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Proportional Representation, Gini Coefficients, and the Principle of Transfers

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  • Tom Van Puyenbroeck

    (Faculty of Economics of the Hogeschool-Universiteit Brussel, tom.vanpuyenbroeck@hubrussel.be)

Abstract

While various authors have appealed to Dalton's Principle of Transfers, the Lorenz curve, and the Gini Coefficient to assess disproportionality in proportional representation systems, some additional clarifications are warranted with regard to these concepts and their proper application to the disproportionality issue. This article shows that the three concepts keep their full power and internal consistency if one considers the proportional representation problem as one of maximizing equality of seat/vote ratios among individual voters. Inconsistencies arise if parties are taken as the relevant unit of account. If one insists on comparing parties, then the appropriate concern is rather with their `deviation from proportionality'. To assess that concept, measures of seat mobility are better suited than genuine inequality measures.

Suggested Citation

  • Tom Van Puyenbroeck, 2008. "Proportional Representation, Gini Coefficients, and the Principle of Transfers," Journal of Theoretical Politics, , vol. 20(4), pages 498-526, October.
    • Handle: RePEc:sae:jothpo:v:20:y:2008:i:4:p:498-526
    DOI: 10.1177/0951629808093778
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    References listed on IDEAS

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    1. Moyes, Patrick, 1987. "A new concept of Lorenz domination," Economics Letters, Elsevier, vol. 23(2), pages 203-207.
    2. Ram Mudambi, 1997. "A complete information index for measuring the proportionality of electoral systems," Applied Economics Letters, Taylor & Francis Journals, vol. 4(2), pages 101-104.
    3. Luc Lauwers & Tom Puyenbroeck, 2006. "The Balinski–Young Comparison of Divisor Methods is Transitive," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 26(3), pages 603-606, June.
    4. Luc Lauwers & Tom Van Puyenbroeck, 2006. "The Hamilton Apportionment Method Is Between the Adams Method and the Jefferson Method," Mathematics of Operations Research, INFORMS, vol. 31(2), pages 390-397, May.
    5. Kakwani, Nanok C, 1977. "Measurement of Tax Progressivity: An International Comparison," Economic Journal, Royal Economic Society, vol. 87(345), pages 71-80, March.
    6. repec:bla:ecopol:v:14:y:2002:p:83-98 is not listed on IDEAS
    7. repec:bla:econom:v:64:y:1997:i:254:p:233-44 is not listed on IDEAS
    8. Theil, Henri, 1969. "The Desired Political Entropy," American Political Science Review, Cambridge University Press, vol. 63(2), pages 521-525, June.
    9. Fields, Gary S. & Ok, Efe A., 1996. "The Meaning and Measurement of Income Mobility," Journal of Economic Theory, Elsevier, vol. 71(2), pages 349-377, November.
    10. Paul H. Edelman, 2006. "Minimum Total Deviation Apportionments," Studies in Choice and Welfare, in: Bruno Simeone & Friedrich Pukelsheim (ed.), Mathematics and Democracy, pages 55-64, Springer.
    11. Tapan Mitra & Efe A. Ok, 1998. "The measurement of income mobility: A partial ordering approach," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 12(1), pages 77-102.
    12. Suits, Daniel B, 1977. "Measurement of Tax Progressivity," American Economic Review, American Economic Association, vol. 67(4), pages 747-752, September.
    13. Sen, Amartya, 1973. "On Economic Inequality," OUP Catalogue, Oxford University Press, number 9780198281931.
    14. Vani K. Borooah, 2002. "The Proportionality of Electoral Systems: Electoral Welfare and Electoral Inequality," Economics and Politics, Wiley Blackwell, vol. 14(1), pages 83-98.
    15. Berrebi, Z M & Silber, Jacques G, 1987. "Dispersion, Asymmetry and the Gini Index of Inequality," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 28(2), pages 331-338, June.
    16. Galeotti, Gianluigi, 1994. "On Proportional Non-representation," Public Choice, Springer, vol. 80(3-4), pages 359-370, September.
    17. Atkinson, Anthony B., 1970. "On the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 2(3), pages 244-263, September.
    18. Friedrich Pukelsheim & Albert W. Marshall & Ingram Olkin, 2002. "A majorization comparison of apportionment methods in proportional representation," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 19(4), pages 885-900.
    19. Udo Ebert, 1999. "Using equivalent income of equivalent adults to rank income distributions," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 16(2), pages 233-258.
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    Cited by:

    1. Miguel Martínez-Panero & Verónica Arredondo & Teresa Peña & Victoriano Ramírez, 2019. "A New Quota Approach to Electoral Disproportionality," Economies, MDPI, vol. 7(1), pages 1-17, March.

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