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A solution to a problem raised in Luce and Marley (2005)

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dc.contributor.authorMarley, A.A.J.
dc.contributor.authorDuncan, L.R.
dc.contributor.authorKocsis, I.
dc.date.issued2008
dc.description.abstractLuce 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 ⊕.
dc.identifier.citationJournal of Mathematical Psychology, 2008; 52(1):64-68
dc.identifier.doi10.1016/j.jmp.2007.06.003
dc.identifier.issn0022-2496
dc.identifier.urihttps://hdl.handle.net/1959.8/154681
dc.language.isoen
dc.publisherAcademic Press
dc.rightsCopyright 2007 Elsevier
dc.source.urihttps://doi.org/10.1016/j.jmp.2007.06.003
dc.subjectjoint receipt
dc.subjectranked additive utility
dc.subjectranked bisymmetry functional equation
dc.titleA solution to a problem raised in Luce and Marley (2005)
dc.typeJournal article
pubs.publication-statusPublished
ror.mmsid9915911084201831

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