Inference of preference heterogeneity from choice data

Suppose an analyst observes inconsistent choices from either a single decision-maker, or a population of agents. Can the analyst determine whether this inconsistency arises from choice error (imperfect maximization of a single preference) or from preference heterogeneity (deliberate maximization of multiple preferences)? I model choice data as generated from imperfect maximization of a small number of preferences. The main results show that (a) simultaneously minimizing the number of inferred preferences and the number of unexplained observations can exactly recover the number of underlying preferences with high probability; (b) simultaneously minimizing the richness of the set of preferences and the number of unexplained observations can exactly recover the choice implications of the decision maker's underlying preferences with high probability.