We report a laboratory experiment that enables us to study systematically the substantive and procedural rationality of decision making under uncertainty. By using novel graphical representations of budget sets over bundles of state-contingent commodities, we generate a very rich data set well-suited to studying behavior at the level of the individual subject. We test the data for consistency with the maximization hypothesis, and we recover underlying preferences using both nonparametric and parametric methods. We find that individual behaviors are complex and highly heterogeneous. In spite of this heterogeneity, we identify ‘prototypical’ heuristics that inform subjects’ decision rules. To account for these heuristics, we propose a type-mixture model based on Expected Utility Theory employing only combinations of three heuristics which correspond to the behavior of individuals who are infinitely risk averse, risk neutral, and expected utility maximizers with intermediate risk aversion. The decision rules of the type-mixture model accord well with the large-scale features of the data at the level of the individual subject.