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On party-proportional representation under district distortions


  • Gabrielle Demange

    (PSE - Paris-Jourdan Sciences Economiques - CNRS - Centre National de la Recherche Scientifique - ENPC - École des Ponts ParisTech - EHESS - École des hautes études en sciences sociales - INRA - Institut National de la Recherche Agronomique - ENS Paris - École normale supérieure - Paris, PSE - Paris School of Economics)


The paper presents the problem of choosing the representatives in an assembly when the whole electoral region is subdivided into electoral districts. Because of the two dimensions, geographical (districts) and political (parties), the problem is called bi-apportionment. Often the allocation of seats to districts is pre-determined and furthermore distorted ---meaning that the ratios of the number of assigned seats to population size vary significantly across districts. The paper surveys proposed bi-apportionment methods with a focus on the conflict that may arise between party-proportional representation under district distortions.

Suggested Citation

  • Gabrielle Demange, 2011. "On party-proportional representation under district distortions," PSE Working Papers halshs-00623031, HAL.
  • Handle: RePEc:hal:psewpa:halshs-00623031
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    References listed on IDEAS

    1. Michel Balinski & Gabrielle Demange, 1989. "Algorithm for Proportional Matrices in Reals and Integers," Post-Print halshs-00585327, HAL.
    2. Gallagher, Michael, 1992. "Comparing Proportional Representation Electoral Systems: Quotas, Thresholds, Paradoxes and Majorities," British Journal of Political Science, Cambridge University Press, vol. 22(04), pages 469-496, October.
    3. M. L. Balinski & G. Demange, 1989. "An Axiomatic Approach to Proportionality Between Matrices," Mathematics of Operations Research, INFORMS, vol. 14(4), pages 700-719, November.
    4. Marjorie B. Gassner, 1991. "Biproportional Delegations," Journal of Theoretical Politics, , vol. 3(3), pages 321-342, July.
    5. Sebastian Maier & Petur Zachariassen & Martin Zachariasen, 2010. "Divisor-Based Biproportional Apportionment in Electoral Systems: A Real-Life Benchmark Study," Management Science, INFORMS, vol. 56(2), pages 373-387, February.
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    Cited by:

    1. Biró, Péter & Kóczy, László Á. & Sziklai, Balázs, 2015. "Fair apportionment in the view of the Venice Commission’s recommendation," Mathematical Social Sciences, Elsevier, vol. 77(C), pages 32-41.
    2. Kóczy Á., László & Biró, Péter & Sziklai, Balázs, 2012. "Választókörzetek igazságosan?
      [Fair apportionment of voting districts in Hungary]
      ," Közgazdasági Szemle (Economic Review - monthly of the Hungarian Academy of Sciences), Közgazdasági Szemle Alapítvány (Economic Review Foundation), vol. 0(11), pages 1165-1186.

    More about this item


    Party-proportional representation; (bi-)apportionment; (bi-)divisor methods; fair shares;

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