Some Problems for Convex Bayesians
This addresses foundational issues in Bayesian decision theory for researchers in statistics and AI, but it is incremental as it builds on existing critiques.
The paper identifies problems in convex Bayesian decision making, such as its inability to incorporate certain constraints and vulnerability to a Dutch Book-like argument, and proposes set-based Bayesianism as a more tractable alternative that avoids these issues.
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.