Ordinal utility models of decision making under uncertainty

Abstract

This paper studies two models of rational behavior under uncertainty whose predictions are invariant under ordinal transformations of utility. The ‘quantile utility’ model assumes that the agent maximizes some quantile of the distribution of utility. The ‘utility mass’ model assumes maximization of the probability of obtaining an outcome whose utility is higher than some fixed critical value. Both models satisfy weak stochastic dominance. Lexicographic refinements satisfy strong dominance.

The study of these utility models suggests a significant generalization of traditional ideas of riskiness and risk preference. We define one action to be riskier than another if the utility distribution of the latter crosses that of the former from below. The single crossing property is equivalent to a ‘minmax spread’ of a random variable. With relative risk defined by the single crossing criterion, the risk preference of a quantile utility maximizer increases with the utility distribution quantile that he maximizes. The risk preference of a utility mass maximizer increases with his critical utility value.