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Utility Theory with Inexact Preferences and Degrees of Preference

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Part of the book series: The University of Western Ontario Series in Philosophy of Science ((WONS,volume 1))

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.

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Bibliography

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

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Google Scholar 

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

    Article  Google Scholar 

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

    Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Chipman, J. S., ‘Consumption Theory Without Transitive Indifference’, in Preferences, Utility, and Demand (ed. by J. S. Chipman, L. Hurwicz, M. K. Richter, and H. Sonnenschein), Harcourt Brace/Jovanovich, 1971.

    Google Scholar 

  • Debreu, G., ‘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, California, 1960.

    Google Scholar 

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

    Article  Google Scholar 

  • Fishburn, P. C., ‘Intransitive Indifference in Preference Theory: A Survey’, Operations Research 18 (1970a) 207–28.

    Article  Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

  • Frisch, R., ‘Sur une problème d’économie pure’, Norsk Mathematisk Forenings Skrifter, Seril 1, 16 (1926) 1–40.

    Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Hurwicz, L. and Richter, M. K., ‘Revealed Preference Without Demand Continuity Assumptions’, in Preferences, Utility, and Demand (ed. by J. S. Chipman, L. Hurwicz, M. K. Richter, and H. Sonnenschein), Harcourt/Brace/Jovanovich, 1971.

    Google Scholar 

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

    Article  Google Scholar 

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

    Google Scholar 

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

    Article  Google Scholar 

  • Lange, O., ‘Notes on the Determinateness of the Utility Function’, Review of Economic Studies 2 (1934b) 75–7.

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Google Scholar 

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

    Article  Google Scholar 

  • Pareto, V., Manuel d’Economie Politique, 2nd ed., Marcel Giard, Paris, 1927.

    Google Scholar 

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

    Article  Google Scholar 

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

    Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Samuelson, P. A, ‘A Note on the Pure Theory of Consumer’s Behaviour’, Economica, N.S. 5 (1938b) 61–71 and 353–4.

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Slutsky, E., ‘Sulla Teoria del Bilancio del Consomatore’, Giornale degli Economist 51 (1915) 1–26.

    Google Scholar 

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

    Article  Google Scholar 

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

    Google Scholar 

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

    Article  Google Scholar 

  • Suppes, P. and J. L. Zinnes, ‘Basic Measurement Theory’, in Handbook of Mathematical Psychology, Vol. 1 (ed. by R. D. Luce, R. R. Bush, and E. Galanter), John Wiley and Sons, New York, 1963.

    Google Scholar 

  • von Neumann, J. and Morgenstern, O., Theory of Games and Economic Behavior, 2nd ed., Princeton University Press, Princeton, New Jersey, 1947.

    Google Scholar 

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

    Article  Google Scholar 

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© 1972 D. Reidel Publishing Company, Dordrecht-Holland

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Fishburn, P.C. (1972). Utility Theory with Inexact Preferences and Degrees of Preference. In: Leach, J., Butts, R., Pearce, G. (eds) Science, Decision and Value. The University of Western Ontario Series in Philosophy of Science, vol 1. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-2571-3_11

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  • DOI: https://doi.org/10.1007/978-94-010-2571-3_11

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-277-0327-9

  • Online ISBN: 978-94-010-2571-3

  • eBook Packages: Springer Book Archive

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