandalism on my talk page edits:
It's all right here: Is This Chronology Correct?
So, if anybody wants to put in a good word for me, I'd be much obliged. Please note, I'm pretty sure I will get this promptly dismissed, but any support is appreciated. Glkanter ( talk) 04:25, 22 December 2009 (UTC)
On this RfC/U, Rick Block and Dicklyon are trying to make a case that I am disruptive, don't edit the article often enough(?),incivil, interrupt consensus building, chase other editors away, contribute nothing of value, too aggressive with my POV, have bad breath, etc. I'm holding my own on the RfC. It's gotten pretty ugly. So, if anybody would like to drop a supportive word about good ol' Glkanter, now would be a good time. By reading the RfC, you will also learn a lot about the inner thought processes of some well known editors. Thanks. Glkanter ( talk) 22:22, 26 December 2009 (UTC)
Thank you. Glkanter ( talk) 15:10, 23 December 2009 (UTC)
I think there are 2 POVs regarding how to 'cherish' the MHP paradox.
Some of us, including myself, love the simplicity. Nothing happens. Heated Arguments over 1/2 vs 2/3 ensue. More than once, even.
Other people like the complexity, and 'what ifs' that the MHP could be with just a little tweaking. The permutations can approach Game Theory scenarios.
Since it was a great paradox before Morgan and conditional, I consider the 'simplicity' people the ones who accurately support how Selvin's MHP paradox should be presented in the Wikipedia Article. Glkanter ( talk) 15:35, 23 December 2009 (UTC)
1. The simple solutions are not solving the correct problem.
2. Morgan's paper, published in 1991, can claim to recognize and describe the Monty Hall Problem Paradox, first published by Selvin in 1975, equally as well (and equally importantly) as Selvin's original paper, which relied only on simple solutions.
I'd like to see the people arguing in support of those 2 arguments come out and directly say it. Once you clearly state your positions, the other editors, using reliably published sources can then address your objections to the proposed changes. Glkanter ( talk) 18:32, 23 December 2009 (UTC)
In the RfC that Rick Block and Dicklyon filed on me RfC Glkanter one of the 'complaints' was that I argue on the MHP talk pages too much, at the expense of actually editing the MHP article. The associated 'remedy' was that I modify the MHP article more frequently and discuss my reasons for doing so less often.
Now, that's no reason to slap me with an RfC, but the point is well taken. I've asked for a 'freeze' on the article of some sort at least twice in the last couple of weeks. Meanwhile, some editors just make edits without discussing them first.
So, consistent with my stated understanding of the various literature on the MHP, and in accordance with Rick's criticism/suggestion as conveyed via Wikipedia's formal RfC procedure, I will begin to thoughtfully edit the article as I understand the consensus has approved. Glkanter ( talk) 15:51, 24 December 2009 (UTC)
How about I start with the FAQs on the talk page? That looks like pure Morgan POV, a clear violation of NPOV. Anybody want to clean it up, or should I just delete it?
Glkanter (
talk)
16:47, 24 December 2009 (UTC)
Here's another one. Id like to change the 'Simple solution' heading to something like 'Original Paradox explanation' or 'Selvin's Proof' or 'vos Savant's Popular Solution'? I'd like to get the point across concisely that it was this level of understand from which all the excitement about the paradox came. Not to be confused with the 'conditional solution' or, non-solution without the equal goat door constraint being equal to exactly 1/2, that came out some 15 years later.
Glkanter (
talk)
16:03, 25 December 2009 (UTC)
Then a transition section that says 'For many people, this is all the understanding they need, and was Selvins and vos Savant's point. Others may want to continue further into this article...' And as long as there's no bad-mouthing the 'original' solutions, you 'conditional' guys can pretty much do what you want with the article from there. Glkanter ( talk) 16:10, 25 December 2009 (UTC)
Rick, the current text includes this:
I still disagree that using a different problem is a means of challenging a particular problem. Originalists would argue that all you've demonstrated is the difference between puzzles with different premises. I would further argue that with the contestant being aware of Monty's left door bias, this is no longer the MHP about a game show that Selvin and vos Sovant made so famous. Glkanter ( talk) 06:38, 27 December 2009 (UTC)
When asked how he was able to sculpt the venerated 'David', Michelangelo replied, 'It was easy really. I removed everything that didn't look like David'. —Preceding unsigned comment added by Glkanter ( talk • contribs) 23:51, 8 December 2009 (UTC)
This is most of the 'greeting' to the talk page of the FAQs. Probably only seen by other editors.
I think this can be improved. Anybody mind if I take a shot at it? Glkanter ( talk) 23:32, 26 December 2009 (UTC)
I appreciate your help with this, Rick. I'm suggesting we would edit this. What then? Glkanter ( talk) 19:27, 27 December 2009 (UTC)
<noinclude>{{FAQ page}}</noinclude>
<noinclude>blah blah blah</noinclude>
Variants - Slightly Modified Problems section.
Since the MHP is from the contestant's POV, there should be some narrative about what the POV's in this whole section represent. Are they the contestant's? Is it a premise in each different problem that it's no longer the contestant's POV? What about addressing the Monty Hall problem from 'not-the-contestant's POV' for comparison purposes? This would be beneficial to the readers, I believe. Glkanter ( talk) 16:55, 27 December 2009 (UTC)
Selvin's - simple: 2/3 & 1/3, always switching doubles your likelihood of getting the car
Morgan's - conditional, no symmetry: between 1/2 and 1 (?), never to your disadvantage to switch
Morgan's - conditional, with symmetry: 2/3 & 1/3, always switching doubles your likelihood of getting the car
Have I summarized the above properly? Glkanter ( talk) 11:03, 27 December 2009 (UTC)
If so, maybe the article could transition from:
Simple, to conditional - with symmetry (they are equivalent), to conditional - no symmetry (leftmost door variant). Glkanter ( talk) 11:30, 27 December 2009 (UTC)
I disagree with your recent reverts to the article, Rick.
I just checked the Morgan paper, and they do not use the word 'variant' or any derivative of it when describing the problems.
I think this is an uncommon usage, and does not clearly indicate to the reader exactly what is being described. I don't think adding 'Slightly Modified Problem' to a heading, and replacing 1 instance of 'variant' in the article also with 'slightly modified problem' is 'pointy'. Different than your POV, perhaps, but that does not necessarily make it, or any other edits I may make in good faith, 'pointy'. Glkanter ( talk) 19:45, 27 December 2009 (UTC)
In an attempt to see exactly who thinks what I have set up some questions on User:Martin_Hogbin/Monty_Hall_problem/dissenters. Everyone is welcome to add their answers. Please comment briefly only in the comment section and have discussions about the questions on the associated talk page.
Whether we have external mediation or not I am sure it will help if everyone answers the questions on this page. I am trying to determine of we have two distinct camps, a single axis of opinion, or just randomly scattered views on the subject. Are there any other questions that editors feel will help sort out the differences of opinion here? I have just added a few extra ones. Martin Hogbin ( talk) 11:36, 28 December 2009 (UTC)
Explain the problem to me please. Glkanter ( talk) 01:45, 28 December 2009 (UTC)
If you're here because you've been invited to comment, there are ,two,. three (related) suggestions.
Please indicate in subsections below whether you favor or oppose each of these suggested changes.
The intent is to try to determine whether there is community consensus for any of these changes. I would suggest one subsection per user who is commenting, and to avoid endless arguments, restricting your comments to your own section (this is modeled after the process used at Wikipedia:Arbitration Committee). I've precreated sections for everyone I've explicitly invited to comment. -- Rick Block ( talk) 15:31, 2 December 2009 (UTC)
In this section please summarize the changes you're suggesting. I'll be asking the set of folks I mentioned to Glkanter above to come here and offer their opinions, so please keep it as brief as possible. Please let me know when you think this section is ready for others to comment on. -- Rick Block ( talk) 01:07, 1 December 2009 (UTC)
We should take the current K & W statement as our starting definition of the MHP.
The primary solution and explanation should not use conditional probability
The Morgan paper clearly does not answer the question as stated in the article and thus should not be regarded as our ultimate reliable source.
The Morgan solution should be introduced in a later section of the article that deals with variations of the problem.
(referring to JeffJor's suggestion)
(referring to Glkanter's suggestion)
I really don't know jack about probability and whatnot, but I still tend to agree with Glkanter's points. I came to this article through looking up various paradoxes and this was a really neat one that I got to try out in the real world (see simulation question above). As I understand it the "Monty Hall problem" states that the host chooses randomly, so any other discussion about host behavior should be limited to the "Variants" section under "Other host behaviors". Just my 2 cents, Colincbn ( talk) 02:41, 1 December 2009 (UTC)
By my count, that's 4 in favor of the proposed changes, and 0 against. I've been championing these changes since October, 2008, Martin prior to that, and countless other editors for about 5 years. When can we declare an end to the pointless filibustering, acknowledge a consensus, and move on? Rick, will you be offering your comments? Have you contacted the others? Glkanter ( talk) 22:29, 1 December 2009 (UTC)
About Martin Hogbin's suggestion - :I agree 100% with your proposed changes. I would like to add my 2 cents to the rationale, however. Morgan is criticizing and solving something other than the Monty Hall game show problem in the article. The introduction of the contestant being aware of any 'host behaviour' when selecting from 2 remaining goats changes the Problem Statement of both vos Savant/Whitaker and Karauss & Wang from "Suppose you are on a game show" to the converse, "Suppose you are not on a game show". Individual contestants on game shows are never provided more information than the 'average' contestant will have. There can be no 'condition'. It's illogical. Glkanter ( talk) 15:33, 2 December 2009 (UTC)
[Repeated in part from comments below]
The point of separating the articles is not to eliminate any POVs. It is to emphasize them. To not let one facet of the MHP (simple solution w nonintuitive result) become overpowered by the other (good teaching tool for conditional probabilites). If we don't physically separate them, we need to more clearly divide the article. The first part should be about the classic (unconditional) MHP, as stated by MvS (not K&W), and listing the set of assumptions she has said (and 99.9% of readers agree) are implied: interchangable doors, and any kind bias becomes irrelevant because of interchangeable doors. Then a section about game protocals (part of what some call host stratgies) such as always opening a door or revealing a goat, WITHOUT mention of bias or conditional problems. This mostly exists. Finally, you can cite Gillman (not Morgan) as a reference that introduces the possibility that the conditional problem is intended, but matters only if there is a bias. Use the K&W statement here, not Gillman's misquote. Gillman is better than Morgan because it is clearer, includes placement bias, and does not launch into possibilities that we are never told how to use. I think this is pretty consistent with Martin's suggestion. JeffJor ( talk) 17:44, 4 December 2009 (UTC)
As a matter of fundamental Wikipedia policy, articles MUST be written from a neutral point of view. What the proponents of these changes are essentially suggesting is that this article take the POV that the interpretation of the problem described by a significant number of reliable sources (the Morgan et al. reference and others) is invalid. Even if this were a stance taken by reliable sources (which, as far as I know, is not the case), by relegating the "Morgan" interpretation to a "variant" subsection or splitting it into a POV fork this article would then be taking the "anti-Morgan" POV. I've made this point to these editors numerous times before, but yet they keep tendentiously arguing that the "Morgan" POV is wrong, or the Morgan et al. reference has errors, or (most recently) that the Morgan POV is NOT about the "real" Monty Hall problem (as if by convincing me that their POV is "correct" I would then agree with the changes they're suggesting).
I sincerely hope the "consensus" from this process is against making these changes, because even if there is a consensus for these changes they cannot be implemented - doing so would violate Wikipedia policy. -- Rick Block ( talk) 04:01, 3 December 2009 (UTC)
You all realize Martin's proposal implies the article will not even mention conditional probability except in a "variant" section, don't you? How anyone can think this is not a blatant POV issue escapes me. -- Rick Block ( talk) 20:19, 3 December 2009 (UTC)
I have to state the opposite view, which is that you have taken a ridiculously pro-Morgan POV. There are many reliable sources that relate to the MHP and not all of them have a host door choice parameter. Those that do generally quote Morgan as the source for this.
The article already takes a problem statement from a reliable source (K & W) and that same source confirms that this is how most people view the problem. In that statement, the host is defined to choose a legal goat door randomly. It is thus a simple matter of fact that the Morgan paper does not address that problem in so far as it allows a door choice parameter where none is permitted by the problem statement.
The Morgan paper clearly addresses a scenario where where the player is somehow aware of the host's policy for choosing a legal goat door. This rather bizarre scenario is not the one described by our problem statement and thus it should be viewed as a variant of the MHP as it is most commonly understood. Martin Hogbin ( talk) 21:30, 3 December 2009 (UTC)
I thought I made it clear we were to use arbcom style rules here, which are that you only comment in your own section (it really does help keep the threads from getting absurdly long). However, since you've been rude enough to post here I'll respond to each of you, BUT please do not continue this as a thread here.
Glkanter asks why so dramatic? The argument has shifted from "present an unconditional analysis first (and don't criticize it)" to "exclude the conditional analysis completely (except as a variant)". This is a huge difference.
Glkanter asks why I haven't responded about his "Is The Contestant Aware?" question. Why should I? Glkanter has repeatedly demonstrated a complete lack of comprehension of nearly everything I've ever said. It's like trying to explain something to a cat. At some point you just have to give up. However, I'll give it another go. Meow, meeeow, meow, meowww. I'm not sure I have that quite right since I don't speak cat, but it's probably about as comprehensible to him as anything else I could say.
Martin (incorrectly) claims again that the Morgan et al. paper does not address the K&W version of the problem. Quote from the paper: "Incidentally, Pr(Ws | D3) = 2/3 iff p = q = 1/2". This is the solution to the K&R version of the problem statement. The Morgan et al. paper (and the Gillman paper and many, many others who approach the problem conditionally) absolutely address the K&R version. Because they also address other versions doesn't mean they don't address the K&R version.
Martin and Glkanter are both apparently completely incapable of understanding the main point of the Morgan et al. paper (and the Gillman paper, and what Grinstead and Snell have to say) which is that the MHP is fundamentally a conditional probability problem and that there's a difference between an unconditional and conditional solution. What these sources are saying is that a conditional solution clearly addresses the MHP (as they view the problem), but an unconditional solution doesn't unless it's accompanied by some argument for why it applies to the conditional case as well (and there are many valid arguments, but no argument at all which is what is generally provided with most unconditional solutions is not one of them). The fact that the problem can be (and typically is meant to be) defined in such a way that unconditional and conditional solutions have the same numeric answer in no way invalidates what these sources say. To have the article take the stance that the conditional solution is invalid (which would be truly absurd), or that the criticism these sources make of unconditional solutions is incorrect, or that a conditional solution applies only to a "variant" is making the article take a POV. This would be a direct violation of a FUNDAMENTAL Wikipedia policy. -- Rick Block ( talk) 01:53, 4 December 2009 (UTC)
Delayed response (am not a very active editor at all these days), but here it is.
Statement
Motivation. The purpose of an encyclopedia is to present a "best" selection from the body of knowledge about each topic, being POV neutral as well as reader-neutral. -- glopk ( talk) 18:53, 29 December 2009 (UTC)
Thanks for the invitation to comment. In my opinion, Martin Hogbin's suggestion seems the post prudent. The Monty Hall problem as popularly explained doesn't rely on conditional probability, and the Whitman explanation seems sufficient for anyone who is not a mathematician. Wikipedia is a general-purpose encyclopedia, and as such main articles should focus on explaining topics as they are popularly understood, with specific scientific analysis relegated to separate articles.
And, to be honest, the article as it stands is much harder to read and understand (as a layperson) than it was several years ago. NPOV isn't "pleasing everyone equally"; don't let efforts towards neutrality wind up hurting the article. - Chardish ( talk) 02:53, 6 December 2009 (UTC)
Just from reading the present Wikipedia article, I agree with Martin Hogbin's suggestion, because I don't see why allowing the host to prefer one goat over the other is a more relevant generalization than allowing the host other behaviors. Melchoir ( talk) 06:47, 3 December 2009 (UTC)
I fully support Rick's view. Nijdam ( talk) 10:34, 3 December 2009 (UTC)
To make my position crystal clear: there is no such as an unconditional solution. There are different problems: an unconditional problem and a conditional one. The latter generally being called the MHP. Nijdam ( talk) 22:24, 3 December 2009 (UTC)
I haven't been watching this article for a while; glad to see the K&W treatment up front; that looks like the most sensible article I've seen on it. As for the Morgan conditional approach, I think it's an unnecessary distraction, but it's out there in mainstream reliable sources about the topic, so we ought to cover it in the article. I think Martin Hogbin's proposal sounds best. Dicklyon ( talk) 05:01, 3 December 2009 (UTC)
I agree with Rick Block that the other two proposals essentially violate WP:NPOV; but I disagree that moving the conditional stuff to a more minor position is a problem; his heavy promotion of the conditional approach violates WP:UNDUE in my opinion. Dicklyon ( talk) 16:29, 3 December 2009 (UTC)
I have long since given up on following these discussions, and am not even a very active editor these days. However, since somebody went to the length of creating a heading for me, here are my general recommendations -- for whatever they are worth:
– Henning Makholm ( talk) 07:13, 3 December 2009 (UTC)
I summarize my position in two points:
Boris Tsirelson ( talk) 06:44, 9 December 2009 (UTC)
Being invited by Glkanter, I quote here some paragraphs of a discussion that happened on my talk page on February 2009. As far as I understand, my position is close to that of JeffJor. Boris Tsirelson ( talk) 17:20, 2 December 2009 (UTC)
Why split? Because of different importance. The "conditional" article will be, say, of middle importance, while the "unconditional" article – of high importance. We surely have our point of view about importance (rather than content). Boris Tsirelson ( talk) 05:54, 4 December 2009 (UTC)
The quotes follow.
Each time giving the course "Introduction to probability" for our first-year students (math+stat+cs) I spend 20-30 min on the Monty Hall paradox. I compare two cases: (a) the given case: the host knows what's behind the doors, and (b) the alternative case: he does not know, and it is his good luck that he opens a door which has a goat. Im addition I treat the case of 100 (rather than 3) doors (just like Monty Hall problem#Increasing the number of doors). And, I believe, students understand it.
I have no idea, why some people spend much more time on the Monty Hall paradox (and even publish papers). (Boris Tsirelson)
This simple little problem is deeper than it might appear, and likely well worth more than 20-30 mins of lecture time. Perhaps even worth revisiting once or twice during a term to explore its more subtle aspects. (Rick Block)
Deeper than it might appear? OK, why not; but still, for now I am not enthusiastic to deep into it. Tastes differ. I find it more instructive, to restrict myself to the simpler, symmetric case, and compare the two cases mentioned above.
If an article leaves many readers puzzled, why it is unnecessarily complicated, it is a drawback. (Boris Tsirelson)
If a problem that appears so simple to me, like the Monty Hall problem, is not sufficiently solved using my unconditional proof, in what circumstances is the unconditional proof appropriate? Thank you. (Glkanter)
The unconditional argument shows that "always switch" is better than "never switch". This is what it can do. Let me add: if you (that is, the player) are not informed about possible asymmetry then you cannot do better than these two strategies, either "always switch" or "never switch". (Boris Tsirelson)
I'll start with a clear statement and give some more detailed information afterwards:
If one surveys the available literature literature/publications on the topic, you pretty much get an relatively obvious outline for the article: original problem (in vos savant's column), unconditional solution (basically vos savant and/or various math sources), conditional solution (Morgan and almost in any math source), various problem variation and caveats, history of the problem, application of the problem outside the math domain. Which is essentially for the most part, what we already had and what Rick managed to maintain. In that context I fully agree with Henning Makholm's comments above, who puts it fairly well. The article wouldn't have such problems if all participants would follow that rationale.
The fuzz over quality or minor mistakes in Morgan's paper is a somewhat ridiculous distraction, since Morgan's paper is not needed to argue the conditional solution or caveats to the unconditional solution at all. There is plenty of other math literature dealing with the problem in more or less the same manner.
My personal advice would be to pass the article for final thorough review and modification to the math or a science portal. During that review neither of the 4 disagreeing authors (JeffJor, Glkanter, Martin Hogbin, Rick Block) are allowed to participate/edit. After that review the article should be fully protected for good.
I've seen what happened to the German version, that had similar problems (without a Rick Block around to constantly remain some standard). So we had a lot of people with a somewhat fanatic approach constantly pushing for their favoured explanation and constantly ignoring wiki standards, common sense and more important the available literature on the subject. As result mathematicians and scientists basically dumped the article and gave up on improving it.An effect this article has partially seen as well.-- Kmhkmh ( talk) 16:45, 4 December 2009 (UTC)
No comment right now. But a lot of Christmas break reading to do here, to catch up. Happy Wikipedia Christmas, everyone! Gill110951 ( talk) 13:27, 20 December 2009 (UTC)
(I welcome you all back to my screen. This article has improved a lot over the last year.)
Morgan et al. (1991) seem to assume that the doors are statically numbered, having the same numbers through repeated experiment. Vos Savant however writes in her column: "You pick a door, say #1, and the host opens another door, say #3". This may mean that after a door is picked, we (always) call it #1, while the opened door is (always) called #3. Such dynamic numbering can make it easier to discuss and calculate the given options. The consequences of the assumption of Morgan et al. are further explained in this article under "Probabilistic solution - 1991".
The Morgan paper classifies solution F5 as "incorrect because it does not use the information in the number of the door shown". This is only true assuming statical numbering. In this context it is questionable why Morgan et al. quote vos Savant wrongly, writing "You pick door No. 1, and the host opens No. 3". Heptalogos ( talk) 14:11, 30 December 2009 (UTC)
The Morgan paper is not about Monty Hall, but about a question in a column of vos Savant, starting with "Suppose you're on a game show". All exact information is, of course, in the paper, so no other sources are relevant. Heptalogos ( talk) 19:44, 30 December 2009 (UTC)
The source I mention, "Morgan et al. (1991)", is probably the most argued source in this article. It is in the article reference list mentioned as: "Morgan, J. P., Chaganty, N. R., Dahiya, R. C., & Doviak, M. J. (1991). "Let's make a deal: The player's dilemma," American Statistician 45: 284-287." Heptalogos ( talk) 20:11, 30 December 2009 (UTC)
If you're suggesting to move or continue discussion about the specific arguments used in the Morgan source, to or on the arguments subpage, then that's fine with me. But I'm doing more than that, namely introducing a new element to the global dilemma, which is the method of numbering doors. Heptalogos ( talk) 20:43, 30 December 2009 (UTC)
The Morgan paper is quite clear about the disctinction between conditional and unconditional. I quote: the unconditional problem, which may be stated as follows: "You will be offered the choice of three doors, and after you choose the host will open a different door, revealing a goat. What is the probability that you win if your strategy is to switch?" The distinction is made by opening a specific door, instead of "a different door". This is mentioned elsewhere in the paper several times. I agree that No. 3 is an example and might be No. 2 as well, but the paper assumes that there is an essential difference between "the open door" and "door No. x, which is open". To my opinion these are only labels which don't make any difference, unless of course one assumes that a specific door is labelled the same through repeated experiment. Heptalogos ( talk) 21:40, 30 December 2009 (UTC)
I want this article to explain how the conditional probability could actually differ from the overall probability (I refer to chapter "Probabilistic solution - 1991"), when the distinction between both is made by information (a door number) which seems to have no statistic dependency or influence on the requested probability. To my opinion, the average intelligent reader of this paradox, who has no mathematical skills, still doesn't understand the necessicity of using the relatively complex method of conditional solution. I agree that the discussion about the necessicity itself should preferably be held elsewhere, but an elementary explanation key in the article should be, I guess, in the idea of a static door position through repeated experiment, whatever it means. The meaning of that I would like to be explained. Heptalogos ( talk) 23:45, 30 December 2009 (UTC)
I propose adding an external link to http://www.opentradingsystem.com/quantNotes/Monty_Hall_problem_.html
The link in question contains derivation of solution in a general context developed on other examples. —Preceding unsigned comment added by Kaslanidi ( talk • contribs) 20:27, 30 December 2009 (UTC)
I object, per WP:ELNO points 1, 4, and 11. - MrOllie ( talk) 20:32, 30 December 2009 (UTC)
My 'POV' is that this paradox twists peoples' brains a lot, just the way it is. Whatever 'is' means.
So a sequenced roll out of how the problem became published, then controversial twice would help the interested reader. What could make more sense then to describe the events roughly as they occurred, and beliefs/understandings changed, or maybe they didn't.
Let the reader decide for himself, or herself.
Yes, 'sequenced roll out' really means 'chronological'. Forgive me.
Pretty radical, eh? Just tell the story as the sources do, and let the reader draw his own conclusions. Whoda thunk it? Glkanter ( talk) 20:35, 30 December 2009 (UTC)
Simple solution is not a solution at all
"This is the same topic discussed in more detail three sections down (about the subtly different question), and indeed Morgan et al. argue the "simple" solution is not a solution at all." -- Rick Block ( talk) 16:28, 26 October 2008 (UTC) —Preceding unsigned comment added by Glkanter ( talk • contribs)
@Rick, you seem to be putting up an Aunt Sally (Strawman argument). You seem to be implying that I want to remove the POV of Morgan and others who agree with them from the article. That is not the case. I have always suggested that the article should start with the simple non-conditional solutions and then, after discussing these thoroughly, move on to the conditional case discussed by Morgan and others. It is clear, from your reposted quote above (I had not noticed that it had been reposted) that you believe that the Morgan paper should somehow veto or overrule all other sources no matter what they say. Martin Hogbin ( talk) 22:54, 26 December 2009 (UTC)
I think Rick Block and Nijdam are fillibustering and ownershipping against beneficial changes to this article.
I see no point in waiting for either form of mediation unless Nijdam indicates he will accept the findings.
Rick filed an RfC against me last week, the first item of which is 'only edited the article 1 time.' Now, as you've seen yesterday, every edit I make, he or Nijdam at his request, reverts.
If at least 2 people are with me, I'll proceed. Glkanter ( talk) 17:31, 28 December 2009 (UTC)
Case link
I've re-opened the case at MedCab and volunteered to assume the role of mediator in a discussion aimed at resolving an on-going dispute here. Additionally, I've issued invitations to participate in the discussion to all involved parties listed in the mediation request. While anyone is welcome to offer input, I ask that those who participate do their best to be concise and refrain from assumption/presumption regarding other's perspectives.
As mediator, my primary goal is to step in as an uninvolved party and help find some common ground from which to proceed. It is not my task to pass judgment on anyone's opinion in the discussion and there is no 'right' or 'wrong' beyond that which is dictated by Wikipedia policy.
I have read the article and understand its subject matter and all it details. As I begin delving through the talk page archives, I'll open the discussion with a call for opening statements. If you feel any archived passages are significant in summarizing the situation, it would help to include links, but please conclude your first post with a Summary of Position (your opinion as it relates to the matter). And remember...concise ;-)
--
(
talk)
05:28, 29 December 2009 (UTC)
I want the article clearly mention the remark made by some sources that the so called "simple solution" is not complete. It doesn't need initially mentioning the technical term "conditional probability". To make my point clear: the following resoning:
is not complete and better should read:
Something alike holds for the so called "combined doors solution" and most of the other simple ways of understanding. That's all. Nijdam ( talk) 08:36, 29 December 2009 (UTC)
I'd like to add that the (a) MHP always involves enumerated doors and a decision to switch offered to the player after a door is opened, seen by the player who has to decide. This is in my opinion and of many (most) sources the only relevant problem. Nijdam ( talk) 11:48, 31 December 2009 (UTC)
The MHP is essentially a simple mathematical puzzle that most people get wrong. At least the first part of the article should concentrate on giving a simple, clear, and convincing solution that does not involve conditional probability. All diagrams and explanations in this section should not show or discuss the possible difference that the door opened by the host might make, although I would be happy to include, 'this action does not give the player any new information about what is behind the door she has chosen' as in Nijdam's second statement above. The first section should give aids to understanding and discuss why many people get the solution wrong, without the use of conditional probability. The first section should be supported by sources which do not mention conditional probability
The simple solution section should be followed by an explanation of why some formulations of the problem require the use of conditional probability, with reference to the paper by Morgan et al. and other sources. It should also include the various variations of the basic problem and other, more complex, issues. Martin Hogbin ( talk) 10:19, 29 December 2009 (UTC)
I want the article to clearly mention that the remarks made by some sources, that the so called "simple solution" is not complete, is not shared by all sources. It need not mention "conditional probability" beyond saying that due to the symmetry forced by being a game show, the simple solution is equivalent to the symmetric 'conditional solution'.
I think I agree with Nijdam on the text, although they are both OR. It's consistent with my 1st talk page edit, using an IP address in October, 2008:
I'd like to see 3 solution sections: Selvin's simple solution of 1975, transitions to Selvin's symmetrically equivalent conditional solution of 1975 (where the discussion of the simple solution's criticisms occurs), transitioning to Morgan's conditional non-solution of 1991.
I'd like to see the word 'variant' either stricken, or augmented by 'slightly different problem'.
I'd like to see a lot of 'blather' removed from the article. Too much time and effort is spent in the various remaining sections explaining the conditional solution, for no real reader benefit. Glkanter ( talk) 10:39, 29 December 2009 (UTC)
And the 'Variants - Slightly Modified Problems' section needs work. The MHP is from the contestant's state of knowledge (SoK). The versions in this section are not. This needs to be normalized for the reader in a few possible ways: An explicit statement that the contestant is aware of these new conditions (in which case these are no longer game show problems), or the explicit statement these problems are not from the contestant's SoK, and a comparison of the MHP from a non-contestant's SoK. Glkanter ( talk) 13:14, 29 December 2009 (UTC)
First, I think the basic issue is an NPOV issue. The primary question is whether the article currently expresses a "pro-Morgan" POV, i.e. takes the POV of the Morgan et al. source that "unconditional" solutions are unresponsive to the question and are therefore "false" solutions - and, if so, what should the remedy be.
There are a variety of sub-issues we need to discuss but I think the main event is how the solution section is presented. I strongly object to splitting the solution section into separate sections (this was done some time ago, well after the last FARC), which inherently favors whatever solution is presented in the first such section. I mildly object to including the "combining doors" explanation in the solution section rather than in a subsequent "aid to understanding" section.
What I would like is for the article to represent in an NPOV fashion both a well-sourced "unconditional" simple solution (e.g. vos Savant's or Selvin's) and a well-sourced conditional solution of the symmetric case (e.g. Chun's, or Morgan et al.'s, or Gillman's, or Grinstead and Snell's) in a single "Solution" section, more or less like the suggestion above (see #Proposed unified solution section - somewhat modified just now). This follows the guidelines at Wikipedia:Make technical articles accessible, specifically most accessible parts up front, add a concrete example, add a picture, and do not "dumb-down".
Once we address this basic issue I think the other issues will be easier. -- Rick Block ( talk) 19:43, 29 December 2009 (UTC)
-- K10wnsta ( talk) 22:01, 1 January 2010 (UTC):Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, "Do you want to pick door No. 2?" Is it to your advantage to switch your choice?
Hello K10wnsta. There are several editors here keen to get on with improving this article. Are you still intending to mediate? Martin Hogbin ( talk) 10:08, 4 January 2010 (UTC)
And a fruitful start (continuation) in 2010! Nijdam ( talk) 11:45, 31 December 2009 (UTC)
Say, the 'forgetful' Monty?
Marilyn vos Savant says this is really a 'random' Monty, who might reveal a car.
I expand this to say, if it's random, then anyone, including the contestant could open the doors.
And if it's the contestant, then we're really talking about 'Deal Or No Deal'.
Does it makes sense to criticize the original solutions to the MHP based on an analysis of Deal or No Deal? Not in my book. Glkanter ( talk) 17:21, 1 January 2010 (UTC)
Another Straw Man from Rick. Both sides go in the article. Why not chronologically? I've been saying this for a week. Your's and Morgan's POV not dominating the current article? Don't make me laugh. Now, why not answer for yourself, as a sentient being, what does "Suppose you're on a game show...' mean? Without hiding behind Wikipedia's policies. It's OK, we're on a talk page. Glkanter ( talk) 01:16, 4 January 2010 (UTC)
So, by watching, you realize he nods his head at where the car is. Now the female contestant has a 100% likelihood of selecting the car.
This is equivalent to Morgan's argument about a left-most door bias. It's published, but pretty darn stupid.
There is no contestant, or viewer, awareness of a host bias on a game show. And the puzzle begins, 'Suppose you're on a game show...' Glkanter ( talk) 17:20, 5 January 2010 (UTC)
I have now shown that in order to get an answer (probability of winning by switching) of anything other than 2/3, Morgan have had to assume that we know that the producer places the car randomly, but we do not know that the host opens a legal door randomly. Is there anyone here who can justify that odd POV.? Martin Hogbin ( talk) 10:12, 4 January 2010 (UTC)
I disagree on 1 point, Martin. "Suppose you're on a game show..." means the car placement and host choice, as far as the contestant is concerned, are random. This is true whether it's a hypothetical game show, or a mathematical puzzle. Because that is the host/contestant relationship on a game show. And it's every bit as much a premise of this math puzzle as '1 car and 2 goats' which is clearly stated. Because 'Suppose you're on a game show...' has also been clearly stated. Glkanter ( talk) 18:44, 4 January 2010 (UTC)
JeffJor, I'm with you on this 100%. So, living with the requirement that since they're published, Morgan and its ilk must be included in the article, how would you apply your argument to the article? Bear in mind, imho, the conclusion that 'Morgan's paper does not address the MHP' is, unfortunately, OR. Unless you have a source? Seymann just couldn't quite say it. Glkanter ( talk) 18:03, 7 January 2010 (UTC)