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Preferences, Summation, and Social Welfare Functions

Author

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  • Peter C. Fishburn

    (Research Analysis Corporation, McLean, Virginia)

Abstract

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
    DOI: 10.1287/mnsc.16.3.179
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    Citations

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    Cited by:

    1. Tilman Börgers & Yan-Min Choo, 2017. "Revealed Relative Utilitarianism," CESifo Working Paper Series 6613, CESifo.
    2. Meulendijks, P.J.F.G., 1987. "An exercise in welfare economics (II)," Other publications TiSEM 5702d824-5ea8-49ea-b6a9-1, Tilburg University, School of Economics and Management.
    3. Federico Echenique & Joseph Root & Fedor Sandomirskiy, 2022. "Efficiency in Random Resource Allocation and Social Choice," Papers 2203.06353, arXiv.org, revised Aug 2022.
    4. 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.
    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. Martin Shubik, 1973. "Game Theory and Political Science," Cowles Foundation Discussion Papers 351, Cowles Foundation for Research in Economics, Yale University.
    7. 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.
    8. 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.
    9. Josep Freixas & Xavier Molinero, 2009. "On the existence of a minimum integer representation for weighted voting systems," Annals of Operations Research, Springer, vol. 166(1), pages 243-260, February.

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