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Divisor-Based Biproportional Apportionment in Electoral Systems: A Real-Life Benchmark Study

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Author Info

  • Sebastian Maier

    ()
    (Institute of Mathematics, University of Augsburg, D-86135 Augsburg, Germany)

  • Petur Zachariassen

    ()
    (University of the Faroe Islands, FO-100 T├│rshavn, Faroe Islands)

  • Martin Zachariasen

    ()
    (Department of Computer Science, University of Copenhagen, DK-2100 Copenhagen, Denmark)

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    Abstract

    Biproportional apportionment methods provide two-way proportionality in electoral systems where the electoral region is subdivided into electoral districts. The problem is to assign integral values to the elements of a matrix that are proportional to a given input matrix, and such that a set of row- and column-sum requirements are fulfilled. In a divisor-based method for biproportional apportionment, the problem is solved by computing appropriate row and column divisors, and by rounding the quotients. We present a comprehensive experimental evaluation of divisor-based biproportional apportionment in an electoral system context. By performing experiments on real-life benchmark instances (election data with multimember districts), we evaluate the general quality of divisor-based apportionments with respect to, e.g., deviation from quota, reversal orderings, and occurrences of ties. For example, we studied the frequency in which a party with a higher vote count in a district ended up with fewer seats in that district.

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    File URL: http://dx.doi.org/10.1287/mnsc.1090.1118
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    Bibliographic Info

    Article provided by INFORMS in its journal Management Science.

    Volume (Year): 56 (2010)
    Issue (Month): 2 (February)
    Pages: 373-387

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    Handle: RePEc:inm:ormnsc:v:56:y:2010:i:2:p:373-387

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    Related research

    Keywords: electoral systems; divisor-based biproportional apportionment; computer simulation;

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    1. repec:hal:wpaper:halshs-00623031 is not listed on IDEAS
    2. repec:hal:wpaper:halshs-00644439 is not listed on IDEAS
    3. Demange, Gabrielle, 2012. "On party-proportional representation under district distortions," Mathematical Social Sciences, Elsevier, vol. 63(2), pages 181-191.

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