Multiattribute utility theory without expected utility foundations

Methods for determining the form of utilities are needed for the implementation of utility theory in specific decisions. An important step forward was achieved when utility theorists characterized useful parametric families of utilities, and simplifying decompositions of multiattribute utilities. The standard development of these results is based on expected utility theory which is now known to be descriptively invalid. The empirical violations of expected utility impair the credibility of utility assessments. This paper shows, however, that parametric and multiattribute utility results are robust against the major violations of expected utility. They retain their validity under non-expected utility theories that have been developed to account for actual choice behavior. To be precise, characterizations of parametric and multiattribute representations are extended to rank dependent utility, state dependent utility, Choquet expected utility, and prospect theory. Added after publication: Our Theorems 1 and 2 were essentially already given as Theorems 4 and 3, respectively, in Udo Ebert (1988), "Measurement of Inequality: An Attempt at Unification and Generalization," Social Choice and Welfare 5, 147-169. We discovered this only after publication. Comments: Only after publication, John Miyamoto and I discovered that Theorem 1 had been obtained before as Theorem 4 in Ebert (1988, Social Choice and Welfare 5), and Theorem 2 as Ebert's Theorem 3 (pointed out to me by Alain Chateauneuf in June 1998). p. 320/321: In Lemma 1, Int(C) should be replaced by C{best and worst outcomes}, because the interior in Wakker (1993a) is with respect to the preference topology. (Pointed out to me by Han Bleichrodt in August 2001.)