Mixture-Dependent Preference for Commitment

The literature on temptation and self-control is motivated by evidence of a preference for commitment. This literature has typically put forth models for preferences over menus of lotteries that satisfy the Independence axiom. Independence requires that the ranking of two menus is not affected if each is mixed (probabilistically) with a common third menu. In particular, the preference for commitment is invariant under Independence. We argue that intuitive behavior may require that the preference for commitment be affected by such mixing, and hence be mixture-dependent. To capture such behavior, we generalize Gul and Pesendorfer (2001) by replacing their Independence axiom with a suitably adapted version of the Mixture-Betweenness axiom of Chew (1989)- Dekel (1986). Axiomatizing the model involves a novel extension of the Mixture Space Theorem to preferences that satisfy Mixture-Betweenness.