Will_Newsome comments on What Evidence Filtered Evidence? - Less Wrong

43 Post author: Eliezer_Yudkowsky 29 September 2007 11:10PM

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Comment author: Will_Newsome 22 November 2011 08:10:04PM *  2 points [-]

On a game show, you are given the choice of three doors leading to three rooms. You know that in one room is $100,000, and the other two are empty. The host asks you to pick a door, and you pick door #1. Then the host opens door #2, revealing an empty room. Do you want to switch to door #3, or stick with door #1?

The answer depends on the host's algorithm. If the host always opens a door and always picks a door leading to an empty room, then you should switch to door #3. If the host always opens door #2 regardless of what is behind it, #1 and #3 both have 50% probabilities of containing the money. If the host only opens a door, at all, if you initially pick the door with the money, then you should definitely stick with #1.

Which means that (when Monty's algorithm isn't given or when there's uncertainty about how accurate the problem statement is) people who don't switch are making a very defensible choice by the laws of decision theory. For what plausible reason would he (open a door and) offer to let you switch unless he stood to gain if you did? (Answer: To trick you on the meta level, of course.)