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Sen cycles and externalities

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  • Piggins, Ashley
  • Salerno, Gillian

Abstract

It has long been understood that externalities of some kind are responsible for Sen’s (1970) theorem on the impossibility of a Paretian liberal. However, Saari and Petron (2006) show that for any social preference cycle generated by combining the weak Pareto principle and individual decisiveness, every decisive individual must suffer at least one strong negative externality. We show that this fundamental result only holds when individual preferences are strict. Building on their contribution, we prove a general theorem for the case of weak preferences.

Suggested Citation

  • Piggins, Ashley & Salerno, Gillian, 2016. "Sen cycles and externalities," MPRA Paper 73676, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:73676
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    References listed on IDEAS

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    1. Donald Saari & Anne Petron, 2006. "Negative externalities and Sen’s liberalism theorem," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 28(2), pages 265-281, June.
    2. Gaertner, Wulf & Pattanaik, Prasanta K & Suzumura, Kotaro, 1992. "Individual Rights Revisited," Economica, London School of Economics and Political Science, vol. 59(234), pages 161-177, May.
    3. Julian H. Blau, 1975. "Liberal Values and Independence," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 42(3), pages 395-401.
    4. Saari,Donald G., 2001. "Decisions and Elections," Cambridge Books, Cambridge University Press, number 9780521808163.
    5. Saari,Donald G., 2008. "Disposing Dictators, Demystifying Voting Paradoxes," Cambridge Books, Cambridge University Press, number 9780521731607.
    6. Donald Saari, 2011. "Source of complexity in the social and managerial sciences: an extended Sen’s theorem," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 37(4), pages 609-620, October.
    7. Maurice Salles, 2008. "Limited Rights as Partial Veto and Sen’s Impossibility Theorem," Studies in Choice and Welfare, in: Prasanta K. Pattanaik & Koichi Tadenuma & Yongsheng Xu & Naoki Yoshihara (ed.), Rational Choice and Social Welfare, pages 11-23, Springer.
    8. Lingfang (Ivy) Li & Donald Saari, 2008. "Sen’s theorem: geometric proof, new interpretations," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 31(3), pages 393-413, October.
    9. Suzumura, Kotaro, 2011. "Chapter Twenty-Three - Welfarism, Individual Rights, and Procedural Fairness," 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 2, chapter 23, pages 605-685, Elsevier.
    10. Mathias Risse, 2001. "What to Make of the Liberal Paradox?," Theory and Decision, Springer, vol. 50(2), pages 169-196, March.
    11. Campbell, Donald E & Kelly, Jerry S, 1997. "Sen's Theorem and Externalities," Economica, London School of Economics and Political Science, vol. 64(255), pages 375-386, August.
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    13. Sugden, Robert, 1985. "Liberty, Preference, and Choice," Economics and Philosophy, Cambridge University Press, vol. 1(2), pages 213-229, October.
    14. K. J. Arrow & A. K. Sen & K. Suzumura (ed.), 2011. "Handbook of Social Choice and Welfare," Handbook of Social Choice and Welfare, Elsevier, edition 1, volume 2, number 2.
    15. Sen, Amartya Kumar, 1970. "The Impossibility of a Paretian Liberal," Scholarly Articles 3612779, Harvard University Department of Economics.
    16. Sen, Amartya, 1970. "The Impossibility of a Paretian Liberal," Journal of Political Economy, University of Chicago Press, vol. 78(1), pages 152-157, Jan.-Feb..
    17. Anne Pétron & Donald G. Saari, 2006. "Negative externalities and Sen's liberalism thorem," Post-Print halshs-00094539, HAL.
    18. Saari,Donald G., 2001. "Decisions and Elections," Cambridge Books, Cambridge University Press, number 9780521004046.
    19. Adrian Van Deemen & Agnieszka Rusinowska (ed.), 2010. "Collective Decision Making," Theory and Decision Library C, Springer, number 978-3-642-02865-6, March.
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    21. Peter Bernholz, 1982. "Externalities as a Necessary Condition for Cyclical Social Preferences," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 97(4), pages 699-705.
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    Cited by:

    1. Keith L. Dougherty & Julian Edward, 2022. "The effect of unconditional preferences on Sen’s paradox," Theory and Decision, Springer, vol. 93(3), pages 427-447, October.

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    More about this item

    Keywords

    Sen’s impossibility theorem; Liberal paradox; Saari-Petron theorem; Externalities; Social preference cycles;
    All these keywords.

    JEL classification:

    • D6 - Microeconomics - - Welfare Economics
    • D7 - Microeconomics - - Analysis of Collective Decision-Making

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