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 - 1. The decision maker is constant risk averse (CRA) if adding the sam e constant to two distributions, or multiplying them by the same positive c onstant, will not change the preference relation between them. We combine t hese two axioms with the betweenness axiom and continuity, and prove a repr esentation theorem. A technical curiosity is that the functions we get sati sfy the betweenness axiom, yet are not necessarily Gateaux (nor Frechet) di fferentiable. (C) 2000 Elsevier Science B.V. All rights reserved.