A solution to a problem raised in Luce and Marley ( 2005 )
نویسندگان
چکیده
Luce and Marley [2005. Ranked additive utility representations of gambles: Old and new axiomatizations. Journal of Risk and Uncertainty, 30, 21–62] examined various relations between mathematical forms for the utility of joint receipt of gambles and for the utility of uncertain gambles. Their assumptions lead to a bisymmetry functional equation which, when the gambles are ranked, is defined on a restricted domain. Maksa [1999. Solution of generalized bisymmetry type equations without surjectivity. Aequationes Mathematicae, 57, 50–74] solved the general case and Kocsis [2007. A bisymmetry equation on restricted domain. Aequationes Mathematicae, 73, 280–284] presents the solution for the ranked case. The latter solution allows us to solve open problem 5 in Luce and Marley (2005) by showing that the assumptions of their Theorem 19 for an order-preserving ranked additive utility (RAU) representation U imply that U is a ranked weighted utility (RWU) representation that is additive over . r 2007 Elsevier Inc. All rights reserved.
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A Simple Axiomatization of Binary Rank-Dependent Utility of Gains (Losses)
This work was supported in part by National Science Foundation Grants SBR-9520107 (Luce) and SBR-9730076 (Grofman, Marley, Regenwetter) to the University of California, Irvine. We thank Rolf Johnson and Bethany Knapp for pointing out that an earlier version of this result worked only for subjective expected utility, not the rank-dependent generalization. Address correspondence and reprint reque...
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