Categorize and randomize: a permissive model of stochastic choice

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.