Discrete choice and stochastic utility maximization

In this paper we study the relationship between discrete or qualitative choice models and the hypothesis of stochastic utility maximization. Except for computational problems it is relatively easy to derive choice probabilities from a given random utility specification. We consider the reverse question: under which conditions is a given set of choice probabilities compatible with stochastic utility maximization? We distinguish between global compatibility, i.e. compatibility for all possible values of the observed utility components, and local compatibility, i.e. compatibility on a subset of the Euclidean space of appropriate dimension. We give a simple derivation of the necessary and. sufficient conditions for global compatibility. We also discuss local compatibility on various subsets, and we give a necessary and sufficient condition for local compatibility given a natural choice of this subset