IDEAS home Printed from https://ideas.repec.org/a/spr/operea/v19y2019i2d10.1007_s12351-017-0292-y.html
   My bibliography  Save this article

Beyond the Cambridge Compromise algorithm towards degressively proportional allocations

Author

Listed:
  • Katarzyna Cegiełka

    (Wrocław University of Economics)

  • Janusz Łyko

    (Wrocław University of Economics)

  • Radosław Rudek

    (Wrocław University of Economics)

Abstract

Although proportional allocation methods are well-known and widely used in the parliamentary tradition, they cannot be applied in a wide variety of cases. Such problems occur in the European Parliament, where a constitutional principle is to assure that less populous countries will not be dominated by the others, which implies that allocations have to be degressively proportional. However, under this assumption an exhaustive search of the solution space is intractable. To solve the problem, the Cambridge Compromise algorithm was proposed, which is durable, transparent, impartial to politics and unambiguous, but the allocations obtained are not degressively proportional. Therefore, we propose an allocation algorithm derived from operations research that inherits the transparency of the Cambridge Compromise and produces an unambiguous degressively proportional allocation. Hence, the paper aims at testing our alternative allocation method and comparing its outcomes during computational analysis.

Suggested Citation

  • Katarzyna Cegiełka & Janusz Łyko & Radosław Rudek, 2019. "Beyond the Cambridge Compromise algorithm towards degressively proportional allocations," Operational Research, Springer, vol. 19(2), pages 317-332, June.
    • Handle: RePEc:spr:operea:v:19:y:2019:i:2:d:10.1007_s12351-017-0292-y
    DOI: 10.1007/s12351-017-0292-y
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s12351-017-0292-y
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s12351-017-0292-y?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. Serafini, Paolo, 2012. "Allocation of the EU Parliament seats via integer linear programming and revised quotas," Mathematical Social Sciences, Elsevier, vol. 63(2), pages 107-113.
    2. Friedrich Pukelsheim & Albert W. Marshall & Ingram Olkin, 2002. "A majorization comparison of apportionment methods in proportional representation," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 19(4), pages 885-900.
    3. H. J. J. te Riele, 1978. "The proportional representation problem in the Second Chamber: an approach via minimal distances," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 32(4), pages 163-179, December.
    4. Luc Lauwers & Tom Van Puyenbroeck, 2006. "The Hamilton Apportionment Method Is Between the Adams Method and the Jefferson Method," Mathematics of Operations Research, INFORMS, vol. 31(2), pages 390-397, May.
    5. Bautista, Joaquin & Companys, Ramon & Corominas, Albert, 2001. "Solving the generalized apportionment problem through the optimization of discrepancy functions," European Journal of Operational Research, Elsevier, vol. 131(3), pages 676-684, June.
    6. Grimmett, Geoffrey R., 2012. "European apportionment via the Cambridge Compromise," Mathematical Social Sciences, Elsevier, vol. 63(2), pages 68-73.
    7. Florek, Jan, 2012. "A numerical method to determine a degressive proportional distribution of seats in the European Parliament," Mathematical Social Sciences, Elsevier, vol. 63(2), pages 121-129.
    8. Słomczyński, Wojciech & Życzkowski, Karol, 2012. "Mathematical aspects of degressive proportionality," Mathematical Social Sciences, Elsevier, vol. 63(2), pages 94-101.
    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. Katarzyna Cegielka & Piotr Dniestrzanski & Arkadiusz Maciuk & Maciej Szczecinski, 2022. "The Implications of Possible Enlargements of the European Union for the Configuration of Power in the European Parliament," European Research Studies Journal, European Research Studies Journal, vol. 0(2), pages 145-159.
    2. Katarzyna Cegiełka & Piotr Dniestrzański & Janusz Łyko & Arkadiusz Maciuk & Maciej Szczeciński, 2021. "A neutral core of degressively proportional allocations under lexicographic preferences of agents," Eurasian Economic Review, Springer;Eurasia Business and Economics Society, vol. 11(4), pages 667-685, December.

    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. Janusz Łyko & Radosław Rudek, 2017. "Operations research methods in political decisions: a case study on the European Parliament composition," Computational and Mathematical Organization Theory, Springer, vol. 23(4), pages 572-586, December.
    2. Katarzyna Cegiełka & Piotr Dniestrzański & Janusz Łyko & Arkadiusz Maciuk & Maciej Szczeciński, 2021. "A neutral core of degressively proportional allocations under lexicographic preferences of agents," Eurasian Economic Review, Springer;Eurasia Business and Economics Society, vol. 11(4), pages 667-685, December.
    3. Słomczyński, Wojciech & Życzkowski, Karol, 2012. "Mathematical aspects of degressive proportionality," Mathematical Social Sciences, Elsevier, vol. 63(2), pages 94-101.
    4. Katarzyna Cegielka & Piotr Dniestrzanski & Arkadiusz Maciuk & Maciej Szczecinski, 2022. "The Implications of Possible Enlargements of the European Union for the Configuration of Power in the European Parliament," European Research Studies Journal, European Research Studies Journal, vol. 0(2), pages 145-159.
    5. 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.
    6. Tom Van Puyenbroeck, 2008. "Proportional Representation, Gini Coefficients, and the Principle of Transfers," Journal of Theoretical Politics, , vol. 20(4), pages 498-526, October.
    7. 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.
    8. José Gutiérrez, 2015. "Majorization comparison of closed list electoral systems through a matrix theorem," Annals of Operations Research, Springer, vol. 235(1), pages 807-814, December.
    9. Balázs R Sziklai & Károly Héberger, 2020. "Apportionment and districting by Sum of Ranking Differences," PLOS ONE, Public Library of Science, vol. 15(3), pages 1-20, March.
    10. 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.
    11. Blanca L Delgado-Márquez & Michael Kaeding & Antonio Palomares, 2013. "A more balanced composition of the European Parliament with degressive proportionality," European Union Politics, , vol. 14(3), pages 458-471, September.
    12. 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.
    13. Laszlo A. Koczy & Balazs Sziklai, 2018. "Bounds on Malapportionment," CERS-IE WORKING PAPERS 1801, Institute of Economics, Centre for Economic and Regional Studies.
    14. de Mouzon, Olivier & Laurent, Thibault & Le Breton, Michel, 2020. "One Man, One Vote Part 2: Measurement of Malapportionment and Disproportionality and the Lorenz Curve," TSE Working Papers 20-1089, Toulouse School of Economics (TSE).
    15. Gianfranco Gambarelli, 1999. "Maximax Apportionments," Group Decision and Negotiation, Springer, vol. 8(6), pages 441-461, November.
    16. Rose, Richard & Bernhagen, Patrick & Borz, Gabriela, 2012. "Evaluating competing criteria for allocating parliamentary seats," Mathematical Social Sciences, Elsevier, vol. 63(2), pages 85-89.
    17. Heinrich Lothar & Pukelsheim Friedrich & Schwingenschlögl Udo, 2004. "Sainte-Laguë’s chi-square divergence for the rounding of probabilities and its convergence to a stable law," Statistics & Risk Modeling, De Gruyter, vol. 22(1), pages 43-60, January.
    18. Paul Edelman, 2015. "Voting power apportionments," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 44(4), pages 911-925, April.
    19. Steven J Brams & D Marc Kilgour, 2012. "Narrowing the field in elections: The Next-Two rule," Journal of Theoretical Politics, , vol. 24(4), pages 507-525, October.
    20. Brams,S.L. & Kaplan,T.R., 2002. "Dividing the indivisible : procedures for allocating cabinet ministries to political parties in a parliamentary system," Center for Mathematical Economics Working Papers 340, Center for Mathematical Economics, Bielefeld University.

    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:operea:v:19:y:2019:i:2:d:10.1007_s12351-017-0292-y. 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.