A Theory of Reference-Dependent Utility

Abstract

This paper characterizes a class of twice continuously differentiable objective-probability preference representations exhibiting endogenous reference dependence under risk. Weak rank-dependent utility (WRDU) preserves objective probabilities, partitions outcomes at an endogenous reference point, and evaluates lotteries through a gainloss representation in which the reference point maximizes a penalized functional. The first-order condition yields a virtual loss-aversion index equal to the ratio of marginal utilities across the loss and gain domains, recovering both the utility-based index of Köbberling and Wakker (2005) and the slope ratio of Tversky and Kahneman (1992) as special cases. The main theorem shows that, within a class satisfying affine admissibility, loss-factorization, dispersion monotonicity, and attenuation, the derivative-ratio form is uniquely admissible. In this class, WRDU generates the modal Allais pattern on an admissible region and blocks the Rabin calibration implication through range-dependent attenuation. The result is conditional and does not claim uniqueness over all behavioral models of risky choice.

arXiv commentA lengthy Internet Appendix with applications and instructions to implement the model is attached to the paper. The paper itself is around 25 pages