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

Author

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  • Fabrice Barthelemy

    (THEMA, Universite de Cergy-Pontoise)

  • Mathieu Martin

    (THEMA, Universite de Cergy-Pontoise)

Abstract

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.

Suggested Citation

  • Fabrice Barthelemy & Mathieu Martin, 2011. "A comparison between the methods of apportionment using power indices: the case of the U.S. presidential elections," THEMA Working Papers 2011-13, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
    • Handle: RePEc:ema:worpap:2011-13
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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, September.
    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," Revue d'économie régionale et urbaine, Armand Colin, vol. 0(2), pages 259-281.
    3. 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.
    4. 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.
    5. Philip Straffin, 1977. "Homogeneity, independence, and power indices," Public Choice, Springer, vol. 30(1), pages 107-118, June.
    6. Sven Berg, 1999. "On Voting Power Indices and a Class of Probability Distributions: With applications to EU data," Group Decision and Negotiation, Springer, vol. 8(1), pages 17-31, January.
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    8. Moshé Machover & Dan S. Felsenthal, 2001. "The Treaty of Nice and qualified majority voting," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 18(3), pages 431-464.
    9. Shapley, L. S. & Shubik, Martin, 1954. "A Method for Evaluating the Distribution of Power in a Committee System," American Political Science Review, Cambridge University Press, vol. 48(3), pages 787-792, September.
    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. 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. 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.
    3. Weber, Matthias, 2016. "Two-tier voting: Measuring inequality and specifying the inverse power problem," Mathematical Social Sciences, Elsevier, vol. 79(C), pages 40-45.
    4. Zineb Abidi & Matthieu Leprince & Vincent Merlin, 2020. "Power Inequality in Inter-communal Structures: The Simulated Impact of a Reform in the Case of the Municipalities in Western France," Post-Print halshs-02996998, HAL.
    5. Ibrahima Dia & Eric Kamwa, 2020. "The Voting Power in the Inter-communal Council of Martinique and Guadeloupe [Le Pouvoir de Vote dans les Etablissements Publics de Coopération Intercommunale de la Martinique et de la Guadeloupe]," Post-Print hal-01631190, HAL.

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    More about this item

    Keywords

    Banzhaf index; methods of apportionment; distances; balance population-power.;
    All these keywords.

    JEL classification:

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

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