  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 theory. The number~$e$ can then be used as a measure of how
far the data is to expected utility theory. We apply our methodology to data
from three large-scale experiments. Many subjects in those experiments are
consistent with utility maximization, but not with expected utility
maximization. Our measure of distance to expected utility is correlated with
subjects' demographic characteristics.
