Two Violations of Expected Utility Theory - An Alternative Solution

Abstract

Two well-known violations of Expected Utility Theory (EUT) are the Allais Paradox and the preference reversal between gamble choices and gamble bids. The Allais Paradox undermines the independence axiom, according to which the preferences for two gambles should be unaffected by an independent third gamble. There have been several proposed solutions that generally involve some form of non-linear probabilities (Machina 1987). The preference-reversal violation has been more problematic as it pre-supposes either non-transitive preferences or alternatively, some response-mode effect (or effects), whereby preferences and valuations are driven by distinct processes and outside influences (Machina 1987). This paper outlines a single solution to the two problems using a new utility framework that incorporates reference points for the agent’s income and needs. Rather than using non-linear probabilities or non-transitive preferences, the new utility framework models a response-mode effect, whereby agents recalibrate their needs in response to each prospect. This recalibration changes the convexity of the agent’s utility curve and, by extension, the agent’s tolerance for risk, which gives rise to the observed EUT violations.