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.

[1]  Johann Pfanzag.  A general theory of measurement applications to utility , 1959 .

[2]  Ralph Roskies,et al.  A measurement axiomatization for an essentially multiplicative representation of two factors , 1965 .

[3]  Constraints on the representation of gambles in prospect theory , 1987 .

[4]  R. Duncan Luce,et al.  Uniqueness and homogeneity of ordered relational structures , 1986 .

[5]  P. Fishburn,et al.  Seven independence concepts and continuous multiattribute utility functions , 1974 .

[6]  Peter C. Fishburn,et al.  Generalized Utility Independence and Some Implications , 1975, Oper. Res..

[7]  J. Miyamoto,et al.  A multiplicative model of the utility of survival duration and health quality. , 1988, Journal of experimental psychology. General.

[8]  A. Tversky.  Additivity, utility, and subjective probability , 1967 .

[9]  R. F. Fagot.  On the psychophysical law and estimation procedures in psychophysical scaling , 1963 .

[10]  J. Neumann,et al.  Theory of games and economic behavior , 1945, 100 Years of Math Milestones.

[11]  Louis Narens,et al.  Classification of concatenation measurement structures according to scale type , 1985 .

[12]  A. Tversky,et al.  Prospect Theory : An Analysis of Decision under Risk Author ( s ) : , 2007 .

[13]  R. Luce,et al.  Simultaneous conjoint measurement: A new type of fundamental measurement , 1964 .

[14]  A. Tversky,et al.  Prospect theory: analysis of decision under risk , 1979 .

[15]  Ralph L. Keeney,et al.  Utility Independence and Preferences for Multiattributed Consequences , 1971, Oper. Res..

[16]  P. Slovic,et al.  Preference Reversals: A Broader Perspective , 1983 .

[17]  R. Luce,et al.  On the possible psychophysical laws. , 1959, Psychological review.

[18]  R. L. Keeney,et al.  Decisions with Multiple Objectives: Preferences and Value Trade-Offs , 1977, IEEE Transactions on Systems, Man, and Cybernetics.

[19]  Uday S. Karmarkar,et al.  Subjectively weighted utility: A descriptive extension of the expected utility model , 1978 .

[20]  Louis Narens,et al.  Measurement: The theory of numerical assignments. , 1986 .

[21]  Peter C. Fishburn,et al.  Independence in Utility Theory with Whole Product Sets , 1965 .

[22]  John M. Miyamoto,et al.  Measurement foundations for multiattribute psychophysical theories based on first order polynomials , 1983 .

[23]  A. Tversky,et al.  The framing of decisions and the psychology of choice. , 1981, Science.

[24]  W. Edwards.  Subjective probabilities inferred from decisions. , 1962, Psychological review.

[25]  Ralph L. Keeney,et al.  Quasi-separable utility functions† , 1968 .

[26]  C. Plott,et al.  Economic Theory of Choice and the Preference Reversal Phenomenon , 1979 .

[27]  Jaap Van Brakel,et al.  Foundations of measurement , 1983 .

[28]  John M. Miyamoto,et al.  Parametric models of the utility of survival duration: Tests of axioms in a generic utility framework , 1989 .

[29]  J. Aczél,et al.  Lectures on Functional Equations and Their Applications , 1968 .

[30]  A. Tversky,et al.  Conjoint-measurement analysis of composition rules in psychology. , 1971 .

[31]  D. Krantz.  Conjoint measurement: The Luce-Tukey axiomatization and some extensions ☆ , 1964 .

[32]  H. Raiffa,et al.  GAMES AND DECISIONS; INTRODUCTION AND CRITICAL SURVEY. , 1958 .

[33]  J. Pratt.  RISK AVERSION IN THE SMALL AND IN THE LARGE11This research was supported by the National Science Foundation (grant NSF-G24035). Reproduction in whole or in part is permitted for any purpose of the United States Government. , 1964 .