Category-dependent Preferences and Stochastic Choice

We introduce a generalisation of (Aguiar’s 2017) random categorisation rule (RCR) that relaxes (Aguiar’s 2017) Acyclicity axiom to an Asymmetry condition. Unlike other alternatives to the RCR, such as the models of Brady and Rehbeck (2016) and Cattaneo et al., (2020), our generalised random categorisation rule (GRCR) relaxes the linearity of preference, rather than varying the random consideration process. We show that the GRCR is also equivalent to allowing linear preferences to be category-dependent, with the requirement that the preferences associated with overlapping categories agree on the intersection. This allows the GRCR to capture intransitivities across categories, which may naturally arise when categorisation is used to frame choices. We provide a characterisation for the GRCR and compare it to the random utility model, as well as to the BR model, the RAM, and the model of Manzini and Mariotti (2014).