Expected Utility Calibration for Continuous Distributions

Recently, Rabin criticized the use of diminishing marginal utility in explaining risk aversion in small gambles with a mathematical theorem, which compares revealed risk averting behavior in small gambles to the risk behavior implied by expected utility theory in somewhat larger gambles, using discrete payoff distributions. To examine whether his criticism holds in more realistic risky situations, we generalize his theorem to the cases of continuous distributions and of continuous choice. The results suggest that the absolute size of the risk may not be as important as the relative size of the possible risk reduction, and that expected utility is likely a poor explanation for any short term risk response. We discuss some rules of thumb for judging the appropriateness of expected utility in practice.