Inference of Preference Heterogeneity from Choice Data
Suppose that an analyst observes inconsistent choices from a decision maker. 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 context-dependent preferences, where contexts vary across observations, and the decision maker errs with small probability in each observation. I show that (a) simultaneously minimizing the number of inferred preferences and the number of unexplained observations can exactly recover the correct number of 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 true preferences with high probability. These results illustrate that selection of simple models, appropriately defined, is a useful approach for recovery of stable features of preference.