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The probability of conflicts in a U.S. presidential type election

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Author Info

  • Marc Feix
  • Dominique Lepelley

    ()

  • Vincent Merlin

    ()

  • Jean-Louis Rouet

    ()

Abstract

In a two candidate election, it might be that a candidate wins in a majority of districts while he gets less vote than his opponent in the whole country. In Social Choice Theory, this situation is known as the compound majority paradox, or the referendum paradox. Although occurrences of such paradoxical results have been observed worldwide in political elections (e.g. United States, United Kingdom, France), no study evaluates theoretically the likelihood of such situations. In this paper, we propose four probability models in order to tackle this issue, for the case where each district has the same population. For a divided electorate, our results prove that the likelihood of this paradox rapidly tends to 20% when the number of districts increases. This probability decreases with the number of states when a candidate receives significatively more vote than his opponent over the whole country. Copyright Springer-Verlag Berlin/Heidelberg 2004

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File URL: http://hdl.handle.net/10.1007/s00199-003-0375-2
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Bibliographic Info

Article provided by Springer in its journal Economic Theory.

Volume (Year): 23 (2004)
Issue (Month): 2 (January)
Pages: 227-257

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Handle: RePEc:spr:joecth:v:23:y:2004:i:2:p:227-257

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Web page: http://link.springer.de/link/service/journals/00199/index.htm

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Related research

Keywords: Voting; Paradox; US presidential election; Probability.;

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Citations

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Cited by:
  1. Nicholas Miller, 2014. "The Alternative Vote and Coombs Rule versus First-Past-the-Post: a social choice analysis of simulated data based on English elections, 1992–2010," Public Choice, Springer, vol. 158(3), pages 399-425, March.
  2. Abraham Diskin & Moshe Koppel, 2010. "Voting power: an information theory approach," Social Choice and Welfare, Springer, vol. 34(1), pages 105-119, January.
  3. Nicolas Houy, 2006. "La Constitution européenne est 50,13 %-stable. Une note comparative sur la stabilité des Constitutions," Revue économique, Presses de Sciences-Po, vol. 57(1), pages 123-134.
  4. Kurrild-Klitgaard, Peter, 2011. "Election inversions, coalitions and proportional representation: Examples from Danish elections," MPRA Paper 35302, University Library of Munich, Germany.
  5. Merlin, Vincent & Valognes, Fabrice, 2004. "The impact of indifferent voters on the likelihood of some voting paradoxes," Mathematical Social Sciences, Elsevier, vol. 48(3), pages 343-361, November.
  6. Lepelley, Dominique & Merlin, Vincent & Rouet, Jean-Louis, 2011. "Three ways to compute accurately the probability of the referendum paradox," Mathematical Social Sciences, Elsevier, vol. 62(1), pages 28-33, July.
  7. Sebastian Bervoets & Vincent Merlin, 2012. "Gerrymander-proof representative democracies," International Journal of Game Theory, Springer, vol. 41(3), pages 473-488, August.
  8. Nicholas Miller, 2012. "Why the Electoral College is good for political science (and public choice)," Public Choice, Springer, vol. 150(1), pages 1-25, January.
  9. Wilson, Mark C. & Pritchard, Geoffrey, 2007. "Probability calculations under the IAC hypothesis," Mathematical Social Sciences, Elsevier, vol. 54(3), pages 244-256, December.

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