Multiple selves or willpower?

For me, explaining and resolving revealed conflicting preferences is the great contribution that behavioural economics has to make. An excellent alternative to the multiple selves model (Ambrus and Rozen 2008, see Martin's post below) is Ozdenoren et al's "Willpower and the control of Visceral Urges" (2006). They extend the conventional discounted utility model to incorporate willpower. Behaviours that appear incompatible with orthodox intertemporal decision theory, such as saving the best til last, are explained by modelling willpower as a depletable resource, the stock of which can be uncertain. Unlike the multiple selves model, which points to a discontinuity and throws its hands in the air, the willpower model is tractable.

Abstract
Psychologists and behavioral economists have documented that individuals often make intertemporal choices that are inconsistent with the conventional economic model. To explain intertemporal choices better, psychologists have offered, and provided experimental support for, a “willpower depletion” model which predicts that a person who exerts self-discipline in one activity will behave as if he has less self discipline available to exert in other activities. We formalize a willpower depletion model and investigate how willpower constraints affect the canonical problem of how to divide a cake (or paycheck or workload) over time to maximize utility. We find that a consumer behaving optimally subject to willpower constraints acts in ways that others have described as anomalous. This consumer reveals a preference for increasing paths of consumption, a preference for commitment, and time-inconsistency in preferences. We also study the optimal allocation of willpower between the intertemporal saving activity and other activities that require self-discipline. Finally, we show how the ability to build willpower by its exercise further influences the optimal path of consumption.