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Measurement theory and the foundations of utilitarianism

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  • John Weymark

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Abstract

Harsanyi used expected utility theory to provide two axiomatizations of weighted utilitarian rules. Sen (and later, Weymark) has argued that Harsanyi has not, in fact, axiomatized utilitarianism because he has misapplied expected utility theory. Specifically, Sen and Weymark have argued that von Neumann-Morgenstern expected utility theory is an ordinal theory and, therefore, any increasing transform of a von Neumann-Morgenstern utility function is a satisfactory representation of a preference relation over lotteries satisfying the expected utility axioms. However, Harsanyi's version of utilitarianism requires a cardinal theory of utility in which only von Neumann-Morgenstern utility functions are acceptable representations of preferences. Broome has argued that von Neumann-Morgenstern expected utility theory is cardinal in the relevant sense needed to support Harsanyi's utilitarian conclusions. His basic point is that a preference binary relation is not a complete description of preferences in the von Neumann-Morgenstern theory. Rather, the preference relation needs to be supplemented by a binary operation, and it is this operation that makes the theory cardinal. Broome does not provide a formal argument in support of this conclusion. In this article, measurement theory is used to critically evaluate Broome's claims. It is shown that the criticisms of Harsanyi's theory by Sen and Weymark can be extended to the more complete description of expected utility theory that is obtained by using the mixture operators that appear in von Neumann and Morgenstern's original description of expected utility theory in addition to a preference relation

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Article provided by Springer in its journal Social Choice and Welfare.

Volume (Year): 25 (2005)
Issue (Month): 2 (December)
Pages: 527-555

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Handle: RePEc:spr:sochwe:v:25:y:2005:i:2:p:527-555

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  1. John C. Harsanyi, 1955. "Cardinal Welfare, Individualistic Ethics, and Interpersonal Comparisons of Utility," Journal of Political Economy, University of Chicago Press, vol. 63, pages 309.
  2. MONGIN, Philippe & d ASPREMONT, Claude, 1996. "Utility theory and ethics," CORE Discussion Papers 1996063, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  3. Fishburn, Peter C, 1989. " Retrospective on the Utility Theory of von Neumann and Morgenstern," Journal of Risk and Uncertainty, Springer, vol. 2(2), pages 127-57, June.
  4. Milton Friedman & L. J. Savage, 1952. "The Expected-Utility Hypothesis and the Measurability of Utility," Journal of Political Economy, University of Chicago Press, vol. 60, pages 463.
  5. Mandler, Michael, 1999. "Dilemmas in Economic Theory: Persisting Foundational Problems in Microeconomics," OUP Catalogue, Oxford University Press, number 9780195100877, September.
  6. Milton Friedman & L. J. Savage, 1948. "The Utility Analysis of Choices Involving Risk," Journal of Political Economy, University of Chicago Press, vol. 56, pages 279.
  7. Blackorby, Charles & Donaldson, David & Weymark, John A., 1999. "Harsanyi's social aggregation theorem for state-contingent alternatives1," Journal of Mathematical Economics, Elsevier, vol. 32(3), pages 365-387, November.
  8. John C. Harsanyi, 1953. "Cardinal Utility in Welfare Economics and in the Theory of Risk-taking," Journal of Political Economy, University of Chicago Press, vol. 61, pages 434.
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Cited by:
  1. Nascimento, Leandro, 2012. "The ex-ante aggregation of opinions under uncertainty," Theoretical Economics, Econometric Society, vol. 7(3), September.
  2. Thibault Gajdos & Feriel Kandil, 2008. "The ignorant observer," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00177374, HAL.
  3. John A Weymark, . "Social Welfare Functions," Vanderbilt University Department of Economics Working Papers vuecon-sub-13-00018, Vanderbilt University Department of Economics.

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