Bayesian Inference and Model Comparison for Random Choice Structures

We consider an environment in which agents face various choice sets, assembled from a finite universe of objects, and choose a single object each time a choice set is presented to them. Models for probabilistic discrete choice give, for each choice set, a discrete probability distribution over that choice set. We use methods of Bayesian model comparison to measure the empirical plausibility of various axioms of probabilistic discrete choice. Our testing ground is a model with very little structure — a priori, there are no restrictions on choice distributions across choice sets. We reanalyze several existing data sets, including ones obtained using experimental designs intended to elicit intransitive revealed preferences. We find empirical evidence in favour of random utility, the hypothesis that all choice probabilities are governed by a random utility function over the universe of objects. We also find evidence against the multiplicative inequality of Sattath and Tversky (1976). Since the multiplicative inequality is a necessary condition for independent random utility, a refinement of random utility stipulating that the utilities of objects are mutually independent, this constitutes evidence against independent random utility.