Rationalizing Choices in a Rich Domain

Two alternatives are independent if they never induce menu effects on each other. We propose a condition, Comparative Richness, which postulates that for every menu and every submenu of it, there is an alternative that is equally desirable as the submenu and independent of each alternative in the menu. We show that under Comparative Richness, (i) some axioms necessary for rationality become sufficient; (ii) several classic axioms without clear implications now characterize new choice models; (iii) interpretable specifications can be derived for existing models; and (iv) departures from rationality can be explicitly quantified.