Reference-dependent self-control: Menu effects and behavioral choices

As is well-known, choices of a decision maker (DM) who attempts self-control in the face of temptation may exhibit menu effects and “non-standard” patterns. Existing models can accommodate some of these patterns but not others; e.g., they can explain self-control undermining menu effects, but not self-control enhancing ones. We introduce a model of self-control with the goal of better understanding and accounting for such effects. The basic idea underlying our model is that the DM experiences a psychological cost if she succumbs to temptation and chooses in a manner that is totally antithetical to her commitment preferences. To mitigate such costs, in any menu, her expression of self-control involves, first, eliminating a subset of alternatives that are worst according to her commitment preferences, with the elimination process being reference-dependent. Then, amongst the remaining alternatives, she chooses the best one according to her temptation preferences. Besides studying menu effects, we characterize the model behaviorally based on a novel axiom called WARP with norms. We also show that the model is well-identified.