Exchangeable capacities, parameters and incomplete theories

Abstract

The de Finetti Theorem on exchangeable predictive priors is generalized to a framework where preference is represented by Choquet expected utility with respect to a belief function (a special capacity). The resulting model provides behavioral foundations for the decision-maker's subjective theory of the environment in which there are factors common to all experiments (or sources of uncertainty), called parameters, but in which her theory is incomplete in that knowledge of the parameter leaves idiosyncratic factors that vary across experiments in a way that is poorly understood.