Yaari''s dual theory without the completeness axiom

Summary. This note shows how Yaari (1987)'s dual theory of choice under risk naturally extends to the case of incomplete preferences. This also provides an axiomatic characterization of a large and widely studied class of stochastic orders used to rank the riskiness of random variables or the dispersion of income distributions (including, e.g., second order stochastic dominance, dispersion, location independent riskiness, see Chateauneuf, Cohen, and Meilijson, 1997).Received: 21 January 2003, Revised: 23 April 2003, JEL Classification Numbers: D81.I wish to thank Erio Castagnoli, Alain Chateauneuf, Paolo Ghirardato, Massimo Marinacci, Efe Ok, Peter Wakker, as well as an associate editor and an anonymous referee for helpful suggestions. The financial support of CNR, MIUR, and Universitá Bocconi is gratefully acknowledged. Part of this research has been done at the Department of Economics of Boston University.