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D_Malik comments on Torture vs. Dust vs. the Presumptuous Philosopher: Anthropic Reasoning in UDT - Less Wrong
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Suppose we modify the situation so that there is an infinite list of possible Theories of Everything, T1, T2, T3, ... With each theory predicting a trillion observers, a trillion trillion observers, a trillion trillion trillion observers, and so on. Additionally, from some other prior info gleaned from scientific insight, the probability of Tn being true is 2^(-n).
SIA here would suggest we live in the universe with the most observers... which in this case doesn't exist.
I don't think this is a good argument against SIA. The most natural interpretation of SIA gives a posterior of zero for each Ti, so it doesn't actually say we "live in the universe with the most people".
"T{i+1} is half a trillion times as likely as Ti" doesn't actually imply "T{i+1} is more likely than Ti", because those probabilities are both zero.