The reflection effect for constant risk averse agents

Assume a decision maker has a preference relation over monetary lotteries. The reflection effect, first observed by Kahneman and Tversky, states that the preference order for two lotteries is reversed once they are multiplied by 2 1. The decision maker is constant risk averse (CRA) if adding the same constant to two distributions, or multiplying them by the same positive constant, will not change the preference relation between them. We combine these two axioms with the betweenness axiom and continuity, and prove a representation theorem. A technical curiosity is ˆ that the functions we get satisfy the betweenness axiom, yet are not necessarily Gateaux (nor ́ Frechet) differentiable.  2000 Elsevier Science B.V. All rights reserved.