  We study identification and linear independence in random utility models. We
characterize the dimension of the random utility model as the cyclomatic
complexity of a specific graphical representation of stochastic choice data. We
show that, as the number of alternatives grows, any linearly independent set of
preferences is a vanishingly small subset of the set of all preferences. We
introduce a new condition on sets of preferences which is sufficient for linear
independence. We demonstrate by example that the condition is not necessary,
but is strictly weaker than other existing sufficient conditions.
