  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.
