New Hope for Relative Overlap Measures of Coherence

Abstract

Abstract Relative overlap measures of coherence have recently been shown to have two devastating properties: (i) according to the plain relative overlap measure, the degree of coherence of any set of propositions cannot be increased by adding further propositions, and (ii) according to the refined relative overlap measure, no set can be more coherent than its most coherent two-element subset. This result has been taken to rule out relative overlap as a foundation for a probabilistic explication of coherence. The present paper shows that this view is premature: we propose a relative overlap measure that does not fall victim to the two properties. The guiding idea is to employ a well-established recipe for the construction of coherence measures and to adapt it to the idea of relative overlap. We show that this new measure keeps up with, or even outperforms, former overlap measures in a set of desiderata for coherence measures and a collection of popular test cases. This result re-establishes relative overlap as a candidate for a proper formalization of coherence.