II. Anthropic reasoning with duplication is not consistent with probability properties

tl;drThere is an impossibility result in anthropic probability: no reasonable probability theory can stay consistent across a duplication event.In particular, it must violate either Bayesian updates-from priors in non-anthropic situations, or the martingale condition – today’s probabilities are expectations of tomorrow’s probabilities.In this post, I’ll extend beyond basic anthropic problems and see what happens when duplicates or copies are allowed. I’ll start with an impossibility result that ...