Multilinear Representations for Ordinal Utility Functions

An ordinal utility function u over two attributes A’, , A’, is additive if there exists a strictly monotonic function cp such that q(u) = v,(.Y,) + u2(x2) for some functions v,, 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 difftculty, and involves a hierarchy of multilinear rather than additive decompositions. 1 19X7 Academic Press. Inc.