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Stuart_Armstrong comments on Avoiding doomsday: a "proof" of the self-indication assumption - Less Wrong
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Note the line "weighted according to the probability of that observer existing".
Imagine flipping a coin twice. If the coin comes heads first, a universe A with one observer is created. If it comes up TH, a universe B with two observers is created, and if it comes up TT, a universe with four observers is created.
From outside, the probabilities are A:1/2, B:1/4, C:1/4. Updating with SIA gives A:1/4, B:1/4, C:1/2.
No uniform priors assumed or needed.