A Representation Theorem for General Revealed Preference


Following Richter (1966), we provide criteria under which a preference relation implied by a finite set of choice observations has a complete extension that can in turn be represented by a utility function. These criteria rely on a mapping over preference relations, the rational closure, which is a generalization of the transitive closure and is employed to construct the complete extension. We illustrate this approach by revisiting the problem of rationalizing incomplete preferences revealed by a sequence of consumption decisions obtained from different budget sets. Our result relaxes the usual assumptions about the consumption space and the structure of budgets generating the observed choices, and allows for a new interpretation of classical revealed preference axioms.