Anthropic Bias Observation Selection Effects in Science and Philosophy Nick Bostrom



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We can assume that the observer-moments share the prior P(w1) = P(w2) = 1/2. Let h be the hypothesis that the coin fell heads, and e the total information available to an observer-moment that knows it has a black beard. As shown in the diagram (where the -observer-moments are those belonging to the possible white-bearded observer) we have:

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