Chance theory: A separation of riskless and risky utility

Abstract

In a temporal context, sure outcomes may yield higher utility than risky ones as they are available for the execution of plans before the resolution of uncertainty. By observing a disproportionate preference for certainty, empirical research points to a fundamental difference between riskless and risky utility. Chance Theory (CT) accounts for this difference and, in contrast to earlier approaches to separate risky and riskless utility, does not violate basic rationality principles like first-order stochastic dominance or transitivity. CT evaluates the lowest outcome of an act with the riskless utility v and the increments over that outcome, called chances, by subjective expected utility (EU) with a risky utility u. As a consequence of treating sure outcomes differently to risky ones, CT is able to explain the EU-paradoxes of Allais (Econometrica, 21(4): 503–546, 1953) that rely on the certainty effect, and also the critique to EU put forward by Rabin (Econometrica, 68(5): 1281–1292, 2000). Moreover, CT separates risk attitudes in the strong sense, captured entirely by u, from attitude towards wealth reflected solely through the curvature ofv.