IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i15p3270-d1202204.html
   My bibliography  Save this article

Axioms and Divisor Methods for a Generalized Apportionment Problem with Relative Equality

Author

Listed:
  • Wenruo Lyu

    (Graduate School of Advanced Integrated Studies in Human Survivability, Kyoto University, Kyoto 606-8306, Japan)

  • Liang Zhao

    (Graduate School of Advanced Integrated Studies in Human Survivability, Kyoto University, Kyoto 606-8306, Japan)

Abstract

The allocation of seats in a legislative body to groups based on their size is a crucial issue in legal and political studies. However, recent findings suggest that an optimal allocation of seats may not be proportional to the size of the groups. For instance, the European Parliament (EP) utilizes a subproportional system known as degressive proportionality. Unfortunately, current apportionment methods for the EP lack a rigorous axiomatic analysis and fail to adequately address equality. Building upon recent research on equality in subproportional settings, this paper proposed a novel generalization of existing axioms and divisor methods for proportionality to encompass subproportionality with relative equality. Specifically, we consider a function f ( p ) = a + b p γ on the standard number of seats for a group of size p , where a , b and γ are given non-negative constants, and a is an integer. This theory is exemplified through an empirical study focused on the EP.

Suggested Citation

  • Wenruo Lyu & Liang Zhao, 2023. "Axioms and Divisor Methods for a Generalized Apportionment Problem with Relative Equality," Mathematics, MDPI, vol. 11(15), pages 1-13, July.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:15:p:3270-:d:1202204
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/15/3270/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/11/15/3270/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Emmanuelle Auriol & Robert Gary-Bobo, 2012. "On the optimal number of representatives," Public Choice, Springer, vol. 153(3), pages 419-445, December.
    2. 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.
    3. G. R. Grimmett & F. Pukelsheim & V. Ram'irez Gonz'alez & W. S{l}omczy'nski & K. .Zyczkowski, 2017. "A 700-seat no-loss composition for the 2019 European Parliament," Papers 1710.03820, arXiv.org.
    4. Raphael Godefroy & Nicolas Klein, 2018. "Parliament Shapes And Sizes," Economic Inquiry, Western Economic Association International, vol. 56(4), pages 2212-2233, October.
    5. Słomczyński, Wojciech & Życzkowski, Karol, 2012. "Mathematical aspects of degressive proportionality," Mathematical Social Sciences, Elsevier, vol. 63(2), pages 94-101.
    6. Carrie Arnold, 2017. "The mathematicians who want to save democracy," Nature, Nature, vol. 546(7657), pages 200-202, June.
    7. Theil, Henri, 1969. "The Desired Political Entropy," American Political Science Review, Cambridge University Press, vol. 63(2), pages 521-525, June.
    Full references (including those not matched with items on IDEAS)

    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. De Santo, Alessia & Le Maux, Benoît, 2023. "On the optimal size of legislatures: An illustrated literature review," European Journal of Political Economy, Elsevier, vol. 77(C).
    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. 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.
    4. Konstantinos Matakos & Riikka Savolainen & Orestis Troumpounis & Janne Tukiainen & Dimitrios Xefteris, 2024. "Electoral Institutions and Intraparty Cohesion," Journal of Political Economy Microeconomics, University of Chicago Press, vol. 2(4), pages 883-916.
    5. Piolatto, Amedeo, 2011. "Plurality versus proportional electoral rule: Which is most representative of voters?," European Journal of Political Economy, Elsevier, vol. 27(2), pages 311-327, June.
    6. Konstantinos Matakos & Orestis Troumpounis & Dimitrios Xefteris, 2015. "Turnout and Polarization Under Alternative Electoral Systems," Studies in Political Economy, in: Norman Schofield & Gonzalo Caballero (ed.), The Political Economy of Governance, edition 127, pages 335-362, Springer.
    7. Wada, Junichiro & Kamahara, Yuta, 2018. "Studying malapportionment using α-divergence," Mathematical Social Sciences, Elsevier, vol. 93(C), pages 77-89.
    8. Aparicio, Sebastian & Audretsch, David & Noguera, Maria & Urbano, David, 2022. "Can female entrepreneurs boost social mobility in developing countries? An institutional analysis," Technological Forecasting and Social Change, Elsevier, vol. 175(C).
    9. Rajeev K. Goel & Michael A. Nelson, 2023. "Which political regimes foster entrepreneurship? An international examination," The Journal of Technology Transfer, Springer, vol. 48(1), pages 126-146, February.
    10. Ocaña, Francisco & Oñate, Pablo, 2011. "IndElec: A Software for Analyzing Party Systems and Electoral Systems," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 42(i06).
    11. Dino Gerardi & Leeat Yariv, 2003. "Committee Design in the Presence of Communication," Cowles Foundation Discussion Papers 1411, Cowles Foundation for Research in Economics, Yale University.
    12. Berger, Helge & Nitsch, Volker & Lybek, Tonny, 2008. "Central bank boards around the world: Why does membership size differ?," European Journal of Political Economy, Elsevier, vol. 24(4), pages 817-832, December.
    13. Emmanuelle Auriol & Robert Gary-Bobo, 2012. "On the optimal number of representatives," Public Choice, Springer, vol. 153(3), pages 419-445, December.
    14. Andreas Bergh & Günther Fink & Richard Öhrvall, 2017. "More politicians, more corruption: evidence from Swedish municipalities," Public Choice, Springer, vol. 172(3), pages 483-500, September.
    15. Pascal Langenbach & Tobias Rommel, 2023. "Even in the best of both worlds, you can't have it all: How German voters navigate the trilemma of mixed-member proportionality," Discussion Paper Series of the Max Planck Institute for Research on Collective Goods 2023_07, Max Planck Institute for Research on Collective Goods.
    16. 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.
    17. Alexander, Jeffrey & Nuchols, Beverly & Bloom, Joan & Lee, Shoou-Yih D., 1993. "Organizational Demography and Turnover: An Examination of Multiform and Non-Linear Heterogeneity," Institute for Research on Labor and Employment, Working Paper Series qt1g50w5xm, Institute of Industrial Relations, UC Berkeley.
    18. Rein Taagepera, 2001. "Party Size Baselines Imposed by Institutional Constraints," Journal of Theoretical Politics, , vol. 13(4), pages 331-354, October.
    19. Emmanuelle Auriol & Robert Gary-Bobo, 2007. "On Robust Constitution Design," Theory and Decision, Springer, vol. 62(3), pages 241-279, May.
    20. Bol, Damien & Matakos, Konstantinos & Troumpounis, Orestis & Xefteris, Dimitrios, 2019. "Electoral rules, strategic entry and polarization," Journal of Public Economics, Elsevier, vol. 178(C).

    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:gam:jmathe:v:11:y:2023:i:15:p:3270-:d:1202204. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.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.