How to Reason about Self-Locating Belief

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Shulman, David
preprint description
When reasoning about self-locating belief, one should reason as if one were a randomly selected bit of information. This principle can be considered to be an application of Bostrom's Strong Self-Sampling Assumption(SSSA)\cite{Bostrom} according to which one should reason as if one were a randomly selected element of some suitable reference class of observer-moments. The reference class is the class of all observer-moments. In order to randomly select an observer-moment from the reference class, one first randomly chooses a possible world $w$ and then selects an observer-moment $z$ from world $w$. The probability that one selects $z$ given that one has chosen $w$ should be proportional to the amount of information that $z$ is capable of representing. There are both wagering arguments and relative frequency arguments that support our theory of anthropic reasoning. Our theory works best when the amount of information represented is finite. The infinite case is represented as a limit of a finite cases. We can learn from experience how best to represent the infinite case as a limit of finite cases and also learn from experience whether our theory or some other theory is the superior theory of anthropic reasoning. In order to test which theory is best, we use standard Bayesian methodology: We just need prior probabilities for the theories that are being tested and then we only have to use Bayes' rule.