Beyond Risk Aversion: Eccentricity In Weighted Expected Utility

In recent survey articles Bell and Farquhar and Machina have brought to the attention of decision scientists an alternative to the expected utility model called weighted expected utility. Developed by MacCrimmon, Chew and Fishburn, this is the simplest alternative to expected utility that permits an interpretation and rationalization of Allais' famous paradox. This paper identifies the two crucial parameters of weighted expected utility -- risk aversion and eccentricity -- by studying demand for insurance. The first of these is a measure that generalizes the Arrow-Pratt risk aversion measure of expected utility. The other, which we call a measure of eccentricity, has no counterpart in expected utility theory. Risk aversion is a concept with which decision analysts are quite comfortable, but eccentricity is simultaneously a new concept and one whose predictions are more subtle than those of risk aversion. In essence, eccentricity is a measure of how susceptible the decision maker is to Allais' paradox or how much he differs from expected utility maximization. Together risk aversion and eccentricity completely determine weighted expected utility and provide insight into the behavior of decision makers under uncertainty, behavior that can be quite different from that predicted by expected utility. Explanations are given of the impact of increases in risk aversion.and eccentricity on demand for insurance. Perhaps the most striking difference is that when the decision maker is eccentric, the standard analysis of decision trees by "averaging out and folding back" provides suboptimal decisions and the losses are magnified as the degree of eccentricity grows.