Categorize and randomize: a permissive model of stochastic choice

Abstract: We model stochastic choices with categorization. The agent preliminarly groups alternatives in homogenous disjoint classes, then randomly chooses one class and randomly picks an item within the selected class. We give a formal definition of a choice generated by this procedure, and provide an axiomatic characterization. The characterizing properties allow an external analyst to elicit that categorization is applied. In a broader interpretation, the model allows to describe the observed choice as the composition of independent subchoices. This composition preserves rationalizability by Random Utility Maximization. A generalization of the model subsumes Luce model and Nested Logit.