Peter_de_Blanc comments on Drawing Two Aces - Less Wrong
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Answering without looking at other comments, will check those after:
The assumption in the first argument is wrong, you in fact have different information than the info you have in scenario 1. In scenario 1, the information you have is "I answer yes when asked if I have a spade"
In this situation you have the information that I have an ace and if I pick one of the aces at random to reveal to you, I reveal that I have a spade.
The relevant likelihoods are DIFFERENT:
P("I have at least one ace, and if I choose one at random (or just the one if I have only one), to reveal to you, I reveal to you I have a spade" | I have both aces) = 1/2
P("You asked me if I have a spade? Well, yes, I do have a spade" | I have both aces) = 1
(modulo standard disclaimers on assigning P = 1 to any state of affairs, of course)
Argument 2 is correct. What changes is the probability that I hold just an ace of spades or just an ace of hearts.
Ditto. Psy-Kosh has correctly observed that argument 2 is correct, and has correctly pointed out the flaw in argument 1.