On Accuracy and Coherence with Infinite Opinion Sets
This work addresses a foundational gap in formal epistemology and decision theory, but it is incremental as it builds on existing finite-set results.
The paper tackles the problem of extending the equivalence between avoiding accuracy dominance and probabilistic coherence from finite to infinite sets of propositions, establishing results that allow the accuracy argument for probabilism to be applied to certain infinite cases, such as countably infinite partitions.
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.