Marley, A.A.J.Duncan, L.R.Kocsis, I.2025-12-172025-12-172008Journal of Mathematical Psychology, 2008; 52(1):64-680022-2496https://hdl.handle.net/1959.8/154681Luce 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 ⊕.enCopyright 2007 Elsevierjoint receiptranked additive utilityranked bisymmetry functional equationJournal article10.1016/j.jmp.2007.06.003