Uncertainty Aversion with Second-order Probabilities and Utilities

• Activity Number: 296
• Type: Invited
• Date/Time: Wednesday, August 14, 2002 : 10:30 AM to 12:20 PM
• Sponsor: Section on Bayesian Stat. Sciences*
• Author(s): Robert Nau*+
• Affiliation(s): Duke University
• Keywords: Subjective probability ; Risk Aversion ; Uncertainty Aversion ; Ambiguity

Abstract

The phenomenon of uncertainty aversion is illustrated by Ellsberg's paradox, in which subjects typically prefer to bet on events with known probabilities rather than events with unknown probabilities in a manner that violates Savage's axioms. One way to rationalize such behavior is to weaken the independence axiom, leading to the Choquet expected utility model in which beliefs are represented by non-additive probabilities. This paper shows that uncertainty aversion can be explained by a simpler model of "partially separable" preferences in which the decision maker has second-order beliefs about first-order probabilities (similar to a hierarchical Bayesian model) and, moreover, is averse to the second-order uncertainty. The uncertainty aversion is described by a second-order utility function. Thus, the decision maker evaluates uncertain prospects by computing the second-order expected utility of a first-order expected utility. This preference model potentially explains both the Ellsberg and Allais paradoxes and does so with smooth indifference curves, whereas Choquet expected utility entails kinked indifference curves. Though non-Bayesian, it supports coherent decision-making.