IDEAS home Printed from https://ideas.repec.org/a/nas/journl/v119y2022pe2109305119.html
   My bibliography  Save this article

Multidimensional political apportionment

Author

Listed:
  • Javier Cembrano

    (a Institute of Mathematics, Technische Universität Berlin, 10623 Berlin, Germany;)

  • José Correa

    (b Department of Industrial Engineering, Universidad de Chile, 8370456 Santiago, Chile;)

  • Victor Verdugo

    (c Institute of Engineering Sciences, Universidad de O’Higgins, 2841959 Rancagua, Chile)

Abstract

A cornerstone in the modern political organization of societies is the existence of a deliberative assembly, reflecting the needs of different population segments. As modern societies become more complex, representation according to dimensions beyond political affiliation and geography is demanded; examples include gender balance and ethnicity. As this dimensionality increases, the task becomes more challenging and requires more sophisticated mathematical tools. In this paper, we initiate the study of multidimensional apportionments and show that, in three and more dimensions, their existence is not guaranteed. However, our main result states that it is possible to elect a house nearly respecting proportionality of representation along several dimensions simultaneously. We finally illustrate the potential of our approach with recent election data.

Suggested Citation

  • Javier Cembrano & José Correa & Victor Verdugo, 2022. "Multidimensional political apportionment," Proceedings of the National Academy of Sciences, Proceedings of the National Academy of Sciences, vol. 119(15), pages 2109305119-, April.
    • Handle: RePEc:nas:journl:v:119:y:2022:p:e2109305119
    as

    Download full text from publisher

    File URL: http://www.pnas.org/content/119/15/e2109305119.full
    Download Restriction: no
    ---><---

    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:nas:journl:v:119:y:2022:p:e2109305119. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: Eric Cain (email available below). General contact details of provider: http://www.pnas.org/ .

    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.