Approximate expected utility rationalization

We propose a new measure of deviations from expected utility, given data on economic choices under risk and uncertainty. In a revealed preference setup, and given a positive number e, we provide a characterization of the datasets whose deviation (in beliefs, utility, or perceived prices) is within e of expected utility theory. The number e can then be used as a distance to the theory. We apply our methodology to three recent large-scale experiments. Many subjects in those experiments are consistent with utility maximization, but not expected utility maximization. The correlation of our measure with demographics is also interesting, and provides new and intuitive findings on expected utility.