Identifying heterogeneous decision rules from choices when menus are unobserved

Consider aggregate choice data from a population with heterogeneity in both preferences (or more general decision rules) and in menus, and where the analyst has limited information about how menus are distributed across the population. We determine what can be inferred from aggregate data about the distribution of preferences by identifying the set of all distributions that are consistent with the preceding. Our main theorem strengthens and generalizes existing results on such identification and provides an alternative analytical approach (using convex capacities) to study the problem.