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A solution to a problem raised in Luce and Marley (2005) |
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| Authors: | A.A.J. Marley R. Duncan Luce |
| Affiliation: | a Department of Psychology, University of Victoria, P.O. Box 3050 STN CSC, Vict., BC, Canada V8W 3P5 b Institute for Mathematical Behavioral Sciences, University of California, Irvine, CA 92697-5100, USA c Faculty of Engineering, University of Debrecen, H-4028 Debrecen, Ótemet? u 2-4., Hungary |
| Abstract: | 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 ⊕. |
| Keywords: | Ranked additive utility Ranked bisymmetry functional equation Joint receipt |
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