IDEAS home Printed from https://ideas.repec.org/a/spr/annopr/v215y2014i1p257-26710.1007-s10479-013-1383-7.html
   My bibliography  Save this article

Apportionments with minimum Gini index of disproportionality: a Quadratic Knapsack approach

Author

Listed:
  • Daniele Pretolani

Abstract

The ultimate goal of proportional apportionment methods is the minimization of disproportionality, i.e., unequal distribution of political representation among voters, or citizens. The Gini index is a well known tool for measuring inequality. In this work we propose a quotient method that minimizes the Gini index of disproportionality. Our method reduces the rounding of quotas to an instance of quadratic knapsack, a widely studied combinatorial optimization problem. Preliminary computational results, including real cases from the EU Parliament and the US House of Representatives, show that the method is effective, since the instances to solve are rather easy. Copyright Springer Science+Business Media New York 2014

Suggested Citation

  • Daniele Pretolani, 2014. "Apportionments with minimum Gini index of disproportionality: a Quadratic Knapsack approach," Annals of Operations Research, Springer, vol. 215(1), pages 257-267, April.
    • Handle: RePEc:spr:annopr:v:215:y:2014:i:1:p:257-267:10.1007/s10479-013-1383-7
    DOI: 10.1007/s10479-013-1383-7
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10479-013-1383-7
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10479-013-1383-7?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    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. Alberto Caprara & David Pisinger & Paolo Toth, 1999. "Exact Solution of the Quadratic Knapsack Problem," INFORMS Journal on Computing, INFORMS, vol. 11(2), pages 125-137, May.
    2. W. David Pisinger & Anders Bo Rasmussen & Rune Sandvik, 2007. "Solution of Large Quadratic Knapsack Problems Through Aggressive Reduction," INFORMS Journal on Computing, INFORMS, vol. 19(2), pages 280-290, May.
    3. Grimmett, Geoffrey R., 2012. "European apportionment via the Cambridge Compromise," Mathematical Social Sciences, Elsevier, vol. 63(2), pages 68-73.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Giovanni M. Giorgi & Stefania Gubbiotti, 2017. "Celebrating the Memory of Corrado Gini: a Personality Out of the Ordinary," International Statistical Review, International Statistical Institute, vol. 85(2), pages 325-339, August.
    2. Kerem Akartunalı & Philip A. Knight, 2017. "Network models and biproportional rounding for fair seat allocations in the UK elections," Annals of Operations Research, Springer, vol. 253(1), pages 1-19, June.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Gabriel Lopez Zenarosa & Oleg A. Prokopyev & Eduardo L. Pasiliao, 2021. "On exact solution approaches for bilevel quadratic 0–1 knapsack problem," Annals of Operations Research, Springer, vol. 298(1), pages 555-572, March.
    2. Britta Schulze & Michael Stiglmayr & Luís Paquete & Carlos M. Fonseca & David Willems & Stefan Ruzika, 2020. "On the rectangular knapsack problem: approximation of a specific quadratic knapsack problem," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 92(1), pages 107-132, August.
    3. Richard J. Forrester & Warren P. Adams & Paul T. Hadavas, 2010. "Concise RLT forms of binary programs: A computational study of the quadratic knapsack problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 57(1), pages 1-12, February.
    4. Nihal Berktaş & Hande Yaman, 2021. "A Branch-and-Bound Algorithm for Team Formation on Social Networks," INFORMS Journal on Computing, INFORMS, vol. 33(3), pages 1162-1176, July.
    5. David Bergman, 2019. "An Exact Algorithm for the Quadratic Multiknapsack Problem with an Application to Event Seating," INFORMS Journal on Computing, INFORMS, vol. 31(3), pages 477-492, July.
    6. Franklin Djeumou Fomeni & Adam N. Letchford, 2014. "A Dynamic Programming Heuristic for the Quadratic Knapsack Problem," INFORMS Journal on Computing, INFORMS, vol. 26(1), pages 173-182, February.
    7. Renaud Chicoisne, 2023. "Computational aspects of column generation for nonlinear and conic optimization: classical and linearized schemes," Computational Optimization and Applications, Springer, vol. 84(3), pages 789-831, April.
    8. Chen, Liang & Chen, Sheng-Jie & Chen, Wei-Kun & Dai, Yu-Hong & Quan, Tao & Chen, Juan, 2023. "Efficient presolving methods for solving maximal covering and partial set covering location problems," European Journal of Operational Research, Elsevier, vol. 311(1), pages 73-87.
    9. Fabio Furini & Emiliano Traversi, 2019. "Theoretical and computational study of several linearisation techniques for binary quadratic problems," Annals of Operations Research, Springer, vol. 279(1), pages 387-411, August.
    10. Caprara, Alberto, 2008. "Constrained 0-1 quadratic programming: Basic approaches and extensions," European Journal of Operational Research, Elsevier, vol. 187(3), pages 1494-1503, June.
    11. Schauer, Joachim, 2016. "Asymptotic behavior of the quadratic knapsack problem," European Journal of Operational Research, Elsevier, vol. 255(2), pages 357-363.
    12. Laszlo A. Koczy & Peter Biro & Balazs Sziklai, 2017. "US vs. European Apportionment Practices: The Conflict between Monotonicity and Proportionality," CERS-IE WORKING PAPERS 1716, Institute of Economics, Centre for Economic and Regional Studies.
    13. Antonin Macé & Rafael Treibich, 2021. "Inducing Cooperation through Weighted Voting and Veto Power," American Economic Journal: Microeconomics, American Economic Association, vol. 13(3), pages 70-111, August.
    14. Jesus Cunha & Luidi Simonetti & Abilio Lucena, 2016. "Lagrangian heuristics for the Quadratic Knapsack Problem," Computational Optimization and Applications, Springer, vol. 63(1), pages 97-120, January.
    15. Grimmett, G.R. & Oelbermann, K.-F. & Pukelsheim, F., 2012. "A power-weighted variant of the EU27 Cambridge Compromise," Mathematical Social Sciences, Elsevier, vol. 63(2), pages 136-140.
    16. Alain Billionnet & Éric Soutif, 2004. "Using a Mixed Integer Programming Tool for Solving the 0–1 Quadratic Knapsack Problem," INFORMS Journal on Computing, INFORMS, vol. 16(2), pages 188-197, May.
    17. Péter Csóka & P. Jean-Jacques Herings, 2018. "Decentralized Clearing in Financial Networks," Management Science, INFORMS, vol. 64(10), pages 4681-4699, October.
    18. W. David Pisinger & Anders Bo Rasmussen & Rune Sandvik, 2007. "Solution of Large Quadratic Knapsack Problems Through Aggressive Reduction," INFORMS Journal on Computing, INFORMS, vol. 19(2), pages 280-290, May.
    19. Yuning Chen & Jin-Kao Hao, 2015. "Iterated responsive threshold search for the quadratic multiple knapsack problem," Annals of Operations Research, Springer, vol. 226(1), pages 101-131, March.
    20. Svante Janson, 2014. "Asymptotic bias of some election methods," Annals of Operations Research, Springer, vol. 215(1), pages 89-136, April.

    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:215:y:2014:i:1:p:257-267:10.1007/s10479-013-1383-7. See general information about how to correct material in RePEc.

    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 bibliographic 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.

    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 (email available below). General contact details of provider: http://www.springer.com .

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

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.