Abstract: We propose a new measure of deviations from expected utility theory. For any positive number e, we give a characterization of the datasets with a rationalization that is within e (in beliefs, utility, or perceived prices) of expected utility (EU) theory, under the assumption of risk aversion. The number e can then be used as a measure of how far the data is to EU theory. We apply our methodology to data from three large-scale experiments. Many subjects in these experiments are consistent with utility maximization, but not with EU maximization. Our measure of distance to expected utility is correlated with the subjects’ demographic characteristics.