Mean-Dispersion Preferences with a Specific Dispersion Function

A popular approach to modeling ambiguity aversion is to decompose preferences into the subjective expected utility of an act and an ambiguity index, or an adjustment factor, or a dispersion function. However, in these approaches the dispersion function (or ambiguity index, or adjustment factor) has very little structure imposed on it, leaving the selection of a specific dispersion function in applications to be rather arbitrary. In this note, working in the Anscombe- Aumann (1963) framework, we provide a simpler axiomatic characterization of mean-dispersion preferences which uniquely identifies the dispersion function from the infinite class of possible alternatives. Given the representation, we also obtain unique identification of subjective probabilities.