Williams Coherence and Beyond

TL;DR

This paper introduces W-coherence, a variant of Williams coherence, for imprecise conditional previsions, demonstrating its consistency, generality, and grounding, and clarifying its relation to other probability consistency notions.

Contribution

The paper proposes W-coherence as a new, well-founded consistency concept for imprecise probabilities, expanding and clarifying the theoretical framework.

Findings

W-coherence ensures key consistency properties.

W-coherence is more general than existing notions.

Comparison clarifies the foundations of imprecise probability coherence.

Abstract

In this paper we discuss the consistency concept of Williams coherence for imprecise conditional previsions, presenting a variant of this notion, which we call W-coherence. It is shown that W-coherence ensures important consistency properties and is quite general and well-grounded. This is done comparing it with alternative or anyway similar known and less known consistency definitions. The common root of these concepts is that they variously extend to imprecision the subjective probability approach championed by de Finetti. The analysis in the paper is also helpful in better clarifying several little investigated aspects of these notions.