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Measurement Theory and the Foundations of Utilitarianism

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  • John a. Weymark

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

Suggested Citation

  • John a. Weymark, 2004. "Measurement Theory and the Foundations of Utilitarianism," Econometric Society 2004 North American Summer Meetings 415, Econometric Society.
  • Handle: RePEc:ecm:nasm04:415
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    Cited by:

    1. Fleurbaey, Marc, 2009. "Two variants of Harsanyi's aggregation theorem," Economics Letters, Elsevier, vol. 105(3), pages 300-302, December.
    2. Gebhard Geiger, 2012. "Multi-attribute non-expected utility," Annals of Operations Research, Springer, vol. 196(1), pages 263-292, July.
    3. Thibault Gajdos & Feriel Kandil, 2008. "The ignorant observer," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 31(2), pages 193-232, August.
    4. Yaron Azrieli & Semin Kim, 2014. "Pareto Efficiency And Weighted Majority Rules," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 55, pages 1067-1088, November.
    5. ,, 2012. "The ex-ante aggregation of opinions under uncertainty," Theoretical Economics, Econometric Society, vol. 7(3), September.
    6. John A. Weymark, 2011. "On Kolm’s Use of Epistemic Counterfactuals in Social Choice Theory," Studies in Choice and Welfare, in: Marc Fleurbaey & Maurice Salles & John A. Weymark (ed.), Social Ethics and Normative Economics, pages 279-301, Springer.
    7. Courard-Hauri David & Lauer Stephen A., 2012. "Taking "All Men Are Created Equal" Seriously: Toward a Metric for the Intergroup Comparison of Utility Functions Through Life Values," Journal of Benefit-Cost Analysis, De Gruyter, vol. 3(3), pages 1-30, August.
    8. Yaron Azrieli & Semin Kim, 2014. "Pareto Efficiency And Weighted Majority Rules," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 55(4), pages 1067-1088, November.
    9. Gebhard Geiger, 2020. "Conditional non-expected utility preferences induced by mixture of lotteries: a note on the normative invalidity of expected utility theory," Annals of Operations Research, Springer, vol. 289(2), pages 431-448, June.
    10. Lu Li, 2021. "Opening up the black box: Technological transparency and prevention," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 88(3), pages 665-693, September.
    11. Aki Lehtinen, 2011. "A welfarist critique of social choice theory," Journal of Theoretical Politics, , vol. 23(3), pages 359-381, July.
    12. John A Weymark, 2012. "Social Welfare Functions," Vanderbilt University Department of Economics Working Papers vuecon-sub-13-00018, Vanderbilt University Department of Economics.

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    More about this item

    Keywords

    expected utility; utilitarianism; von Neumann-Morgenstern; Harsanyi;
    All these keywords.

    JEL classification:

    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement

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