Utility Theory: Axioms Versus ‘Paradoxes’

Abstract

Few attempts have yet been made to interrelate the major axiom systems of expected utility theory such as those presented by von Neumann-Morgenstern, Marschak, Savage, and Arrow. This paper attempts to consolidate the theoretical and empirical research on these axioms by showing the correspondences among the major axioms of each system and highlighting their similarities and differences in dealing with concepts such as probability and utility. Allais, Ellsberg, and others have proposed decision problems which are designed to elicit choices which violate the utility axioms. To the extent that people accept the axioms, choices which violate the axioms can be considered 'paradoxical'. Whether people make such choices is an empirical matter, and we therefore investigate the rate of violation in previous and new experimental studies. Our results show that although there is considerable violation of the utility axioms, the rate can fall drastically as the probability and pay-off parameters are varied away from critical levels. To provide a better understanding of the implications of the axioms and their relationship to some of the decision 'paradoxes', we have stated the implications as 'rules'. Since the subjects were asked to rate the appeal of each rule as a decision norm, we can determine the relative attractiveness of each rule and can show the relationship between subjects' actual choices and their agreement with the rules which guide choice. We found that people often prefer rules which contradict choices they have made.