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October 1

Monty Hall and Condorcet

Perhaps someone would consider whether there is a connection between the Monty Hall problem and Condorcet's voting paradox. — Preceding unsigned comment added by 99.169.83.78 (talk) 05:49, 1 October 2014 (UTC)[reply]

I've pondered it a bit, but only based upon my own recollection of the former and a quick skim of the latter ...but I've also considered the possibility that this is a homework problem, so I have to ask[1]: do you think there is a connection and if so, what is it? El duderino ^(abides) 10:45, 1 October 2014 (UTC)[reply]

Well, on the face of it, Monty hall problem is fully solved, and several variants can also be analytically solved. In contrast, the "paradox" is simply that the Condorcet criterion does not allow for condorcet methods to satisfy Independence_of_irrelevant_alternatives, because of Arrow's_impossibility_theorem. So both phenomenon are fairly well understood (with some careful analysis), but both issues can be counterintuitive and surprising to first time learners. So I'd say the similarities have more to do with human psychology than any strong connections in the mathematical structures. Another connection is that I taught both of these topics in the same class in 2005 :) SemanticMantis (talk) 15:06, 1 October 2014 (UTC)[reply]

One rather trivial connection may be an argument that what appears to be a choice for one item is technically a choice for more than one item. In the Monty Hall problem, when you choose a single door - you actually choose two doors. You choose the door you chose and you choose the door which is removed (the winning door is never removed). So, you chose 2/3 doors and there is 1/3 doors left. In the Condorcet voting problem, when you choose someone as your 3rd choice, you are actually choosing support for your 1 and 2 choice. So, your choice is actually a compound choice for more than one person. It is not, as many thing, a full vote for #1, a half vote for #2, and a third vote for #3. It is a full vote #1 against #2 and #3. It is a full vote for #2 against #3. 209.149.115.99 (talk) 17:42, 3 October 2014 (UTC)[reply]