Probabilism for Stochastic Theories

TL;DR

This paper defends an analog of probabilism for stochastic theories within the C*-algebraic framework, showing how rational estimates for chances relate to states and coherence notions in quantum foundations.

Contribution

It establishes an accuracy-dominance result linking chance estimates to states in the C*-algebraic framework and explores the relationship between different notions of rational coherence.

Findings

Establishes that chance estimates avoiding accuracy-dominance correspond to states on the algebra.

Shows conditions under which full coherence and sufficient coherence align.

Identifies quantum states that are sufficiently coherent but not fully coherent.

Abstract

I defend an analog of probabilism that characterizes rationally coherent estimates for chances. Specifically, I demonstrate the following accuracy-dominance result for stochastic theories in the C*-algebraic framework: supposing an assignment of chance values is possible if and only if it is given by a pure state on a given algebra, your estimates for chances avoid accuracy-dominance if and only if they are given by a state on that algebra. When your estimates avoid accuracy-dominance (roughly: when you cannot guarantee that other estimates would be more accurate), I say that they are sufficiently coherent. In formal epistemology and quantum foundations, the notion of rational coherence that gets more attention requires that you never allow for a sure loss (or 'Dutch book') in a given sort of betting game; I call this notion full coherence. I characterize when these two notions of rational coherence align, and I show that there is a quantum state giving estimates that are sufficiently coherent, but not fully coherent.