Two Forms of Inconsistency in Quantum Foundations

TL;DR

This paper explores two types of inconsistency in quantum foundations, linking Dutch Book arguments and contextuality hierarchies to better understand rational incoherence in hidden variable models.

Contribution

It establishes a deep connection between Dutch Book inconsistencies and the hierarchy of contextuality, offering a new perspective on quantum rationality issues.

Findings

Hierarchy of contextuality corresponds to a hierarchy of Dutch Book violations

Different Dutch Book strengths relate to different levels of contextuality

Partial assessment of normative interpretation of Dutch Books in quantum models

Abstract

Recently, there has been some discussion of how Dutch Book arguments might be used to demonstrate the rational incoherence of certain hidden variable models of quantum theory (Feintzeig and Fletcher 2017). In this paper, we argue that the 'form of inconsistency' underlying this alleged irrationality is deeply and comprehensively related to the more familiar 'inconsistency' phenomenon of contextuality. Our main result is that the hierarchy of contextuality due to Abramsky and Brandenburger (2011) corresponds to a hierarchy of additivity/convexity-violations which yields formal Dutch Books of different strengths. We then use this result to provide a partial assessment of whether these formal Dutch Books can be interpreted normatively.