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army1987 comments on How should Eliezer and Nick's extra $20 be split - Less Wrong
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I think that either I have communicated badly, or you are making a big math mistake. (or both)
Say we believe A with probability p and B with probability 1-p. (We therefore believe not A with probability 1-p and not B with probability p.
You claim that if we learn A and B are equivalent then we should assign probability 1 to A. However, a symmetric argument says that we should also assign probability 1 to not A. (Since not A and not B are equivalent and we assigned probabilities adding up to 1.)
This is a contradiction.
Is that clear?
Yes. Woops.