Theory and Decision

, Volume 51, Issue 2–4, pp 329–349

The Domain and Interpretation of Utility Functions: An Exploration

Article

Abstract

This paper proposes an exploration of the methodology of utility functions that distinguishes interpretation from representation. While representation univocally assigns numbers to the entities of the domain of utility functions, interpretation relates these entities with empirically observable objects of choice. This allows us to make explicit the standard interpretation of utility functions which assumes that two objects have the same utility if and only if the individual is indifferent among them. We explore the underlying assumptions of such an hypothesis and propose a non-standard interpretation according to which objects of choice have a well-defined utility although individuals may vary in the way they treat these objects in a specific context. We provide examples of such a methodological approach that may explain some reversal of preferences and suggest possible mathematical formulations for further research.

Utility representation interpretation preference reversal 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

REFERENCES

  1. Arrow, K.J. (1951), Social Choice and Individual Values, New York: John Wiley and Sons.Google Scholar
  2. Aumann, R.J. (1998), Common priors: A reply to Gul, Econometrica 66, 929-938.CrossRefGoogle Scholar
  3. Barbera, S., Hammond, P.J. and Seidl, C. (eds) (1998), Handbook of Utility Theory: Vol. 1: Principles. Dordrecht / Boston / London: Kluwer Academic Publishers.Google Scholar
  4. De Finetti, B. (1937), La prévision: ses lois logiques, ses sources subjectives. Paris, France: Institut Henri Poincaré.Google Scholar
  5. De Finetti, B. (1974), Theory of Probability, Chichester, UK: John Wiley and Sons.Google Scholar
  6. Fishburn, P.C. (1970), Intransitive indifference in preference theory: A survey, Operations Research 18, 207-228.Google Scholar
  7. Fishburn, P.C. (1989), Retrospective on the utility theory of von Neumann and Morgenstern, Journal of Risk and Uncertainty 2, 127-158.CrossRefGoogle Scholar
  8. Fishburn, P.C. and Wakker, P. (1995), The invention of the independence condition for preferences, Management Science 41, 1130-1144.CrossRefGoogle Scholar
  9. Herstein, I.N. and Milnor, J. (1953), An axiomatic approach to measurable utility, Econometrica 21, 291-297.CrossRefGoogle Scholar
  10. Hsee, C.J., Loewenstein, G.F., Blount, S. and Bazerman, M.H. (1999), Preference reversals between joint and separate evaluation of options: A review and theoretical analysis, Psychological Bulletin 125, 576-590.CrossRefGoogle Scholar
  11. Irwin, J.R., Slovic, P., Lichtenstein, S. and McClelland, G.H. (1993), Preference reversals and the measurement of environmental values, Journal of Risk and Uncertainty 6, 5-18.CrossRefGoogle Scholar
  12. Krantz, D., Luce, R.D., Suppes, P. and Tversky, A. (1971), Foundations of Measurement, Volume 1: Additive and Polynomial Representations. New York and London: Academic Press.Google Scholar
  13. Le Menestrel, M. (1998), A note on embedding von Neumann and Morgenstern utility theory in a qualitative context, INSEAD Working Papers, 52.Google Scholar
  14. Le Menestrel, M. (1999), A model of rational behavior combining processes and consequences. Unpublished Ph.D. Dissertation.Google Scholar
  15. Le Menestrel, M. (2001), A process approach to the utility for gambling, Theory and Decision 50, 249-262.CrossRefGoogle Scholar
  16. Luce, D.R. (1996), The ongoing dialog between empirical science and measurement theory, Journal of Risk and Uncertainty 5, 5-27.Google Scholar
  17. Luce, D.R. and Narens, L. (1987),Measurement scales on the continuum, Science 236, 1527-1532.Google Scholar
  18. Malinvaud, E. (1952),Note on von Neumann-Morgenstern's strong independence axiom, Econometrica 20, 679.CrossRefGoogle Scholar
  19. Marschak, J. (1950), Rational behavior, uncertain prospects, and measurable utility, Econometrica 18, 111-141.CrossRefGoogle Scholar
  20. Nash, J.F. (1950), The bargaining problem, Econometrica 18, 155-162.CrossRefGoogle Scholar
  21. Quine, W.V.O. (1975), On empirically equivalent systems of the world, Erkenntnis 9, 313-328.CrossRefGoogle Scholar
  22. Savage, L.J. (1954), The Foundations of Statistics, New York; 2nd edition revised and enlarged 1972, Dover.Google Scholar
  23. Sen, A. (1986), Information and invariance in normative choice. In Social Choice and Public Decision Making (pp. 29-55). Cambridge, UK: Cambridge University Press.Google Scholar
  24. Sen, A. (1997),Maximization and the act of choice, Econometrica 65, 745-779.CrossRefGoogle Scholar
  25. Shapley, L.S. (1953), A value for n-person games. In: H. Kuhn and A.W. Tucker, (eds.), Contributions to the Theory of Games, Vol. II (pp. 305-317). Princeton, NJ, Princeton University Press.Google Scholar
  26. Sounderpandian, J. (1992), Transforming continuous utility into additive utility using Kolmogorov's theorem, Journal of Multi-Criteria Decision Analysis 1, 93-99.Google Scholar
  27. Starmer, C. (1999), Experiments in economics: Should we trust the dismal scientists in white coats?, Journal of Economic Methodology 6, 1-30.Google Scholar
  28. Stigler, G. J. (1950), The development of utility theory: I, II, Journal of Political Economy 58, 307-327, 373-396.CrossRefGoogle Scholar
  29. von Neumann, J. and Morgenstern, O. (1944), Theory of Games and Economic Behavior. Princeton, NJ: Princeton University Press. Second edition 1947, Third edition 1953.Google Scholar
  30. von Neumann, J. (1951), The general and logical theory of automata. In: L.A. Jeffries (ed.), Cerebral Mechanisms in Behavior: The Hixon Symposium. New York: John Wiley and Sons.Google Scholar

Copyright information

© Kluwer Academic Publishers 2001

Authors and Affiliations

  1. 1.Departament d'Economia i EmpresaUniversitat Pompeu FabraBarcelonaSpain

Personalised recommendations