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Roberts' Weak Welfarism Theorem : A Minor Correction

Author

Listed:
  • Hammond, Peter J.

    (Department of Economics, University of Warwick)

Abstract
Roberts' "weak neutrality" or "weak welfarism" theorem concerns Sen social welfare functionals which are de ned on an unrestricted domain of utility function profiles and satisfy independence of irrelevant alternatives, the Pareto condition, and a form of weak continuity. Roberts (1980) claimed that the induced welfare ordering on social states has a one-way representation by a continuous, monotonic real-valued welfare function defined on the Euclidean space of interpersonal utility vectors | that is, an increase in this welfare function is sufficient, but may not be necessary, for social strict preference. A counter-example shows that weak continuity is insufficient; a minor strengthening to pairwise continuity is proposed instead and its sufficiency demonstrated. JEL Codes: D71

Suggested Citation

  • Hammond, Peter J., 2020. "Roberts' Weak Welfarism Theorem : A Minor Correction," CRETA Online Discussion Paper Series 66, Centre for Research in Economic Theory and its Applications CRETA.
    • Handle: RePEc:wrk:wcreta:66
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    File URL: https://warwick.ac.uk/fac/soc/economics/research/centres/creta/papers/manage/creta66_-_peter_hammond.pdf
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    References listed on IDEAS

    as
    1. Kevin W. S. Roberts, 1980. "Interpersonal Comparability and Social Choice Theory," The Review of Economic Studies, Review of Economic Studies Ltd, 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. Ron Lavi & Ahuva Mu’alem & Noam Nisan, 2009. "Two simplified proofs for Roberts’ theorem," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 32(3), pages 407-423, March.
    4. Claude D'Aspremont & Louis Gevers, 1977. "Equity and the Informational Basis of Collective Choice," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 44(2), pages 199-209.
    5. 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.
    6. P. Mongin & C. d'Aspremont, 1996. "Utility theory and ethics," THEMA Working Papers 96-32, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
    7. Graciela Chichilnisky & Peter J. Hammond & Nicholas Stern, 2020. "Fundamental utilitarianism and intergenerational equity with extinction discounting," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 54(2), pages 397-427, March.
    8. 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.
    9. Sen, Amartya K, 1977. "On Weights and Measures: Informational Constraints in Social Welfare Analysis," Econometrica, Econometric Society, vol. 45(7), pages 1539-1572, October.
    10. 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.
    11. 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.

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    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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