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Social Aggregation Rules and Continuity

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  • Graciela Chichilnisky

Abstract

It is shown that any continuous social aggregation rule for smooth preferences cannot simultaneously satisfy the properties of anonymity and respect of unanimity. This is true even when all individual preferences are linear. The relationship between the conditions on the social rule studied here and those of Arrow's paradox is discussed. The first result requires that the normalized gradient of the social choice rule be definable in the interior of the choice space, thus indicating a direction of increase of social preference. A second impossibility result extends the first to cases where the gradient of the social preference may vanish in the interior of the choice space.

Suggested Citation

  • Graciela Chichilnisky, 1982. "Social Aggregation Rules and Continuity," The Quarterly Journal of Economics, Oxford University Press, vol. 97(2), pages 337-352.
  • Handle: RePEc:oup:qjecon:v:97:y:1982:i:2:p:337-352.
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    File URL: http://hdl.handle.net/10.2307/1880762
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    Cited by:

    1. Michele Lombardi & Kaname Miyagishima & Roberto Veneziani, 2016. "Liberal Egalitarianism and the Harm Principle," Economic Journal, Royal Economic Society, vol. 126(597), pages 2173-2196, November.
    2. Campbell, Donald E. & Kelly, Jerry S., 1996. "Continuous-valued social choice," Journal of Mathematical Economics, Elsevier, vol. 25(2), pages 195-211.
    3. Wu-Hsiung Huang, 2014. "Singularity and Arrow’s paradox," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 42(3), pages 671-706, March.
    4. Lauwers, Luc, 2000. "Topological social choice," Mathematical Social Sciences, Elsevier, vol. 40(1), pages 1-39, July.
    5. repec:ebl:ecbull:v:4:y:2004:i:6:p:1-6 is not listed on IDEAS
    6. Luc Lauwers, 2009. "The topological approach to the aggregation of preferences," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 33(3), pages 449-476, September.
    7. 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.
    8. Graciela Chichilnisky, 1985. "Von Neumann-Morgenstern Utilities and Cardinal Preferences," Mathematics of Operations Research, INFORMS, vol. 10(4), pages 633-641, November.
    9. Graciela Chichilnisky, 1996. "An axiomatic approach to sustainable development," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 13(2), pages 231-257, April.
    10. Nick Baigent & Daniel Eckert, 2004. "Abstract Aggregations and Proximity Preservation: An Impossibility Result," Theory and Decision, Springer, vol. 56(4), pages 359-366, June.
    11. Chichilnisky, Graciela, 1983. "Social choice and game theory: recent results with a topological approach," MPRA Paper 8059, University Library of Munich, Germany.
    12. Graciela Chichilnisky, 1996. "A robust theory of resource allocation," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 13(1), pages 1-10, January.
    13. Chichilnisky, Graciela, 1984. "Manipulations and repeated games in future markets," MPRA Paper 8083, University Library of Munich, Germany.
    14. Daniel Eckert, 2004. "Proximity Preservation in an Anonymous Framework," Economics Bulletin, AccessEcon, vol. 4(6), pages 1-6.
    15. Chichilnisky, Graciela, 2009. "Avoiding extinction: equal treatment of the present and the future," Economics - The Open-Access, Open-Assessment E-Journal, Kiel Institute for the World Economy (IfW), vol. 3, pages 1-25.
    16. Muto, Nozomu & Sato, Shin, 2016. "Bounded response of aggregated preferences," Journal of Mathematical Economics, Elsevier, vol. 65(C), pages 1-15.
    17. Shmuel Nitzan, 2010. "Demystifying the ‘metric approach to social compromise with the unanimity criterion’," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 35(1), pages 25-28, June.
    18. Munnich, Akos & Maksa, Gyula & J. Mokken, Robert, 1999. "Collective judgement: combining individual value judgements," Mathematical Social Sciences, Elsevier, vol. 37(3), pages 211-233, May.
    19. Wu-Hsiung Huang, 2009. "Is a continuous rational social aggregation impossible on continuum spaces?," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 32(4), pages 635-686, May.
    20. Ju, Biung-Ghi, 2004. "Continuous selections from the Pareto correspondence and non-manipulability in exchange economies," Journal of Mathematical Economics, Elsevier, vol. 40(5), pages 573-592, August.
    21. François-Régis Mahieu, 1991. "« Dictature » et expression des normes dans la théorie économique des choix collectifs," Revue Économique, Programme National Persée, vol. 42(3), pages 459-468.

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