  In recent years there has been an influx of papers which use graph theoretic
tools to study stochastic choice. Fiorini (2004) serves as a base for this
literature by providing a graphical representation of choice probabilities and
showing that every interior node of this graph must satisfy inflow equals
outflow. We show that this inflow equals outflow property is almost
characteristic of choice probabilities. In doing so, we characterize choice
probabilities through graph theoretic tools. We offer two applications of this
result to random utility. First, we offer a novel axiomatization of random
utility on an incomplete domain. Second, we construct a new hypothesis test for
random utility which offers computational improvements over the hypothesis test
of Kitamura and Stoye (2018).

Theoretical Economics;Combinatorics