Perceived Repeated Risk and the Allais Paradox

Abstract

Empirical evidence on the common ratio effect, a version of the Allais paradox, indicates that people are nonlinearly sensitive to probabilities. The leading explanation of this effect is prospect theory and its nonlinear weights applied to probabilities. We propose an alternative explanation: expected utility under the perception that one-shot risks will be repeated. We follow a stream of literature which suggests that evolutionary forces have shaped human tendencies to choose actions which are adapted to recurrent situations. We show that expected utility under perceived repeated risk can explain the common ratio effect and give rise to nonlinear sensitivity to probabilities. We provide several classes of utilities that can satisfy conditions that are necessary and sufficient for the existence of a common ratio effect. These utility functions have context-dependent inflection points: a zero inflection point that resets itself in each choice frame and other non-zero inflection points around which an individual is increasingly absolute risk averse. We argue that such inflection points may arise from frequent social comparison of the outcomes from one-shot risks.

Keywords: expected utility theory, prospect theory, common ratio effect, nonlinear sensitivity to probabilities

JEL Classification: A10, D81