We model a boundedly rational agent who suffers from limited attention. The agent considers each feasible alternative with a given (unobservable) probability, the attention parameter, and then chooses the alternative that maximizes a preference relation within the set of considered alternatives. We show that this random choice rule is the only one for which the impact of removing an alternative on the choice probability of any other alternative is asymmetric and menu independent. Both the preference relation and the attention parameters are identified uniquely by stochastic choice data.

Theories of bounded rationality often assume a rich dataset of choices from many overlapping menus, limiting their practical applicability. In contrast, we study the problem of identifying the distribution of cognitive characteristics in a population of agents from a minimal dataset that consists of aggregate choice shares from a single menu, and includes no observable covariates of any kind. With homogeneous preferences, we find that “consideration capacity” and “consideration probability” distributions can both be recovered effectively if the menu is sufficiently large. This remains true generically when tastes are heterogeneous with a known distribution. When the taste distribution is unknown, we show that joint choice share data from three “occasions” are generically sufficient for full identification of the cognitive distribution, and also provide substantial information about tastes.