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Social choice with infinite populations: construction of a rule and impossibility results

Author

Listed:
  • Graciela Chichilnisky

    (Department of Economics, Columbia University, 405 Law Memorial Library, New York, NY 10027, USA)

  • Geoffrey Heal

    (Program on Information and Resources, Columbia University, 405 Law Memorial Library, New York, NY 10027, USA)

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.

Suggested Citation

  • Graciela Chichilnisky & Geoffrey Heal, 1997. "Social choice with infinite populations: construction of a rule and impossibility results," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 14(2), pages 303-318.
    • Handle: RePEc:spr:sochwe:v:14:y:1997:i:2:p:303-318
    Note: Received: 30 October 1994/Accepted: 22 April 1996
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    Citations

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    Cited by:

    1. Chichilnisky, Graciela, 2010. "The foundations of statistics with black swans," Mathematical Social Sciences, Elsevier, vol. 59(2), pages 184-192, March.
    2. Marcus Pivato, 2021. "Intertemporal Choice with Continuity Constraints," Mathematics of Operations Research, INFORMS, vol. 46(3), pages 1203-1229, August.
    3. 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.
    4. Chichilnisky, Graciela, 1983. "Social choice and game theory: recent results with a topological approach," MPRA Paper 8059, University Library of Munich, Germany.
    5. 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.
    6. 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.
    7. Lauwers, Luc, 2000. "Topological social choice," Mathematical Social Sciences, Elsevier, vol. 40(1), pages 1-39, July.
    8. Chichilnisky, Graciela, 2009. "The topology of fear," Journal of Mathematical Economics, Elsevier, vol. 45(12), pages 807-816, December.
    9. 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.
    10. 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.
    11. Pivato, Marcus, 2008. "Sustainable preferences via nondiscounted, hyperreal intergenerational welfare functions," MPRA Paper 7461, University Library of Munich, Germany.
    12. Pivato, Marcus & Vergopoulos, Vassili, 2017. "Subjective expected utility representations for Savage preferences on topological spaces," MPRA Paper 77359, University Library of Munich, Germany.
    13. Pivato, Marcus & Vergopoulos, Vassili, 2018. "Subjective expected utility with topological constraints," MPRA Paper 85749, University Library of Munich, Germany.

    More about this item

    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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