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Roberts' Weak Welfarism Theorem: A Minor Correction

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  • Peter J. Hammond

Abstract

September 1999 Roberts' "weak neutrality" or "weak welfarism" theorem concerns Sen social welfare functionals which are defined on an unrestricted domain of utility function profiles and satisfy independence of irrelevant alternatives, the Pareto condition, and a form of weak continuity. Roberts claimed that the induced welfare ordering on social states has a one-way representation by a continuous, monotonic real-valued function defined on the Euclidean space of interpersonal utility vectors. A counter-example shows that weak continuity is insufficient; a minor strengthening to pairwise continuity is proposed instead and its sufficiency demonstrated. Journal of Economic Literature classification: D71 Keywords: social welfare functionals, weak welfarism.

Suggested Citation

  • Peter J. Hammond, 1999. "Roberts' Weak Welfarism Theorem: A Minor Correction," Working Papers 99021, Stanford University, Department of Economics.
  • Handle: RePEc:wop:stanec:99021
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    File URL: http://www-econ.stanford.edu/faculty/workp/swp99021.pdf
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    References listed on IDEAS

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    1. Kevin W. S. Roberts, 1980. "Interpersonal Comparability and Social Choice Theory," Review of Economic Studies, Oxford University Press, vol. 47(2), pages 421-439.
    2. Georges Bordes & Peter J. Hammond & Michel Le Breton, 2005. "Social Welfare Functionals on Restricted Domains and in Economic Environments," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 7(1), pages 1-25, February.
    3. Blackorby, Charles & Donaldson, David & Weymark, John A, 1984. "Social Choice with Interpersonal Utility Comparisons: A Diagrammatic Introduction," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 25(2), pages 327-356, June.
    4. Mongin, P & d'Aspremont, C, 1996. "Utility Theory and Ethics," Papers 9632, Paris X - Nanterre, U.F.R. de Sc. Ec. Gest. Maths Infor..
    5. Blackorby, Charles & Donaldson, David, 1982. "Ratio-Scale and Translation-Scale Full Interpersonal Comparability without Domain Restrictions: Admissible Social-Evaluation Functions," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 23(2), pages 249-268, June.
    6. John A. Weymark & Kai-yuen Tsui, 1997. "Social welfare orderings for ratio-scale measurable utilities," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 10(2), pages 241-256.
    7. Roberts, Kevin, 1983. "Social choice rules and real-valued representations," Journal of Economic Theory, Elsevier, vol. 29(1), pages 72-94, February.
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    Cited by:

    1. d'Aspremont, Claude & Gevers, Louis, 2002. "Social welfare functionals and interpersonal comparability," Handbook of Social Choice and Welfare, in: K. J. Arrow & A. K. Sen & K. Suzumura (ed.),Handbook of Social Choice and Welfare, edition 1, volume 1, chapter 10, pages 459-541, Elsevier.
    2. Mongin, Philippe, 2019. "Interview of Peter J. Hammond," The Warwick Economics Research Paper Series (TWERPS) 1190, University of Warwick, Department of Economics.
    3. Georges Bordes & Peter J. Hammond & Michel Le Breton, 2005. "Social Welfare Functionals on Restricted Domains and in Economic Environments," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 7(1), pages 1-25, February.
    4. Yukinori Iwata, 2014. "On the informational basis of social choice with the evaluation of opportunity sets," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 43(1), pages 153-172, June.

    More about this item

    Keywords

    social welfare functionals; weak welfarism;

    JEL classification:

    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations

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