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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.

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Paper provided by Stanford University, Department of Economics in its series Working Papers with number 99021.

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Date of creation: Sep 1999
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Handle: RePEc:wop:stanec:99021

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Keywords: social welfare functionals; weak welfarism;

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  1. MONGIN, Philippe & d'ASPREMONT, Claude, . "Utility theory and ethics," CORE Discussion Papers RP -1423, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  2. 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 249-68, June.
  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 327-56, June.
  4. 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, 02.
  5. Roberts, Kevin W S, 1980. "Interpersonal Comparability and Social Choice Theory," Review of Economic Studies, Wiley Blackwell, vol. 47(2), pages 421-39, January.
  6. Roberts, Kevin, 1983. "Social choice rules and real-valued representations," Journal of Economic Theory, Elsevier, vol. 29(1), pages 72-94, February.
  7. John A. Weymark & Kai-yuen Tsui, 1997. "Social welfare orderings for ratio-scale measurable utilities," Economic Theory, Springer, vol. 10(2), pages 241-256.
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Cited by:
  1. D'ASPREMONT, Claude & GEVERS, Louis, . "Social welfare functionals and interpersonal comparability," CORE Discussion Papers RP -1564, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  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, 02.
  3. Yukinori Iwata, 2014. "On the informational basis of social choice with the evaluation of opportunity sets," Social Choice and Welfare, Springer, vol. 43(1), pages 153-172, June.

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