A Theory of Revealed Indirect Preference

A preference over menus is said to be an indirect preference if it is induced by a preference over the objects that make up those menus, i.e., a menu A is ranked over B whenever A contains an object that is preferred to every object in B. The basic question we address in this paper is the following: suppose an observer has partial information of an agent’s ranking over certain menus; what necessary and sufficient conditions on those rankings guarantee the existence of a preference over objects that induces the observed menu rankings? Our basic result has a wide variety of applications. (1) It gives a characterization of rankings over prices that could be extended to a bona fide indirect utility function. (2) It leads to a generalization of Afriat’s (1967) theorem that allows for imperfectly observed choices. (3) It could be used to characterize observations that are consistent with a multiple preferences model. (4) It leads to a characterization of a model of choice generated by minimax regret.