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

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  • Fabrice Barthélémy

    ()
    (THEMA, Université de Cergy-Pontoise)

  • Mathieu MARTIN

    ()
    (THEMA, Université de Cergy-Pontoise)

Abstract

In this paper, we compare the five more famous methods of apportionment, the methods of 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. The populations are the ones of the different States of the U.S. We then compare the apportionment methods in terms of their ability to bring closer the power of the States to their relative population: this ensures that every citizen in the country gets the same power. 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 2007-26.

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Date of creation: 2007
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Handle: RePEc:ema:worpap:2007-26

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Keywords: Banzhaf index; methods of apportionment; distances; balance population-power.;

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  1. 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.
  2. 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.
  3. 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," Revue d'économie régionale et urbaine, Armand Colin, vol. 0(2), pages 259-281.
  4. 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.
  5. Laruelle,Annick & Valenciano,Federico, 2011. "Voting and Collective Decision-Making," Cambridge Books, Cambridge University Press, number 9780521182638, April.
  6. 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.
  7. 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.
  8. 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.
  9. 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.
  10. 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.
  11. Philip Straffin, 1977. "Homogeneity, independence, and power indices," Public Choice, Springer, vol. 30(1), pages 107-118, June.
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Cited by:
  1. Kóczy, László Á., 2012. "Beyond Lisbon: Demographic trends and voting power in the European Union Council of Ministers," Mathematical Social Sciences, Elsevier, vol. 63(2), pages 152-158.
  2. Marc FLEURBAEY & Dominique LEPELLEY & Vincent MERLIN, 2011. "Introduction to the Special Issue on New Developments in Social Choice and Welfare Theories," Annales d'Economie et de Statistique, ENSAE, issue 101-102, pages 7-12.

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