Some Problems for Convex Bayesians

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.
Comment: Appears in Proceedings of the Eighth Conference on Uncertainty in Artificial Intelligence (UAI1992)