Rejecting Small Gambles under Expected Utility: A Recent Controversy
Roberto Serrano
(Brown University)
September 14th
Lubrano Conference Room

Abstract

A recent literature (e.g., Rabin (2000), Rabin and Thaler (2001)) concludes that expected utility theory is fundamentally unfit to explain decisions under uncertainty. The claim is based on a theorem establishing the relationship between behavior towards small-stakes and large-stakes gambles. In particular, it is shown there that if an expected utility maximizer were to reject a small gamble over a range of wealth levels, he would paradoxically reject extremely favorable large gambles. The authors appeal to introspection to justify the reasonableness of the ``rejecting small gambles'' assumption, thereby reaching their conclusion: the decision maker cannot possibly be maximizing expected utility.

Our starting point is to point out that rejecting a gamble over a given range of wealth levels imposes a lower bound on risk aversion. Comparing the lower bound on risk aversion implied by Rabin's thought experiments to empirical evidence on how decision makers really behave in many real-life circumstances involving risk, we conclude that the levels of risk aversion implied by Rabin's introspection exercises are unrealistically high. It follows that expected utility is not at fault, and the explanation for the paradoxical behavior found in the rejection of large gambles can be attributed to his assumption of rejecting small gambles over too big a range of wealth levels. Finally, if we impose the ``rejecting small gambles'' assumption over a range of wealth levels consistent with the empirical evidence, paradoxical rejections of large gambles are no longer found.