Random categorization and bounded rationality

In this study we introduce a new stochastic choice rule that categorizes objects in order to simplify the choice procedure. At any given trial, the decision maker deliberately randomizes over mental categories and chooses the best item according to her utility function within the realized consideration set formed by the intersection of the mental category and the menu of alternatives. If no alternative is present both within the considered mental category and within the menu the decision maker picks the default option. We provide the necessary and sufficient conditions that characterize this model in a complete stochastic choice dataset in the form of an acyclicicity restriction on a stochastic choice revealed preference and other regularity conditions. We recover the utility function uniquely up to a monotone transformation and the probability distribution over mental categories uniquely. This model is able to accommodate violations of IIA (independence of irrelevant alternatives), of stochastic transitivity, and of the Manzini-Mariotti menu independence notion (i-Independence). A generalization of the categorizing procedure accommodates violations of regularity and thus provides an alternative model to random utility.