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 ⊕ .
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