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Right. In a sense, P(E) is one over the number of possible people in the universe (scaled by how much of configuration space 'you' are).

Observing your existence only changes your probabilities if your nonexistence was also, causally, an option. In order for there to be an infinite number of possible people in the universe, but only this exponential prior distribution, the probability that any given chunk of stuff is 'you' has to go to zero.

This kinda confused me, I think because P(E) does not represent what I'd colloquially expect - I'm pretty sure now that it's a sampling probability, not a global probability.

I don't see why. If there's an x% chance of a given chunk of stuff in universe U_1 being you, and there's a 50% chance of universe U_1, then there should at least be an x/2% chance of a given chunk of stuff being you, right? And those calculations don't actually use that it's an exponential decrease. It could have been P(U_n) = 1/Σ(n) and it would still apply.