Marginal stochastic choice

Models of stochastic choice typically use conditional choice probabilities given menus as the primitive for analysis, but in the field these are often hard to observe. We consider the case where an analyst has access to a marginal stochastic choice dataset containing the marginal distributions of available menus and of choices, but not to conditional choice frequencies. The Random Utility Model (RUM) has no testable implications for such datasets, but any restriction on the domain of feasible preference orders does limit the set of rationalizable marginals. The Luce model can also rationalize essentially any dataset, but unlike RUM its parameters can be identified. We also demonstrate that additional testable implications for the marginals may arise when the distribution of menus is endogenous.