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Compromises Between Cardinality and Ordinality in Preference Theory and Social Choice

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  • Michael Mandler

    (Royal Holloway College, University of London)

Abstract

By taking sets of utility functions as a primitive description of agents, we define an ordering over assumptions on utility functions that gauges their implicit measurement requirements. Cardinal and ordinal assumptions constitute two types of measurement requirements, but several standard assumptions in economics lie between these extremes. We first apply the ordering to different theories for why consumer preferences should be convex and show that diminishing marginal utility, which for complete preferences implies convexity, is an example of a compromise between cardinality and ordinality. In contrast, the Arrow-Koopmans theory of convexity, although proposed as an ordinal theory, relies on utility functions that lie in the cardinal measurement class. In a second application, we show that diminishing marginal utility, rather than the standard stronger assumption of cardinality, also justifies utilitarian recommendations on redistribution and axiomatizes the Pigou-Dalton principle. We also show that transitivity and order-density (but not completeness) characterize the ordinal preferences that can be induced from sets of utility functions, present a general cardinality theorem for additively separable preferences, and provide sufficient conditions for orderings of assumptions on utility functions to be acyclic and transitive.

Suggested Citation

  • Michael Mandler, 2001. "Compromises Between Cardinality and Ordinality in Preference Theory and Social Choice," Cowles Foundation Discussion Papers 1322, Cowles Foundation for Research in Economics, Yale University.
  • Handle: RePEc:cwl:cwldpp:1322
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    File URL: http://cowles.yale.edu/sites/default/files/files/pub/d13/d1322.pdf
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    References listed on IDEAS

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    1. Kevin W. S. Roberts, 1980. "Interpersonal Comparability and Social Choice Theory," Review of Economic Studies, Oxford University Press, vol. 47(2), pages 421-439.
    2. Sen, Amartya, 1970. "Interpersonal Aggregation and Partial Comparability," Econometrica, Econometric Society, vol. 38(3), pages 393-409, May.
    3. Dubra, Juan & Maccheroni, Fabio & Ok, Efe A., 2004. "Expected utility theory without the completeness axiom," Journal of Economic Theory, Elsevier, vol. 115(1), pages 118-133, March.
    4. G. Hanoch & H. Levy, 1969. "The Efficiency Analysis of Choices Involving Risk," Review of Economic Studies, Oxford University Press, vol. 36(3), pages 335-346.
    5. Hammond, Peter J, 1976. "Equity, Arrow's Conditions, and Rawls' Difference Principle," Econometrica, Econometric Society, vol. 44(4), pages 793-804, July.
    6. Kevin W. S. Roberts, 1980. "Possibility Theorems with Interpersonally Comparable Welfare Levels," Review of Economic Studies, Oxford University Press, vol. 47(2), pages 409-420.
    7. Debreu, Gerard, 1976. "Least concave utility functions," Journal of Mathematical Economics, Elsevier, vol. 3(2), pages 121-129, July.
    8. Kaushik Basu, 1982. "Determinateness of the Utility Function: Revisiting a Controversy of the Thirties," Review of Economic Studies, Oxford University Press, vol. 49(2), pages 307-311.
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    More about this item

    Keywords

    Cardinal utility; ordinal utility; measurement theory; utilitarianism;

    JEL classification:

    • D11 - Microeconomics - - Household Behavior - - - Consumer Economics: Theory
    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement

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