Accept & Reject Statement-Based Uncertainty Models

TL;DR

This paper introduces a unified framework for modeling uncertainty using accept and reject statements about gambles, connecting existing models and extending their applicability, including to symmetry judgments.

Contribution

It generalizes existing acceptability frameworks, provides translations to preference relations, and links to prevision-based models, enhancing understanding and flexibility.

Findings

Unified accept/reject uncertainty model framework

Connections established with preference and prevision models

Application demonstrated in symmetry judgment modeling

Abstract

We develop a framework for modelling and reasoning with uncertainty based on accept and reject statements about gambles. It generalises the frameworks found in the literature based on statements of acceptability, desirability, or favourability and clarifies their relative position. Next to the statement-based formulation, we also provide a translation in terms of preference relations, discuss---as a bridge to existing frameworks---a number of simplified variants, and show the relationship with prevision-based uncertainty models. We furthermore provide an application to modelling symmetry judgements.