Nonparametric Analysis of Random Utility Models Robust to Nontransitive Preferences

The Random Utility Model (RUM) is the gold standard in describing the behavior of a population of consumers. The RUM operates under the assumption of transitivity in consumers' preference relationships, but the empirical literature has regularly documented its violation. In this paper, I introduce the Random Preference Model (RPM), a novel framework for understanding the choice behavior in a population akin to RUMs, which preserves monotonicity and accommodates nontransitive behaviors. The primary objective is to test the null hypothesis that a population of rational consumers generates cross-sectional demand distributions without imposing constraints on the unobserved heterogeneity or the number of goods. I analyze data from the UK Family Expenditure Survey and find evidence that contradicts RUMs and supports RPMs. These findings underscore RPMs' flexibility and capacity to explain a wider spectrum of consumer behaviors compared to RUMs. This paper generalizes the stochastic revealed preference methodology of McFadden & Richter (1990) for finite choice sets to settings with nontransitive and possibly nonconvex preference relations.