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A characterization of two disproportionality and malapportionment indices: the Duncan and Duncan index and the Lijphart index

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  • D. Bouyssou

    (Université Paris-Dauphine, PSL Research University)

  • T. Marchant

    (Ghent University)

  • M. Pirlot

    (Université de Mons)

Abstract

Disproportionality indices aim at measuring to what extent the composition of a parliament differs from the distribution of the votes among parties. Malapportionment indices measure to what extent the number of parliament seats attached to each district differs from the distribution of the population among districts. Since there exist many different such indices, some conditions have recently been proposed for assessing the merits of the various indices. In this paper, we propose a characterization of two disproportionality and malapportionment indices: the Duncan and Duncan index (also called Loosemore–Hanby) and the Lijphart index.

Suggested Citation

  • D. Bouyssou & T. Marchant & M. Pirlot, 2020. "A characterization of two disproportionality and malapportionment indices: the Duncan and Duncan index and the Lijphart index," Annals of Operations Research, Springer, vol. 284(1), pages 147-163, January.
    • Handle: RePEc:spr:annopr:v:284:y:2020:i:1:d:10.1007_s10479-018-3073-y
    DOI: 10.1007/s10479-018-3073-y
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    References listed on IDEAS

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    1. Bouyssou, Denis & Marchant, Thierry, 2007. "An axiomatic approach to noncompensatory sorting methods in MCDM, I: The case of two categories," European Journal of Operational Research, Elsevier, vol. 178(1), pages 217-245, April.
    2. Bouyssou, Denis & Marchant, Thierry, 2007. "An axiomatic approach to noncompensatory sorting methods in MCDM, II: More than two categories," European Journal of Operational Research, Elsevier, vol. 178(1), pages 246-276, April.
    3. Moshe Koppel & Abraham Diskin, 2009. "Measuring disproportionality, volatility and malapportionment: axiomatization and solutions," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 33(2), pages 281-286, August.
    4. Loosemore, John & Hanby, Victor J., 1971. "The Theoretical Limits of Maximum Distortion: Some Analytic Expressions for Electoral Systems," British Journal of Political Science, Cambridge University Press, vol. 1(4), pages 467-477, October.
    5. 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.
    6. William Thomson, 2001. "On the axiomatic method and its recent applications to game theory and resource allocation," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 18(2), pages 327-386.
    7. Hannu Nurmi, 2014. "Some remarks on the concept of proportionality," Annals of Operations Research, Springer, vol. 215(1), pages 231-244, April.
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    Cited by:

    1. Denis Bouyssou & Thierry Marchant & Marc Pirlot, 2021. "Axiomatic characterization of the χ 2 dissimilarity measure," Working Papers hal-03463741, HAL.

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