A Bayesian General Theory of Anthropic Reasoning

Abstract

A non-ad hoc, general theory of anthropic reasoning can be constructed based on Bostrom's Strong Self-Sampling Assumption that we should reason as if the current moment of our life were a randomly selected member of some appropriate reference class of observer-moments. We do not need to use anything other than standard conditionalization of a hypothetical prior based upon the SSSA in order to estimate probabilities. But we need to make the SSSA precise. We specify exactly what is and what is not an observer, how to choose a reference class and how to select a prior probability distribution that can be used when selecting randomly from the reference class. There are both collective Dutch Book and relative frequency arguments in favor of our rules for choosing priors and reference classes. In order to handle examples like Bostrom's Lazy Adam scenario, a causal anthropic decision theory is developed.

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