Choosing with the Worst in Mind: A Reference-Dependent Model

We develop an axiomataic model of reference-dependent preferences in which reference points are menu-dependent. In particular, we focus on choices from menus of two-attribute alternatives, and the reference point for the given menu is a vector that consists of minimums of each dimension of the menu. We characterize this model by two weakenings of the Weak Axiom of Revealed Preference (WARP) in addition to standard axioms. Our model is consistent with the attraction effect and the compromise effect, well-known deviations from rational choice theory, and it provdies a connection between the two effects and diminishing sensitivity, a widely used behavioral property in economics.  We apply the model to two different contexts, intertemporal choice and risky choice, and diminishing ensitivity has interesting implications. In intertemporal choice, the main implication of the model is that borrowing constraints produce a psychological pressure to move away from the constraints even if they are not binding. This implication provdies a rationale for two emperical puzzles of life-cycle consumption profiles. In risky choice, the model allows different degrees of risk-aversion.