(C) We should have extremely low a prior odds of being amongst the most influential To be very crudely quantitative about this, multiplying the number of humans on earth by the number of stars in the visible universe and the lifetime of the Earth, we quickly end up with estimates of ~1e38 total humans, and so priors on the order of ~1e-38.
I think the prior probability of this being the most important century is less than 1 % based on i) the self-sampling assumption (SSA), ii) a loguniform distribution of the effective computation this century as a fraction of that throughout all time, and iii) all effective computation being more than 10^44 times as large as that this century.
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In agreement with section 2 of Mogensen 2022, the self-sampling assumption says the prior probability of being the most influential person among a population of size N, comprising past, present and future people, is the expected value of 1/​N, not the reciprocal of the expected value of N.
Hi Damon,
I do not think your calculation is correct: