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Fair Apportionment in the View of the Venice Commission's Recommendation


  • László Á. Kóczy

    () (Óbuda University)

  • Balázs Sziklai

    () (Hungarian Academy of Sciences)

  • Péter Biró

    () (Corvinus University)


In this paper we analyze the consequences of the fairness recommendation of the Venice Commission in allocating voting districts among larger administrative regions. This recommendation requires the size of any constituency not to differ from the average constituency size by more than a fixed limit. We show that this minimum difference constraint, while attractive per definition, is not compatible with monotonicity and Hare-quota properties, two standard requirements of apportionment rules. We present an algorithm that efficiently finds an allotment such that the differences from the average district size are lexicographically minimized. This apportionment rule is a well-defined allocation mechanism compatible with and derived from the recommendation of the Venice Commission. Finally, we compare this apportionment rule with mainstream mechanisms using real data from Hungary and the United States.

Suggested Citation

  • László Á. Kóczy & Balázs Sziklai & Péter Biró, 2013. "Fair Apportionment in the View of the Venice Commission's Recommendation," Working Paper Series 1302, Óbuda University, Keleti Faculty of Business and Management.
  • Handle: RePEc:pkk:wpaper:1302

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    References listed on IDEAS

    1. Rose, Richard & Bernhagen, Patrick & Borz, Gabriela, 2012. "Evaluating competing criteria for allocating parliamentary seats," Mathematical Social Sciences, Elsevier, vol. 63(2), pages 85-89.
    2. Demange, Gabrielle, 2012. "On party-proportional representation under district distortions," Mathematical Social Sciences, Elsevier, vol. 63(2), pages 181-191.
    3. Yukio Koriyama & Jean-François Laslier & Antonin Macé & Rafael Treibich, 2013. "Optimal Apportionment," Journal of Political Economy, University of Chicago Press, vol. 121(3), pages 584-608.
    4. Lauwers, Luc & Van Puyenbroeck, Tom, 2008. "Minimally Disproportional Representation: Generalized Entropy and Stolarsky Mean-Divisor Methods of Apportionment," Working Papers 2008/24, Hogeschool-Universiteit Brussel, Faculteit Economie en Management.
    5. 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.
    6. repec:cup:apsrev:v:48:y:1954:i:03:p:787-792_00 is not listed on IDEAS
    7. Laslier, Jean-François, 2012. "Why not proportional?," Mathematical Social Sciences, Elsevier, vol. 63(2), pages 90-93.
    8. Faruk Gul & Wolfgang Pesendorfer, 2010. "Strategic Redistricting," American Economic Review, American Economic Association, vol. 100(4), pages 1616-1641, September.
    9. Grimmett, Geoffrey R., 2012. "European apportionment via the Cambridge Compromise," Mathematical Social Sciences, Elsevier, vol. 63(2), pages 68-73.
    10. Chambers, Christopher P. & Miller, Alan D., 2013. "Measuring legislative boundaries," Mathematical Social Sciences, Elsevier, vol. 66(3), pages 268-275.
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    Cited by:

    1. Bittó, Virág, 2017. "Az Imperiali és Macau politikai választókörzet-kiosztási módszerek empirikus vizsgálata
      [Empirical Analysis of the Imperiali and Macau Apportionment Methods]
      ," MPRA Paper 79554, University Library of Munich, Germany.
    2. Laszlo A. Koczy & Peter Biro & Balazs Sziklai, 2017. "US vs. European Apportionment Practices: The Conflict between Monotonicity and Proportionality," IEHAS Discussion Papers 1716, Institute of Economics, Centre for Economic and Regional Studies, Hungarian Academy of Sciences.

    More about this item


    Apportionment; voting; elections; Venice Commission; proportionality; lexicographic ordering JEL Codes: C71; D72;

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • D72 - Microeconomics - - Analysis of Collective Decision-Making - - - Political Processes: Rent-seeking, Lobbying, Elections, Legislatures, and Voting Behavior

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