Generic utility theory: Measurement foundations and applications in multiattribute utility theory

Abstract

A utility representation is formulated that is generic in the sense that it is implied by many stronger utility theories, yet it does not make assumptions peculiar to particular utility theories. The generic utility representation postulates that the preference order on a subset of two-outcome gambles with fixed probability is represented by an additive combination of the utility of the outcomes. Although many utility theories imply that this representation should be satisfied, standard additive conjoint formalizations do not provide an axiomatization of the generic utility representation because the preference ordering is only defined on a proper subset of a Cartesian product. (The precise specification of the subset is stated in the paper.) An axiomatization of the generic utility representation is presented here, along with proofs of the existence and interval scale uniqueness of the representation. The representation and uniqueness theorems extend additive conjoint measurement to a structure in which the empirical ordering is only defined on a proper subset of a Cartesian product. The generic utility theory is important because formalizations and experimental tests carried out within its framework will be meaningful from the standpoint of any stronger theory that implies the generic utility theory. Expected utility theory, subjective expected utility theory, Kahneman and Tversky's prospect theory ((1979). Econometrica, 47, 263–291), and Luce and Narens' dual bilinear model ((1985). Journal of Mathematical Psychology, 29, 1–72) all imply that selected subsets of gambles satisfy generic utility representations. Thus, utility investigations carried out within the generic utility theory are interpretable from the standpoint of these stronger theories. Formalizations of two-factor additive and multiplicative utility models and of parametric utility models are presented within the generic utility framework. The formalizations illustrate how to develop multiattribute and parametric utility models in the generic utility framework and, hence, within the framework of stronger theories that imply it. In particular, the formalizations show how to develop multiattribute and parametric utility models within prospect theory and the dual bilinear model.