Comment on Drawing Two Aces

Sun, 03 Jan 2010 21:01:16 GMT

The states of knowledge in scenarios 1 and 2 aren't equivalent.

It's true that the same possibilities are ruled out in scenario 2 that are ruled out in scenario 1 (and therefore, the same possibilities remain in both scenarios), but in scenario 2 the observation that one of the cards is the ace of spades does more than rule out possibilities, it also shifts the probability mass from the AS/AH possibility toward the AS/2C and AS/2D possibilities, in such a way that the probability attached to the AS/AH possibility doesn't change.

Put more succinctly, the remaining possibilities are the same in both scenarios, but the probabilities attached to these possibilities are different, so it's not true that the states of knowledge are the same.

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