IDEAS home Printed from https://ideas.repec.org/
MyIDEAS: Login to save this article or follow this journal

A majorization comparison of apportionment methods in proportional representation

  • Friedrich Pukelsheim

    ()

    (Institut für Mathematik, Universität Augsburg, D-86315 Augsburg, Germany)

  • Albert W. Marshall

    (Statistics Department, University of British Columbia, Vancouver BG, V6T 1Z2, Canada)

  • Ingram Olkin

    (Department of Statistics, Stanford University, Stanford CA, 94305-4065, USA)

Registered author(s):

    From the inception of the proportional representation movement it has been an issue whether larger parties are favored at the expense of smaller parties in one apportionment of seats as compared to another apportionment. A number of methods have been proposed and are used in countries with a proportional representation system. These apportionment methods exhibit a regularity of order, as discussed in the present paper, that captures the preferential treatment of larger versus smaller parties. This order, namely majorization, permits the comparison of seat allocations in two apportionments. For divisor methods, we show that one method is majorized by another method if and only if their signpost ratios are increasing. This criterion is satisfied for the divisor methods with power-mean rounding, and for the divisor methods with stationary rounding. Majorization places the five traditional apportionment methods in the order as they are known to favor larger parties over smaller parties: Adams, Dean, Hill, Webster, and Jefferson.

    If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

    File URL: http://link.springer.de/link/service/journals/00355/papers/2019004/20190885.pdf
    Download Restriction: Access to the full text of the articles in this series is restricted

    As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.

    Article provided by Springer in its journal Social Choice and Welfare.

    Volume (Year): 19 (2002)
    Issue (Month): 4 ()
    Pages: 885-900

    as
    in new window

    Handle: RePEc:spr:sochwe:v:19:y:2002:i:4:p:885-900
    Note: Received: 5 August 2000/Accepted: 24 October 2001
    Contact details of provider: Web page: http://link.springer.de/link/service/journals/00355/index.htm

    Order Information: Web: http://link.springer.de/orders.htm

    No references listed on IDEAS
    You can help add them by filling out this form.

    This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

    When requesting a correction, please mention this item's handle: RePEc:spr:sochwe:v:19:y:2002:i:4:p:885-900. 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: (Guenther Eichhorn)

    or (Christopher F Baum)

    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 references are entirely missing, you can add them using this form.

    If the full references list an item that is present in RePEc, but the system did not link 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 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.

    This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.