On Measurable Multiattribute Value Functions Based on Finite-Order Independence of Structural Difference

Abstract

Mathematical modeling of preferences has been widely studied in multiattribute decision analysis. Measurable value functions are based on the concept of a “difference in the strength-of-preference” (Fishburn, 1970) between alternatives. These functions provide an interval scale of measurement for riskless preferences. However, it is practically too difficult to directly identify a measurable multiattribute value function. Therefore, it is necessary to develop conditions that reduce the dimensionality of the functions that are required to identify. These conditions restrict the form of a measurable multiattribute value function in a decomposition theorem. Dyer and Sarin (1979) presented conditions for additive and multiplicative forms of the measurable multiattribute value function. These conditions are called “difference independence” and “weak difference independence”. These conditions correspond to additive independence and utility independence, respectively, in multiattribute utility theory (Keeney and Raiffa, 1976).