Some Problems for Convex Bayesians

TL;DR

This paper critically examines the limitations of convex Bayesian decision making, highlighting issues with constraints and Dutch Book vulnerabilities, and proposes a more general set-based Bayesian approach as a potential solution.

Contribution

It identifies key problems in convex Bayesianism and suggests a broader set-based framework to address these issues.

Findings

Convex Bayesianism struggles with natural constraints.

Dutch Book vulnerabilities can arise under convex Bayesian assumptions.

Set-based Bayesianism offers a promising alternative.

Abstract

We discuss problems for convex Bayesian decision making and uncertainty representation. These include the inability to accommodate various natural and useful constraints and the possibility of an analog of the classical Dutch Book being made against an agent behaving in accordance with convex Bayesian prescriptions. A more general set-based Bayesianism may be as tractable and would avoid the difficulties we raise.