  We readdress the problem of nonparametric statistical testing of random
utility models proposed in Kitamura and Stoye (2018). Although their test is
elegant, it is subject to computational constraints which leaves execution of
the test infeasible in many applications. We note that much of the
computational burden in Kitamura and Stoye's test is due to their test defining
a polyhedral cone through its vertices rather than its faces. We propose an
alternative but equivalent hypothesis test for random utility models. This test
relies on a series of equality and inequality constraints which defines the
faces of the corresponding polyhedral cone. Building on our testing procedure,
we develop a novel axiomatization of the random utility model. Our new axiom
can be interpreted as a condition on surplus allocation in cooperative games.
