Multilinear representations for ordinal utility functions |
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| Institution: | 1. Thales Research & Technology, 1 avenue Augustin Fresnel, Palaiseau Cedex 91767, France;2. Paris School of Economics, Université Paris I – Panthéon-Sorbonne, Paris, France;1. Centre for European Economic Research (ZEW), P.O. Box 103443, D-68034 Mannheim, Germany;2. New School for Social Research and ZEW Research Associate, 79 Fifth Ave., New York, NY 10003, USA;1. Jiangsu Key Laboratory for NSLSCS, School of Mathematical Sciences, Nanjing Normal University, Nanjing 210023, PR China;2. School of Mathematics, Nanjing Normal University Taizhou College, Taizhou 225300, PR China |
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| Abstract: | An ordinal utility function u over two attributes X1, X2 is additive if there exists a strictly monotonic function ϕ such that ϕ(u) = v1(x2) + v2(x2) for some functions v1, v2. Here we consider the class of ordinal utility functions over n attributes for which each pair of attributes is additive, but not necessarily separable, for any fixed levels of the remaining attributes. We show that while this class is more general than those that are ordinally additive, the assessment task is of the same order of difficulty, and involves a hierarchy of multilinear rather than additive decompositions. |
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