The New Palgrave Dictionary of Economics

2018 Edition
| Editors: Macmillan Publishers Ltd

Representation of Preferences

  • Peter C. Fishburn
Reference work entry


Three facets of subjective preferences have played central roles in economics. They are the qualitative structure of an agent’s preferences, numerical representations of preferences, and the use of numerical representations or utility functions in economic analysis. We consider various representations and their ties to qualitative preference structures.

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  1. Allais, M. 1953. Le comportement de l’homme rationnel devant le risque: critique des postulats et axiomes de l’école Americaine. Econometrica 21: 503–546.CrossRefGoogle Scholar
  2. Bernoulli, D. 1738. Specimen theoriae novae de mensura sortis. Commentarii Academiae Scientarium Imperialis Petropolitanae 5: 175–192. Trans. Sommer, L. 1954. Econometrica 22: 23–36.Google Scholar
  3. Cantor, G. 1895. Beiträge zur Begründung der Transfinite Mengenlehre. Mathematische Annalen 46: 481–512. and 49 (1897), 207–246. English translation: Contributions to the founding of the theory of transfinite numbers. New York: Dover, n.d.CrossRefGoogle Scholar
  4. Chew, S.H. 1983. A generalization of the quasilinear mean with applications to the measurement of income inequality and decision theory resolving the Allais paradox. Econometrica 51: 1065–1092.CrossRefGoogle Scholar
  5. Chipman, J.S. 1960. The foundations of utility. Econometrica 28: 193–224.CrossRefGoogle Scholar
  6. Debreu, G. 1964. Continuity properties of Paretian utility. International Economic Review 5: 285–293.CrossRefGoogle Scholar
  7. Debreu, G., and T.C. Koopmans. 1982. Additively decomposed quasiconvex functions. Mathematical Programming 24: 1–38.CrossRefGoogle Scholar
  8. de Finetti, B. 1937. La prévision: ses logiques, ses sources subjectives. Annales de l’Institut Henri Poincaré 7: 1–68. Trans. Kyburg, H.E. 1964. Studies in subjective probability, ed. H.E. Kyburg and H.E. Smokler, 93–158. New York: Wiley.Google Scholar
  9. Dyer, J.S., and R.K. Sarin. 1979. Measurable multiattribute value functions. Operations Research 27: 810–822.CrossRefGoogle Scholar
  10. Ellsberg, D. 1961. Risk, ambiguity, and the savage axioms. Quarterly Journal of Economics 75: 643–669.CrossRefGoogle Scholar
  11. Farquhar, P.H. 1975. A fractional hypercube decomposition theorem for multiattribute utility functions. Operations Research 23: 941–967.CrossRefGoogle Scholar
  12. Farquhar, P.H. 1978. Interdependent criteria in utility analysis. In Multiple criteria problem solving, ed. S. Zionts, 131–180. Berlin: Springer.CrossRefGoogle Scholar
  13. Fishburn, P.C. 1970a. Utility theory for decision making. New York: Wiley.CrossRefGoogle Scholar
  14. Fishburn, P.C. 1970b. Intransitive indifference in preference theory: A survey. Operations Research 18: 207–228.CrossRefGoogle Scholar
  15. Fishburn, P.C. 1974. Lexicographic orders, utilities, and decision rules: A survey. Management Science 20: 1442–1471.CrossRefGoogle Scholar
  16. Fishburn, P.C. 1977. Multiattribute utilities in expected utility theory. In Conflicting objectives in decisions, ed. D.E. Bell, R.L. Keeney, and H. Raiffa, 172–194. New York: Wiley.Google Scholar
  17. Fishburn, P.C. 1980. Lexicographic additive differences. Journal of Mathematical Psychology 21: 191–218.CrossRefGoogle Scholar
  18. Fishburn, P.C. 1981. Subjective expected utility: A review of normative theories. Theory and Decision 13: 139–199.CrossRefGoogle Scholar
  19. Fishburn, P.C. 1982a. The foundations of expected utility. Dordrecht: Reidel.CrossRefGoogle Scholar
  20. Fishburn, P.C. 1982b. Nontransitive measurable utility. Journal of Mathematical Psychology 26: 31–67.CrossRefGoogle Scholar
  21. Fishburn, P.C. 1983. Transitive measurable utility. Journal of Economic Theory 31: 293–317.CrossRefGoogle Scholar
  22. Fishburn, P.C. 1984. SSB utility theory and decision-making under uncertainty. Mathematical Social Sciences 8: 253–285.CrossRefGoogle Scholar
  23. Fishburn, P.C. 1985. Interval orders and interval graphs. New York: Wiley.Google Scholar
  24. Fishburn, P.C., and P.H. Farquhar. 1982. Finite-degree utility independence. Mathematics of Operations Research 7: 348–353.CrossRefGoogle Scholar
  25. Fishburn, P.C., and A. Rubinstein. 1982. Time preference. International Economic Review 23: 677–694.CrossRefGoogle Scholar
  26. Houthakker, H.S. 1961. The present state of consumption theory. Econometrica 29: 704–740.CrossRefGoogle Scholar
  27. Kahneman, D., and A. Tversky. 1979. Prospect theory: An analysis of decision under risk. Econometrica 47: 263–291.CrossRefGoogle Scholar
  28. Keeney, R.L., and H. Raiffa. 1976. Decisions with multiple objectives: Preferences and value tradeoffs. New York: Wiley.Google Scholar
  29. Kirkwood, C.W., and R.K. Sarin. 1980. Preference conditions for multiattribute value functions. Operations Research 28: 225–232.CrossRefGoogle Scholar
  30. Koopmans, T.C. 1960. Stationary ordinal utility and impatience. Econometrica 28: 287–309.CrossRefGoogle Scholar
  31. Koopmans, T.C., P.A. Diamond, and R.E. Williamson. 1964. Stationary utility and time perspective. Econometrica 32: 82–100.CrossRefGoogle Scholar
  32. Krantz, D.H., R.D. Luce, P. Suppes, and A. Tversky. 1971. Foundations of measurement. Volume I: Additive and polynomial representations. New York: Academic.Google Scholar
  33. Loomes, G., and R. Sugden. 1982. Regret theory: An alternative theory of rational choice under uncertainty. Economic Journal 92: 805–824.CrossRefGoogle Scholar
  34. Luce, R.D. 1978. Lexicographic tradeoff structures. Theory and Decision 9: 187–193.CrossRefGoogle Scholar
  35. Machina, M.J. 1982. ‘Expected utility’ analysis without the independence axiom. Econometrica 50: 277–323.CrossRefGoogle Scholar
  36. Mas-Colell, A. 1974. An equilibrium existence theorem without complete or transitive preferences. Journal of Mathematical Economics 1: 237–246.CrossRefGoogle Scholar
  37. Samuelson, P.A. 1947. Foundations of economic analysis. Cambridge, MA: Harvard University Press.Google Scholar
  38. Savage, L.J. 1954. The foundations of statistics, 2nd rev. ed. New York: Wiley. Dover Publications, 1972.Google Scholar
  39. Schmeidler, D. 1984. Subjective probability and expected utility without additivity. Preprint no. 84, Institute for Mathematics and its Applications, University of Minnesota.Google Scholar
  40. Sondermann, D. 1980. Utility representations for partial orders. Journal of Economic Theory 23: 183–188.CrossRefGoogle Scholar
  41. Stigler, G.J. 1950. The development of utility theory I, II. Journal of Political Economy 58: 307–327; 373–396.CrossRefGoogle Scholar
  42. Tversky, A. 1969. Intransitivity of preferences. Psychological Review 76: 31–48.CrossRefGoogle Scholar
  43. von Neumann, J., and O. Morgenstern. 1944. Theory of games and economic behavior. Princeton: Princeton University Press; 2nd ed, 1947; 3rd ed, 1953.Google Scholar

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© Macmillan Publishers Ltd. 2018

Authors and Affiliations

  • Peter C. Fishburn
    • 1
  1. 1.