KatjaGrace comments on Avoiding doomsday: a "proof" of the self-indication assumption - Less Wrong
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SIA does not require a definition of observer. You need only compare the number of experiences exactly like yours (otherwise you can compare those like yours in some aspects, then update on the other info you have, which would get you to the same place).
SSA requires a definition of observers, because it involves asking how many of those are having an experience like yours.