Skip to main content
Log in

Utility theory with inexact preferences and degrees of preference

  • Published:
Synthese Aims and scope Submit manuscript

Abstract

a−b≺* c−d is taken to mean that ‘your’ degree of preference for a over b is less than ‘your’ degree of preference for c over d. Various properties of the strength-of-preference comparison relation ≺* are examined along with properties of simple preferences defined from ≺*. The investigation recognizes an individual's limited ability to make ‘precise’ judgments. Several utility theorems relating a−b ≺* c−d to u(a)−u(b)<u(c)−u(d) are included.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Bibliography

  • Adams, E. W.: 1965, ‘Elements of a Theory of Inexact Measurement’, Philosophy of Science 32 205–28.

    Google Scholar 

  • Allen, R. G. D.: 1934–35, ‘A Note on the Determinateness of the Utility Function’, Review of Economic Studies 2 155–8.

    Google Scholar 

  • Alt, F.: 1936, ‘Über die Messbarkeit des Nutzens’, Zeitschrift für Nationalökonomie 7 161–9.

    Google Scholar 

  • Armstrong, W. E.: 1939, ‘The Determinateness of the Utility Function’, Economic Journal 49 453–67.

    Google Scholar 

  • Armstrong, W. E.: 1948, ‘Uncertainty and the Utility Function’, Economic Journal 58 1–10.

    Google Scholar 

  • Armstrong, W. E.: 1950, ‘A Note on the Theory of Consumer's Behaviour’, Oxford Economic Papers, N.S. 2 119–22.

    Google Scholar 

  • Arrow, K. J.: 1959, ‘Rational Choice Functions and Orderings’, Economica, N.S. 26 121–7.

    Google Scholar 

  • Arrow, K. J.: 1963, Social Choice and Individual Values, 2nd ed., John Wiley and Sons, New York.

    Google Scholar 

  • Baumol, W. J.: 1958, ‘The Cardinal Utility Which is Ordinal’, Economic Journal 68 665–72.

    Google Scholar 

  • Bernardelli, H.: 1934, ‘Notes on the Determinateness of the Utility Function’, Review of Economic Studies 2 69–75.

    Google Scholar 

  • Brown, E. H. P.: 1934, ‘Notes on the Determinateness of the Utility Function’, Review of Economic Studies 2 66–9.

    Google Scholar 

  • Chipman, J. S.: 1960, ‘The Foundations of Utility’, Econometrica 28 193–224.

    Google Scholar 

  • Chipman, J. S.: 1970, ‘Consumption Theory without Transitive Indifference’, in Studies in the Mathematical Foundations of Utility and Demand Theory (ed. by J.S. Chipman, L. Hurwicz, M. K. Richter, and H. Sonnenschein), Harcourt, Brace and World, New York.

    Google Scholar 

  • Debreu, G.: 1960, ‘Topological Methods in Cardinal Utility Theory’, in Mathematical Methods in The Social Sciences, 1959 (ed. by K. J. Arrow, S. Karlin, and P. Suppes), Stanford University Press, Stanford, Calif.

    Google Scholar 

  • Ellsberg, D.: 1954, ‘Classic and Current Notions of “Measurable Utility”’, Economic Journal 64 528–56.

    Google Scholar 

  • Fishburn, P. C.: 1970a, ‘Intransitive Indifference in Preference Theory: A Survey’, Operations Research 18.

  • Fishburn, P. C.: 1970b, Utility Theory for Decision Making, John Wiley and Sons, New York.

    Google Scholar 

  • Fisher, I.: 1925, Mathematical Investigations in the Theory of Value and Prices, Yale University Press, New Haven, Conn. (Reprint of 1892 edition.)

    Google Scholar 

  • Frisch, R.: 1926, ‘Sur un problème d'économie pure’, Norsk Mathematisk Forenings Skrifter, Serie 1, 16, 1–40.

    Google Scholar 

  • Frisch, R.: 1959, ‘A Complete Scheme for Computing All Direct and Cross Demand Elasticities in a Model with Many Sectors’, Econometrica 27, 177–96.

    Google Scholar 

  • Frisch, R.: 1964, ‘Dynamic Utility’, Econometrica 32, 418–24.

    Google Scholar 

  • Hansson, B.: 1968, ‘Choice Structures and Preference Relations’, Synthese 18, 443–58.

    Google Scholar 

  • Hicks, J. R. and Allen, R. G. D.: 1934, ‘A Reconsideration of the Theory of Value’, Economica, N. S. 1, 52–76 and 196–219.

    Google Scholar 

  • Houthakker, H. S.: 1961, ‘The Present State of Consumption Theory’, Econometrica 29, 704–40.

    Google Scholar 

  • Hurwicz, L. and Richter, M. K.: 1970, ‘Revealed Preference without Demand Continuity Assumptions’, in Studies in the Mathematical Foundations of Utility and Demand Theory (ed. by J. S. Chipman, L. Hurwicz, M. K. Richter, and H. Sonnenschein), Harcourt, Brace and World, New York.

    Google Scholar 

  • Krantz, D. H.: 1964, ‘Conjoint Measurement: The Luce-Tukey Axiomatization and Some Extensions’, Journal of Mathematical Psychology 1, 248–77.

    Google Scholar 

  • Krantz, D. H.: 1967, ‘A Survey of Measurement Theory’, Michigan Mathematical Psychology Program MMPP 67-4, University of Michigan, Ann Arbor, Mich.

    Google Scholar 

  • Lange, O.: 1934a, ‘The Determinateness of the Utility Function’, Review of Economic Studies 1, 218–25.

    Google Scholar 

  • Lange, O.: 1934b, ‘Notes on the Determinateness of the Utility Function’, Review of Economic Studies 2, 75–77.

    Google Scholar 

  • Luce, R. D.: 1956, ‘Semiorders and a Theory of Utility Discrimination’, Econometrica 24, 178–91.

    Google Scholar 

  • Luce, R. D.: 1966, ‘Two Extensions of Conjoint Measurement’, Journal of Mathematical Psychology 3, 348–70.

    Google Scholar 

  • Luce, R. D.: 1968, ‘On the Numerical Representation of Qualitative Conditional Probability’, Annals of Mathematical Statistics 39, 481–91.

    Google Scholar 

  • Luce, R. D. and Raiffa, H.: 1957, Games and Decisions, John Wiley and Sons, New York.

    Google Scholar 

  • Luce, R. D. and Tukey, J. W.: 1964, ‘Simultaneous Conjoint Measurement: A New Type of Fundamental Measurement’, Journal of Matheamtical Psychology 1, 1–27.

    Google Scholar 

  • Pareto, V.: 1927, Manuel d'Économie Politique, 2nd ed., Marcel Giard, Paris.

    Google Scholar 

  • Pfanzagl, J.: 1959, ‘A General Theory of Measurement: Applications to Utility’, Naval Research Logistics Quarterly 6, 283–94.

    Google Scholar 

  • Pfanzagl, J. (in cooperation with V. Baumann and H. Huber): 1968, Theory of Measurement, John Wiley and Sons, New York.

    Google Scholar 

  • Richter, M. K.: 1966, ‘Revealed Preference Theory’, Econometrica 34, 635–45.

    Google Scholar 

  • Samuelson, P. A.: 1938a, ‘The Numerical Representation of Ordered Classifications and the Concept of Utility’, Review of Economic Studies 6, 65–70.

    Google Scholar 

  • Samuelson, P. A.: 1938b, ‘A Note on the Pure Theory of Consumer's Behaviour’, Economica, N.S. 5, 61–71 and 353–54.

    Google Scholar 

  • Scott, D.: 1964, ‘Measurement Structures and Linear Inequalities’, Journal of Mathematical Psychology 1, 233–47.

    Google Scholar 

  • Scott, D. and Suppes, P.: 1958, ‘Foundational Aspects of Theories of Measurement’, Journal of Symbolic Logic 23, 113–28.

    Google Scholar 

  • Slutsky, E.: 1915, ‘Sulla Theoria del Bilancio del Consomatore’, Giornale degli Economist 51, 1–26.

    Google Scholar 

  • Stigler, G. J.: 1950, ‘The Development of Utility Theory’, Journal of Political Economy 58, 307–27 and 373–96.

    Google Scholar 

  • Strotz, R. H.: 1953, ‘Cardinal Utility’, American Economic Review 43, 384–97.

    Google Scholar 

  • Suppes, P. and Winet, M.: 1955, ‘An Axiomatization of Utility Based on the Notion of Utility Differences’, Management Science 1, 259–70.

    Google Scholar 

  • Suppes, P. and Zinnes, J. L.: 1963, ‘Basic Measurement Theory’, in Handbook of Mathematical Psychology, Vol. I (ed. by R. D. Luce, R. R. Bush, and E. Galanter), John Wiley and Sons, New York.

    Google Scholar 

  • Von Neumann, J. and Morgenstern, O.: 1947, Theory of Games and Economic Behavior, 2nd ed., Princeton University Press, Princeton, N.J.

    Google Scholar 

  • Weldon, J. C.: 1950, ‘A Note on Measures of Utility’, Canadian Journal of Economics and Political Science 16, 227–33.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Fishburn, P.C. Utility theory with inexact preferences and degrees of preference. Synthese 21, 204–221 (1970). https://doi.org/10.1007/BF00413546

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00413546

Keywords

Navigation