Credence and Belief: Distance- and Utility-based Approaches

Abstract

This paper investigates the question of how subjective probability should relate to binary belief.We propose new distance minimization methods, and develop epistemic decision theoretic accounts. Both approaches can be shown to get “close” to the truth: the first one by getting “close” to a given probability, and the second one by getting expectedly “close” to the truth.More specifically, we study distance minimization with a refined notion of Bregman divergence and expected utility maximization with strict proper scores. Our main results reveal that the two ways to get “close” to the truth can coincide.