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Coscott comments on How should Eliezer and Nick's extra $20 be split - Less Wrong
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If p + q = 1, then p(A or B) = 1. The equivalence statement about A and B that we're updating can be stated as (A or B) iff (A and B). Since probability mass is conserved, it has to go somewhere, and everything but A and B have probability 0, it has to go to the only remaining proposition, which is g(p, q), resulting in g(p, q) = 1. Stating this as p+q was an attempt to find something from which to further generalize.
Oh, I just noticed the problem. When you say p(A or B)=1, that assumes that A and B are disjoint, or equivalently that p(A and B)=0.
The theorem you are trying to use when you say p(A or B)=1 is actually:
p(A or B)=p(A)+p(B)-p(A and B)
Ok, this is a definition discrepancy. The or that I'm using is (A or B) <-> not( (not A) and (not B)).
Edit: I was wrong for a different reason.