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A Comparison Between the Methods of Apportionment Using Power Indices: the Case of the US Presidential Elections

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  • Fabrice Barthelemy
  • Mathieu Martin

Abstract

In this paper we compare five well-known methods of apportionment, advanced respectively by Adams, Dean, Hill, Webster and Jefferson. The criterion used for this comparison is the minimization of the distance between a power vector and a population vector. Power is measured with the well-known Banzhaf power index; the populations are those of the constituent states of the U.S.A. We first explain the conditions under which this comparison has plausibility. We then compare apportionment methods in terms of their capacity to move power in states closer to their populations. The election of the U.S. President by an electoral college is studied by examining 22 censuses since 1790. Our analysis is largely based on that used in the book by Balinski and Young [2001]. The empirical findings are linked to theoretical results.

Suggested Citation

  • Fabrice Barthelemy & Mathieu Martin, 2011. "A Comparison Between the Methods of Apportionment Using Power Indices: the Case of the US Presidential Elections," Annals of Economics and Statistics, GENES, issue 101-102, pages 87-106.
  • Handle: RePEc:adr:anecst:y:2011:i:101-102:p:87-106
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    References listed on IDEAS

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    1. Laruelle,Annick & Valenciano,Federico, 2011. "Voting and Collective Decision-Making," Cambridge Books, Cambridge University Press, number 9780521182638, October.
    2. 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.
    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. 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.
    5. Marc Feix & Dominique Lepelley & Vincent Merlin & Jean-Louis Rouet, 2007. "On the voting power of an alliance and the subsequent power of its members," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 28(2), pages 181-207, February.
    6. 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.
    7. Philip Straffin, 1977. "Homogeneity, independence, and power indices," Public Choice, Springer, vol. 30(1), pages 107-118, June.
    8. 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.
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    Cited by:

    1. Vincent Merlin & Marc Fleurbaey & Dominique Lepelley, 2012. "Introduction to the special issue on new developments in social choice and welfare theories," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 39(2), pages 253-257, July.
    2. Weber, Matthias, 2016. "Two-tier voting: Measuring inequality and specifying the inverse power problem," Mathematical Social Sciences, Elsevier, vol. 79(C), pages 40-45.
    3. 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.

    More about this item

    JEL classification:

    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • D7 - Microeconomics - - Analysis of Collective Decision-Making

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