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Preferences, Summation, and Social Welfare Functions


  • Peter C. Fishburn

    (Research Analysis Corporation, McLean, Virginia)


This paper gives a necessary and sufficient condition for the following proposition, in which \preceq and \preceq i for i - 1,..., n are weak orders on a finite set X. There are real-valued functions f 1 , f 2 ,..., f n on X such that, for all x and y in X and i in {1,...,n}x\preceq i y if and only if f i (x) i (y), and x \preceq y if and only if f l (x) + \cdots + f n (x) l (y) + \cdots + f n (y). The condition can be viewed as an extension of a simple unanimity or dominance condition.

Suggested Citation

  • Peter C. Fishburn, 1969. "Preferences, Summation, and Social Welfare Functions," Management Science, INFORMS, vol. 16(3), pages 179-186, November.
  • Handle: RePEc:inm:ormnsc:v:16:y:1969:i:3:p:179-186

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    References listed on IDEAS

    1. M. E. Salveson, 1956. "A Problem in Optimal Machine Loading," Management Science, INFORMS, vol. 2(3), pages 232-260, April.
    2. M. Beckman & R. Muth, 1956. "An Inventory Policy for a Case of Lagged Delivery," Management Science, INFORMS, vol. 2(2), pages 145-155, January.
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    Cited by:

    1. Donald E. Campbell & Jerry S. Kelly, 2006. "Social Welfare Functions that Satisfy Pareto, Anonymity, and Neutrality, but not IIA," Working Papers 38, Department of Economics, College of William and Mary.
    2. Martin Shubik, 1973. "Game Theory and Political Science," Cowles Foundation Discussion Papers 351, Cowles Foundation for Research in Economics, Yale University.
    3. Hayashida, Tomohiro & Nishizaki, Ichiro & Ueda, Yoshifumi, 2010. "Multiattribute utility analysis for policy selection and financing for the preservation of the forest," European Journal of Operational Research, Elsevier, vol. 200(3), pages 833-843, February.
    4. Tilman Börgers & Yan-Min Choo, 2017. "Revealed Relative Utilitarianism," CESifo Working Paper Series 6613, CESifo Group Munich.
    5. Meulendijks, P.J.F.G., 1987. "An exercise in welfare economics (II)," Research Memorandum FEW 285, Tilburg University, School of Economics and Management.
    6. Molinero, Xavier & Riquelme, Fabián & Serna, Maria, 2015. "Forms of representation for simple games: Sizes, conversions and equivalences," Mathematical Social Sciences, Elsevier, vol. 76(C), pages 87-102.

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