IDEAS home Printed from https://ideas.repec.org/a/spr/annopr/v284y2020i1d10.1007_s10479-018-3073-y.html
   My bibliography  Save this article

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

Author

Listed:
  • D. Bouyssou

    () (Université Paris-Dauphine, PSL Research University)

  • T. Marchant

    () (Ghent University)

  • M. Pirlot

    () (Université de Mons)

Abstract

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
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10479-018-3073-y
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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. Denis Bouyssou & Thierry Marchant, 2007. "An axiomatic approach to noncompensatory sorting methods in MCDM, II: More than two categories," Post-Print hal-02361918, HAL.
    3. 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.
    4. Denis Bouyssou & Thierry Marchant, 2007. "An axiomatic approach to noncompensatory sorting methods in MCDM, I: The case of two categories," Post-Print hal-02361912, HAL.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. Hannu Nurmi, 2014. "Some remarks on the concept of proportionality," Annals of Operations Research, Springer, vol. 215(1), pages 231-244, April.
    Full references (including those not matched with items on IDEAS)

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:annopr:v:284:y:2020:i:1:d:10.1007_s10479-018-3073-y. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Sonal Shukla) or (Springer Nature Abstracting and Indexing). General contact details of provider: http://www.springer.com .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.