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We updated on the fact that we exist. SSA does this a little too: specifically, the fact that you exist means that there is at least one observer. One way to look at it is that there is initially a constant number of souls that get used to fill in the observers of a universe. In this formulation, SIA is the result of the normal Bayesian update on the fact that soul-you woke up in a body.

Suppose there is a 2^(-n) chance of universe U_n with n people for n > 0. Initially, there's nothing paradoxical about this. SIA converges. But look at the evidence you get from existing. Call that E.

P(U_n|E) = knP(U_n) for some k

P(U_n|E) = P(U_n&E)/P(E)

P(U_n|E) < P(U_n)/P(E)

P(E) < P(U_n)/P(U_n|E)

P(E) < P(U_n)/(knP(U_n))

P(E) < 1/kn

Since k is constant and this is true for all n, P(E) = 0

So, existence is infinitely unlikely? Or we must assume a priori that the universe definitely doesn't have more than n people for some n? Or P(U_n&E) is somehow higher than P(U_n)?