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A comparison between the methods of apportionment using power indices: the case of the U.S. presidential elections

  • Fabrice Barthelemy
  • Mathieu Martin

    ()

    (THEMA, Universite de Cergy-Pontoise
    THEMA, Universite de Cergy-Pontoise)

In this paper, we compare five well-known methods of apportionment, the ones by Adams, Dean, Hill, Webster and Jefferson. The criteria used for this comparison is the minimization of a distance between a power vector and a population vector. The power is measured with the well-known Banzhaf power index and the populations are the ones of the different States of the U.S. We first explain under which conditions this comparison makes sense. We then compare the apportionment methods in terms of their ability to bring closer the power of the States to their relative population. The U.S. presidential election by Electors is studied through 22 censuses since 1790. Our analysis is largely based on the book written by Balinski and Young (2001). The empirical findings are linked with theoretical results.

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Paper provided by THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise in its series THEMA Working Papers with number 2011-13.

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Date of creation: 2011
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Handle: RePEc:ema:worpap:2011-13
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  1. Vincent Merlin & Marc Feix & Dominique Lepelley & Jean-Louis Rouet, 2007. "On the Voting Power of an Alliance and the Subsequent Power of its Members," Post-Print halshs-00010168, HAL.
  2. Franck Bisson & Jean Bonnet & Dominique Lepelley, 2004. "La détermination du nombre des délégués au sein des structures intercommunales : une application de l'indice de pouvoir de Banzhaf," Post-Print hal-00149378, HAL.
  3. Philip Straffin, 1977. "Homogeneity, independence, and power indices," Public Choice, Springer, vol. 30(1), pages 107-118, June.
  4. Gelman, Andrew & Katz, Jonathan N. & Tuerlinckx, Francis, 2002. "The Mathematics and Statistics of Voting Power," Working Papers 1141, California Institute of Technology, Division of the Humanities and Social Sciences.
  5. Straffin, Philip Jr., 1994. "Power and stability in politics," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 2, chapter 32, pages 1127-1151 Elsevier.
  6. Laruelle,Annick & Valenciano,Federico, 2008. "Voting and Collective Decision-Making," Cambridge Books, Cambridge University Press, number 9780521873871.
  7. Leech, Dennis, 2002. " Designing the Voting System for the Council of the European Union," Public Choice, Springer, vol. 113(3-4), pages 437-64, December.
  8. Fabrice Barthélémy & Mathieu Martin, 2007. "Critères pour une meilleure répartition des sièges au sein des structures intercommunales. Une application au cas du Val-d'Oise," Revue économique, Presses de Sciences-Po, vol. 58(2), pages 399-425.
  9. Fabrice Barthélémy & Mathieu MARTIN & Vincent MERLIN, 2007. "On the performance of the Shapley Shubik and Banzhaf power indices for the allocations of mandates," THEMA Working Papers 2007-25, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
  10. Gelman, Andrew & Katz, Jonathan N. & Bafumi, Joseph, 2002. "Standard Voting Power Indexes Don't Work: An Empirical Analysis," Working Papers 1133, California Institute of Technology, Division of the Humanities and Social Sciences.
  11. Moshé Machover & Dan S. Felsenthal, 2001. "The Treaty of Nice and qualified majority voting," Social Choice and Welfare, Springer, vol. 18(3), pages 431-464.
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