Mixture Symmetry and Quadratic Utility

The independence axiom of expected utility theory has recently been weakened to the betweenness axiom. In this paper, an even weaker axiom, called mixture symmetry, is presented. The corresponding functional structure is such that utility is a betweenness functional on part of this domain and quadratic in probabilities elsewhere. The experimental evidence against betweenness provides one motivation for the more general theory presented here. Another advantage of the mixture symmetric class of utility functions is that it is sufficiently flexible to permit the disentangling of attitudes toward risk and toward randomization. Copyright 1991 by The Econometric Society.