On Accuracy and Coherence with Infinite Opinion Sets

TL;DR

This paper extends the understanding of the relationship between accuracy dominance and probabilistic coherence from finite to infinite sets of propositions, including countably infinite partitions.

Contribution

It establishes the necessary theoretical results to generalize the classic accuracy argument for probabilism to infinite proposition sets.

Findings

Extended the accuracy-coherence equivalence to infinite proposition sets

Connected accuracy dominance with probabilistic coherence in infinite contexts

Provided foundational results for infinite credence functions

Abstract

There is a well-known equivalence between avoiding accuracy dominance and having probabilistically coherent credences (see, e.g., de Finetti 1974, Joyce 2009, Predd et al. 2009, Schervish et al. 2009, Pettigrew 2016). However, this equivalence has been established only when the set of propositions on which credence functions are defined is finite. In this paper, we establish connections between accuracy dominance and coherence when credence functions are defined on an infinite set of propositions. In particular, we establish the necessary results to extend the classic accuracy argument for probabilism originally due to Joyce (1998) to certain classes of infinite sets of propositions including countably infinite partitions.