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Social Choice with Infinite Populations: Construction of a Rule and Impossibility Results

Author

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  • Chichilnisky, G.
  • Heal, G.M.

Abstract

We provide a simple construction of social choice rules for economies with infinite populations. The rules are continuous, Pareto and non-dictatorial; they are constructed as limits of individual preferences when the limit exists, and otherwise as adequate generalizations. This contrasts with the impossibility results of Arrow (1951) and Chichilnisky (1980), which are valid on economies with finitely many individuals. Our social choice rules are, however, limits of dictatorial rules. This paper was written in 1979.
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Suggested Citation

  • Chichilnisky, G. & Heal, G.M., 1995. "Social Choice with Infinite Populations: Construction of a Rule and Impossibility Results," Papers 95-19, Columbia - Graduate School of Business.
    • Handle: RePEc:fth:colubu:95-19
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    Cited by:

    1. Marcus Pivato, 2021. "Intertemporal Choice with Continuity Constraints," Mathematics of Operations Research, INFORMS, vol. 46(3), pages 1203-1229, August.
    2. Lauwers, Luc, 2000. "Topological social choice," Mathematical Social Sciences, Elsevier, vol. 40(1), pages 1-39, July.
    3. Defrancesco, Edi & Gatto, Paola & Rosato, Paolo, 2014. "A ‘component-based’ approach to discounting for natural resource damage assessment," Ecological Economics, Elsevier, vol. 99(C), pages 1-9.
    4. Chichilnisky, Graciela & Heal, Geoffrey, 1983. "Necessary and sufficient conditions for a resolution of the social choice paradox," Journal of Economic Theory, Elsevier, vol. 31(1), pages 68-87, October.
    5. Pivato, Marcus & Vergopoulos, Vassili, 2017. "Subjective expected utility representations for Savage preferences on topological spaces," MPRA Paper 77359, University Library of Munich, Germany.
    6. Pivato, Marcus & Vergopoulos, Vassili, 2018. "Subjective expected utility with topological constraints," MPRA Paper 85749, University Library of Munich, Germany.
    7. Chichilnisky, Graciela, 2010. "The foundations of statistics with black swans," Mathematical Social Sciences, Elsevier, vol. 59(2), pages 184-192, March.
    8. Birol, Ekin & Koundouri, Phoebe & Kountouris, Yiannis, 2010. "Assessing the economic viability of alternative water resources in water-scarce regions: Combining economic valuation, cost-benefit analysis and discounting," Ecological Economics, Elsevier, vol. 69(4), pages 839-847, February.
    9. Chichilnisky, Graciela, 1983. "Social choice and game theory: recent results with a topological approach," MPRA Paper 8059, University Library of Munich, Germany.
    10. Phoebe Koundouri, 2008. "The Case for Declining Long-Term Discount Rates in the Evaluation of Flood-Defence Investments," DEOS Working Papers 0805, Athens University of Economics and Business.
    11. Groom, Ben & Hepburn, Cameron & Koundouri, Phoebe & Pearce, David, 2007. "Implications of declining discount rates: Climate Change Policy in the UK," MPRA Paper 38428, University Library of Munich, Germany.
    12. Chichilnisky, Graciela, 2009. "The topology of fear," Journal of Mathematical Economics, Elsevier, vol. 45(12), pages 807-816, December.
    13. Pivato, Marcus, 2008. "Sustainable preferences via nondiscounted, hyperreal intergenerational welfare functions," MPRA Paper 7461, University Library of Munich, Germany.

    More about this item

    Keywords

    POPULATION; POLITICS; VOTE; VOTING;
    All these keywords.

    JEL classification:

    • D70 - Microeconomics - - Analysis of Collective Decision-Making - - - General
    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
    • D72 - Microeconomics - - Analysis of Collective Decision-Making - - - Political Processes: Rent-seeking, Lobbying, Elections, Legislatures, and Voting Behavior

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