journal of economic theory 83, 1942 (1998) Constant Risk Aversion* Zvi Safra Faculty of Management, Tel Aviv University, Tel Aviv, 69978, Israel safrazpost.tau.ac.il and Uzi Segal Department of Economics, University of Western Ontario, London, Ontario, N6A 5C2, Canada segalsscl.uwo.ca Received April 6, 1997; revised June 10, 1998 Constant risk aversion means that adding a constant to all outcomes of two distributions, or multiplying all their outcomes by the same positive number, will not change the preference relation between them. We prove several representation theorems, where constant risk aversion is combined with other axioms to imply specific functional forms. Among other things, we obtain a form of disappointment aversion theory without using the concept of reference point in the axioms, and a form of the rank dependent model without making references to the ranking of the outcomes. This axiomatization leads to a natural generalization of the Gini index. Journal of Economic Literature Classification Number: D81.  1998 Academic Press 1. INTRODUCTION Constant risk aversion means that adding the same constant to all out- comes of two distributions, or multiplying all their outcomes by the same positive constant, will not change the preference relation between them. Within the expected utility framework, this assumption implies expected value maximization. But there are many (non-expected utility) functionals that satisfy this requirement, for example, the dual theory of Yaari [30], or functions offered by Roberts [23] and by Smorodinsky [27] (see Example 1 in Section 2 below). article no. ET972457 19 0022-053198 25.00 Copyright  1998 by Academic Press All rights of reproduction in any form reserved. * We thank Chew Soo Hong, Jim Davies, Larry Epstein, Joel Sobel, Shlomo Yitzhaki, and Peter Wakker for their useful comments and suggestions. Zvi Safra thanks the Johns Hopkins University and the Australian National University for their hospitality and the Israel Institute for Business Research for financial support. Uzi Segal thanks the Social Science and Humanities Research Council of Canada for financial support.