Risk, Ambiguity and the Separation of Utility and Beliefs

The theory of subjective expected utility (SEU) has been extended in many recent works, allowing ambiguity to matter for choice. However, a fully satisfactory and general notion of ambiguity aversion, analogous to risk aversion for SEU, is still missing. Using a new preference model which encompasses most of the recent literature, we provide such a definition by building on a comparative notion of ambiguity aversion. The development of the latter is not immediate, since it is necessary to distinguish between differences in ambiguity and risk attitude. The solution offered here is very general as it only requires a richness condition on the set of consequences. Employing the comparative notion, we call `ambiguity averse' a preference relation which is `more ambiguity averse' than a SEU preference with similar risk attitude. We show that ambiguity aversion in this sense has a simple characterization, especially for the specific models that are most popular in the literature. We next build on these ideas to provide a definition of unambiguous act and event. We show that for preferences which have a consistent ambiguity attitude, the sets of these acts and events have a simple and easily checked characterization. As an illustration, we consider the classical Ellsberg 3-color urn problem and find that the notions developed in the paper provide the intuitive answers.