Credence and Belief: Distance- and Utility-Based Approaches

Abstract

AbstractThis 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 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.