20080410, 23:58  #1  
∂^{2}ω=0
Sep 2002
República de California
3×5^{3}×31 Posts 
Monty Hall vs the Psychologists' Holy Grail
And Behind Door Number 1, A Fatal Flaw  New York Times
Quote:
Last fiddled with by ewmayer on 20080410 at 23:58 

20080411, 03:28  #2  
"Richard B. Woods"
Aug 2002
Wisconsin USA
2^{2}×3×641 Posts 
In following the links from that article I eventually found this in Tierney's 1991 article "Behind Monty Hall's Doors: Puzzle, Debate and Answer?" at http://query.nytimes.com/gst/fullpag...pagewanted=all:
Quote:
Here's one way to get the Monty Hall problem right that I find useful. (I didn't see it stated this way in the articles themselves, but I haven't read the readers' comments.) It's a restating of the articles' explanation about the probabilities. I'm not claiming it reveals anything new about the problem, just that I find it a good way to keep the logic straight. (BTW, this applies only to the version wherein Monty is required both to open a nonwinning door that you didn't choose, and to offer you the option of switching from your original choice to the other unopened door.) Monty starts out with information you do not have, even about the doors he does not open, and his choice of door to open is a forced revelation of part of that extra information about the other doors. Monty's choice tells you nothing about what's behind the door you chose (because Monty will never open that door, so his choice of one of the other doors cannot add anything to your information about the door you chose). That's why the probability that the car is behind the door you chose remains unchanged at 1/3 even after Monty opens another door. Monty's choice does tell you something about both of the other doors, not just the one he opens. Since their sum of probabilities remains at 2/3, but the door he opens is revealed to have a probability of 0, then the entire remaining probability of 2/3 must be assigned to the door he did not open (and you did not originally choose).    "The Psychology of Getting Suckered" at http://tierneylab.blogs.nytimes.com/...tingsuckered/ has further explanation. Last fiddled with by cheesehead on 20080411 at 03:55 

20080411, 06:12  #3 
"William"
May 2003
New Haven
3×787 Posts 
Chen starts by saying the monkey has an unmeasureably small preference for one color of M&M, and then assumes the monkey always chooses the one color it prefers. That's what the sidebar is saying  the monkey is ALWAYS picking the one it prefers  so what is the meaning of "slight preference?"
If "slight preference" means the monkey will pick the one it prefers 53% of the time, then statistics has it picking green 51% of the time in the experiment  an even slighter preference. 
20080411, 07:14  #4  
"Richard B. Woods"
Aug 2002
Wisconsin USA
2^{2}·3·641 Posts 
Quote:
(The numbers 1000 and 300 are just pulled out of the air  I'm not looking up the formulas to find out how many are really required to detect 1% and 3%.) So it's not that the monkey is necessarily always choosing a slightlypreferred one  it's that if the monkey does that, it could explain the observed results without demonstrating cognitive dissonance. So the researchers failed to eliminate a possible variable that could affect the explanation of their observed results, and thus did not prove the existence of cognitive dissonance. Last fiddled with by cheesehead on 20080411 at 07:21 

20080411, 13:32  #5  
"Brian"
Jul 2007
The Netherlands
110011000101_{2} Posts 
Quote:


20080411, 15:07  #6  
"Richard B. Woods"
Aug 2002
Wisconsin USA
2^{2}×3×641 Posts 
Quote:
That just further illustrates the trickiness of reasoning about probabilistic situations: One single, seemingly nitpicky addition (or omission) that's easy to overlook or dismiss can completely change the outcome probabilities! (Or perhaps we could view it as a typical peril of translating word problems into numeric equations.) 

20080411, 15:12  #7  
"William"
May 2003
New Haven
3×787 Posts 
Quote:
What I'm saying is that his mathematics is wrong. I'm saying that the effect he notes cannot explain the observed results. I'm saying that his error  the only way he can get to the conclusion (wrong conclusion) that the effect can explain the results is to make the error of assuming a slight preference in the pretrial becomes an absolute preference in the trial. In particular, the sidebar shows 3 scenarios and shows that the monkey prefers green in two of them  hence the monkey prefers green 2/3 of the time. I'm saying the monkey will pick green 53% of the time in the two scenarios he prefers green, and 47% of the time in the one scenario he prefers blue, hence will pick green 51%. The 53% preference cannot explain picking green 2/3 of the time. In fact, any preference becomes diminished in the trial, not augmented. William 

20080411, 15:52  #8  
"Richard B. Woods"
Aug 2002
Wisconsin USA
17014_{8} Posts 
Quote:
I think some more details of the experiment need to be explained. Here is my understanding/guess, based on what's in the articles: It is not necessary that the monkey always have an absolute preference for red over blue  only that it has that preference for the short duration of the time needed to make its first of two successive choices. (At some other time, say 10 minutes later, the monkey could have a preference for blue over red.) What is necessary is that when the researchers offer the second choice, quickly after the first, they do not include the color the monkey chose the first time  no matter what color that is. Quote:
But those are not the only three possible scenarios  they're just the three in which the monkey prefers red over blue. Quote:
BTW, I lost track  where did your 53% came from in the articles? Or if it's not from the articles, would you please define exactly how it was originally derived in your example? Last fiddled with by cheesehead on 20080411 at 16:02 

20080411, 17:10  #9  
"Lucan"
Dec 2006
England
2×3×13×83 Posts 
Quote:
Davar55's reply to my preceding one had settled it unambiguously. David BTW the only way to guarantee a response in these forums is to say something wrong. Thankyou (and indirectly cheesehead) for confirming that my solution was correct:) Last fiddled with by davieddy on 20080411 at 17:46 

20080412, 00:24  #10  
"William"
May 2003
New Haven
3×787 Posts 
Quote:
I made it up to give a numerical example of "small preference," selected as the smallest integer preference that also gives an integer average. 

20080412, 15:22  #11  
"Lucan"
Dec 2006
England
6474_{10} Posts 
Quote:


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