Uncertainty Aversion with Second-Order Utilities and Probabilities

Subjective expected utility theory does not distinguish between attitudes toward uncertainty (ambiguous probabilities) and attitudes toward risk (unambiguous probabilities). Both are explained in terms of nonlinear utility for money rather than properties of events per se, hence, the decision maker displays the same attitude toward all sources of risk and uncertainty. There is ample evidence that real decision makers do not always behave (or even wish to behave) in this way, and instead they often distinguish between risk and uncertainty, as in Ellsberg's (1961) paradox. This paper presents a simple axiomatic model of nonneutral attitudes toward uncertainty and a behavioral test for uncertainty aversion that is applicable even if utility is state dependent. The decision maker may display different degrees of aversion toward gambles on different kinds of events, e.g., being systematically more averse toward gambles on events whose probabilities are more ambiguous. For such a decision maker, the elicitation of preferences among objective gambles may not yield the correct measure of risk aversion for modeling real-world decisions.risk aversion, uncertainty aversion, ambiguity, state-dependent utility, Choquet expected utility, cumulative prospect theory, state-preference theory, Ellsberg's paradox, smooth preferences