Minimizing Inaccuracy for Self-Locating Beliefs

Abstract

One's inaccuracy for a proposition is defined as thesquared difference between the truth value (1 or 0) of theproposition and the credence (or subjective probability, ordegree of belief) assigned to the proposition. One shouldhave the epistemic goal of minimizing the expectedinaccuracies of one's credences. We show that the method ofminimizing expected inaccuracy can be used to solve certainprobability problems involving information loss andself-locating beliefs (where a self-locating belief of atemporal part of an individual is a belief about where orwhen that temporal part is located). We analyze theSleeping Beauty problem, the duplication version of theSleeping Beauty problem, and various related problems.