shinoteki comments on Pascal's Mugging: Tiny Probabilities of Vast Utilities - Less Wrong
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Counterexample: P(3^^^...3)(n "^"s) = 1/2^n P(anything else) = 0 This is normalized because the sum of a geometric series with decreasing terms is finite. You might have been thinking of the fact that if a probability distribution on the integers is monotone decreasing (i.e. if P(n)>P(m) then n <m) then P(n) must decrease faster than 1/n. However, a complexity-based distribution will not be monotone because some big numbers are simple while most of them are complex.