Multiattribute Utility Functions Satisfying Mutual Preferential Independence

The construction of a multiattribute utility function is an important step in decision analysis. One of the most widely used conditions for constructing the utility function is the assumption of mutual preferential independence where trade‐offs among any subset of the attributes do not depend on the instantiations of the remaining attributes. Mutual preferential independence asserts that ordinal preferences can be represented by an additive function of the attributes. This paper derives the most general form of a multiattribute utility function that (i) exhibits mutual preferential independence and (ii) is strictly increasing with each argument at the maximum value of the complement attributes. We show that a multiattribute utility function satisfies these two conditions if and only if it is an Archimedean combination of univariate utility assessments. This result enables the construction of multiattribute utility functions that satisfy additive ordinal preferences using univariate utility assessments and a single generating function. We also provide a nonparametric approach for estimating the generating function of the Archimedean form by iteration.