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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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    File URL: http://www.jstor.org/stable/41615475
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    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. Weber, Matthias, 2016. "Two-tier voting: Measuring inequality and specifying the inverse power problem," Mathematical Social Sciences, Elsevier, vol. 79(C), pages 40-45.
    5. 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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