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On party-proportional representation under district distortions

Author

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  • Gabrielle Demange

    (PSE - Paris-Jourdan Sciences Economiques - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - INRA - Institut National de la Recherche Agronomique - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique, PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement)

Abstract

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," Working Papers halshs-00623031, HAL.
    • Handle: RePEc:hal:wpaper:halshs-00623031
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-00623031v2
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    References listed on IDEAS

    as
    1. Michel L. 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(4), pages 469-496, October.
    3. Gabrielle Demange & Wooders Myrna, 2005. "Group Formation in Economics: Networks, Clubs and Coalitions," Post-Print halshs-00576778, HAL.
    4. Gabrielle Demange & Michel L. Balinski, 1989. "An Axiomatic Approach to Proportionality between Matrices," Post-Print halshs-00670952, HAL.
    5. Friedrich Pukelsheim, 2006. "Current Issues of Apportionment Methods," Studies in Choice and Welfare, in: Bruno Simeone & Friedrich Pukelsheim (ed.), Mathematics and Democracy, pages 167-176, Springer.
    6. Demange,Gabrielle & Wooders,Myrna (ed.), 2005. "Group Formation in Economics," Cambridge Books, Cambridge University Press, number 9780521842716, October.
    7. 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.
    8. Marjorie B. Gassner, 1991. "Biproportional Delegations," Journal of Theoretical Politics, , vol. 3(3), pages 321-342, July.
    9. 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.
    10. Aline Pennisi, 2006. "The Italian Bug: A Flawed Procedure for Bi-Proportional Seat Allocation," Studies in Choice and Welfare, in: Bruno Simeone & Friedrich Pukelsheim (ed.), Mathematics and Democracy, pages 151-165, Springer.
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    Citations

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    Cited by:

    1. Gabrielle Demange, 2018. "New electoral systems and old referendums," PSE Working Papers hal-01852206, HAL.
    2. 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.
    3. 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.

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    Keywords

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