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Measurement theory and the foundations of utilitarianism

  • John Weymark


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. MONGIN, Philippe & d'ASPREMONT, Claude, . "Utility theory and ethics," CORE Discussion Papers RP 1423, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  2. Mandler, Michael, 2001. "Dilemmas in Economic Theory: Persisting Foundational Problems of Microeconomics," OUP Catalogue, Oxford University Press, number 9780195145755, May.
  3. 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.
  4. 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.
  5. 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.
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