IDEAS home Printed from https://ideas.repec.org/a/eee/matsoc/v63y2012i2p94-101.html
   My bibliography  Save this article

Mathematical aspects of degressive proportionality

Author

Listed:
  • Słomczyński, Wojciech
  • Życzkowski, Karol

Abstract

We analyze mathematical properties of apportionment functions in the context of allocating seats in the European Parliament. Some exemplary families of such functions are specified and the corresponding allocations of seats among the Member States of the European Union are presented. We show that the constitutional constraints for the apportionment are so strong that the admissible functions lead to rather similar solutions.

Suggested Citation

  • Słomczyński, Wojciech & Życzkowski, Karol, 2012. "Mathematical aspects of degressive proportionality," Mathematical Social Sciences, Elsevier, vol. 63(2), pages 94-101.
  • Handle: RePEc:eee:matsoc:v:63:y:2012:i:2:p:94-101
    DOI: 10.1016/j.mathsocsci.2011.12.002
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0165489611001399
    Download Restriction: Full text for ScienceDirect subscribers only

    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. Biung-Ghi Ju & Juan Moreno-Ternero, 2011. "Progressive and merging-proof taxation," International Journal of Game Theory, Springer;Game Theory Society, vol. 40(1), pages 43-62, February.
    2. Kaminski, Marek M., 2006. "Parametric rationing methods," Games and Economic Behavior, Elsevier, vol. 54(1), pages 115-133, January.
    3. Moreno-Ternero, Juan D., 2011. "Voting over piece-wise linear tax methods," Journal of Mathematical Economics, Elsevier, vol. 47(1), pages 29-36, January.
    4. Grimmett, Geoffrey R., 2012. "European apportionment via the Cambridge Compromise," Mathematical Social Sciences, Elsevier, vol. 63(2), pages 68-73.
    5. Thomson, William, 2003. "Axiomatic and game-theoretic analysis of bankruptcy and taxation problems: a survey," Mathematical Social Sciences, Elsevier, vol. 45(3), pages 249-297, July.
    6. 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.
    7. Kahneman, Daniel & Tversky, Amos, 1979. "Prospect Theory: An Analysis of Decision under Risk," Econometrica, Econometric Society, vol. 47(2), pages 263-291, March.
    8. Udo Schwingenschlögl, 2008. "Asymptotic Equivalence of Seat Bias Models," Statistical Papers, Springer, vol. 49(2), pages 191-200, April.
    9. Wei Ding & Elmar G. Wolfstetter, 2011. "Prizes and lemons: procurement of innovation under imperfect commitment," RAND Journal of Economics, RAND Corporation, vol. 42(4), pages 664-680, December.
    10. 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.
    11. Ramírez González, V. & Martínez Aroza, J. & Márquez García, A., 2012. "Spline methods for degressive proportionality in the composition of the European Parliament," Mathematical Social Sciences, Elsevier, vol. 63(2), pages 114-120.
    12. Mathias Drton & Udo Schwingenschlögl, 2005. "Asymptotic seat bias formulas," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 62(1), pages 23-31, September.
    13. Matthias Dahm, 2010. "Free mobility and taste-homogeneity of jurisdiction structures," International Journal of Game Theory, Springer;Game Theory Society, vol. 39(1), pages 259-272, March.
    14. 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.
    15. Geoffrey Grimmett & Jean-François Laslier & Friedrich Pukelsheim & Victoriano Ramirez Gonzalez & Richard Rose & Wojciech Slomczynski & Martin Zachariasen & Karol Życzkowski, 2011. "The allocation between the EU member states of the seats in the European Parliament Cambridge Compromise," Working Papers hal-00609946, HAL.
    16. Moberg, Axel, 2012. "EP seats: The politics behind the math," Mathematical Social Sciences, Elsevier, vol. 63(2), pages 78-84.
    17. J. Barkley Rosser, 2009. "Introduction," Chapters, in: J. Barkley Rosser Jr. (ed.), Handbook of Research on Complexity, chapter 1, Edward Elgar Publishing.
    18. al-Nowaihi, Ali & Dhami, Sanjit, 2009. "A value function that explains the magnitude and sign effects," Economics Letters, Elsevier, vol. 105(3), pages 224-229, December.
    19. Kellermann, Thomas, 2012. "The minimum-based procedure: A principled way to allocate seats in the European Parliament," Mathematical Social Sciences, Elsevier, vol. 63(2), pages 102-106.
    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. repec:spr:comaot:v:23:y:2017:i:4:d:10.1007_s10588-017-9243-7 is not listed on IDEAS
    2. Macé, Antonin & Treibich, Rafael, 2012. "Computing the optimal weights in a utilitarian model of apportionment," Mathematical Social Sciences, Elsevier, vol. 63(2), pages 141-151.
    3. Janusz Łyko & Radosław Rudek, 0. "Operations research methods in political decisions: a case study on the European Parliament composition," Computational and Mathematical Organization Theory, Springer, vol. 0, pages 1-15.

    More about this item

    Statistics

    Access and download statistics

    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:eee:matsoc:v:63:y:2012:i:2:p:94-101. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Dana Niculescu). General contact details of provider: http://www.elsevier.com/locate/inca/505565 .

    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 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.

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.