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The paradox of multiple elections

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Author Info

  • Steven J. Brams

    (Department of Politics, New York University, New York, NY 10003, USA)

  • William S. Zwicker

    (Department of Mathematics, Union College, Schenectady, NY 12308, USA)

  • D. Marc Kilgour

    (Department of Mathematics, Wilfrid Laurier University Waterloo, Ontario, Canada N2L 3C5)

Abstract

Assume that voters must choose between voting yes (Y) and voting no (N) on three propositions on a referendum. If the winning combination is NYY on the first, second, and third propositions, respectively, the paradox of multiple elections is that NYY can receive the fewest votes of the 23 = 8 combinations. Several variants of this paradox are illustrated, and necessary and sufficient conditions for its occurrence, related to the "incoherence" of support, are given. The paradox is shown, via an isomorphism, to be a generalization of the well-known paradox of voting. One real-life example of the paradox involving voting on propositions in California, in which not a single voter voted on the winning side of all the propositions, is given. Several empirical examples of variants of the paradox that manifested themselves in federal elections - one of which led to divided government - and legislative votes in the US House of Representatives, are also analyzed. Possible normative implications of the paradox, such as allowing voters to vote directly for combinations using approval voting or the Borda count, are discussed.

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Bibliographic Info

Article provided by Springer in its journal Social Choice and Welfare.

Volume (Year): 15 (1998)
Issue (Month): 2 ()
Pages: 211-236

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Handle: RePEc:spr:sochwe:v:15:y:1998:i:2:p:211-236

Note: Received: 31 July 1996 / Accepted: 1 October 1996
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Cited by:
  1. Bradley, W. James & Hodge, Jonathan K. & Kilgour, D. Marc, 2005. "Separable discrete preferences," Mathematical Social Sciences, Elsevier, vol. 49(3), pages 335-353, May.
  2. Tangian, Andranik S., 2010. "Representativeness of German parties and trade unions with regard to public opinion," WSI Discussion Papers 173, Wirtschafts- und Sozialwissenschaftliches Institut (WSI), Hans-Böckler-Stiftung.
  3. Tangian, Andranik S., 2006. "German parliamentary elections 2005 in the mirror of party manifestos," WSI Discussion Papers 139E, Wirtschafts- und Sozialwissenschaftliches Institut (WSI), Hans-Böckler-Stiftung.
  4. Tangian, Andranik S., 2013. "Decision making in politics and economics: 5. 2013 election to German Bundestag and direct democracy," Working Paper Series in Economics 49, Karlsruhe Institute of Technology (KIT), Department of Economics and Business Engineering.
  5. Laffond, G. & Laine, J., 2006. "Single-switch preferences and the Ostrogorski paradox," Mathematical Social Sciences, Elsevier, vol. 52(1), pages 49-66, July.
  6. Alessandra Casella & Andrew Gelman, 2005. "A Simple Scheme to Improve the Efficiency of Referenda," NBER Working Papers 11375, National Bureau of Economic Research, Inc.
  7. Hannu Nurmi, 2007. "Assessing Borda's Rule and Its Modifications," Discussion Papers 15, Aboa Centre for Economics.
  8. Tuğçe Çuhadaroğlu & Jean Lainé, 2012. "Pareto efficiency in multiple referendum," Theory and Decision, Springer, vol. 72(4), pages 525-536, April.
  9. Kurrild-Klitgaard, Peter, 2011. "Election inversions, coalitions and proportional representation: Examples from Danish elections," MPRA Paper 35302, University Library of Munich, Germany.
  10. Benoît, Jean-Pierre & Kornhauser, Lewis A., 2010. "Only a dictatorship is efficient," Games and Economic Behavior, Elsevier, vol. 70(2), pages 261-270, November.
  11. Conitzer, Vincent & Lang, Jérôme & Xia, Lirong, 2009. "How hard is it to Control Sequential Elections via the Agenda?," Economics Papers from University Paris Dauphine 123456789/3899, Paris Dauphine University.
  12. Lang, Jrme & Xia, Lirong, 2009. "Sequential composition of voting rules in multi-issue domains," Mathematical Social Sciences, Elsevier, vol. 57(3), pages 304-324, May.
  13. Tangian, Andranik S., 2013. "2013 election to German Bundestag from the viewpoint of direct democracy," WSI Discussion Papers 186, Wirtschafts- und Sozialwissenschaftliches Institut (WSI), Hans-Böckler-Stiftung.
  14. Jonathan Hodge & Peter Schwallier, 2006. "How Does Separability Affect The Desirability Of Referendum Election Outcomes?," Theory and Decision, Springer, vol. 61(3), pages 251-276, November.
  15. Nehring, Klaus & Puppe, Clemens, 2007. "Efficient and strategy-proof voting rules: A characterization," Games and Economic Behavior, Elsevier, vol. 59(1), pages 132-153, April.
  16. İpek Özkal-Sanver & M. Sanver, 2006. "Ensuring Pareto Optimality by Referendum Voting," Social Choice and Welfare, Springer, vol. 27(1), pages 211-219, August.
  17. Andranik Tangian, 2013. "German parliamentary elections 2009 from the viewpoint of direct democracy," Social Choice and Welfare, Springer, vol. 40(3), pages 833-869, March.
  18. Steven Brams & D. Kilgour & M. Sanver, 2007. "A minimax procedure for electing committees," Public Choice, Springer, vol. 132(3), pages 401-420, September.
  19. Gilbert Laffond & Jean Lainé, 2008. "The Budget-Voting Paradox," Theory and Decision, Springer, vol. 64(4), pages 447-478, June.
  20. Gilbert Laffond & Jean Lainé, 2009. "Condorcet choice and the Ostrogorski paradox," Social Choice and Welfare, Springer, vol. 32(2), pages 317-333, February.
  21. Andranik Tangian, 2008. "A mathematical model of Athenian democracy," Social Choice and Welfare, Springer, vol. 31(4), pages 537-572, December.

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