komponisto2 comments on My Bayesian Enlightenment - Less Wrong
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Also do we really want to assign a prior probability of 0 that the mathematician is a liar! :)
That's not the point I was making.
I'm not attacking unrealistic idealization. I'm willing to stipulate that the mathematician tells the truth. What I'm questioning is the "naturalness" of Eliezer's interpretation. The interpretation that I find "common-sensical" would be the following:
Let A = both boys, B = at least one boy. The prior P(B) is 3/4, while P(A) = 1/4. The mathematician's statement instructs us to find P(A|B), which by Bayes is equal to 1/3.
Under Eliezer's interpretation, however, the question is to find P(A|C), where C = *the mathematician says* at least one boy (*as opposed to saying* at least one girl).
So if anyone is attacking the premises of the question, it is Eliezer, by introducing the quantity P(C) (which strikes me as contrived) and assigning it a value less than 1.