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The self-indication assumption seems to violate some pretty basic probability. Suppose that there are two possible universes: universe A has one person, and universe B has 99 people. Suppose that the prior probability for each is 50%. Under SIA, you are 1% likely to be each one of these 100 possible people. But that means that universe B has 99% probability, even though we just assigned it 50% probability. It can't change without updating on evidence, which we never did. What happened?

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.