Evaluation of thresholds for power mean-based and other divisor methods of apportionment
AbstractFor divisor methods of apportionment with concave up or concave down rounding functions, we prove explicit formulas for the threshold values--the lower and upper bounds for the percentage of population that are necessary and sufficient for a state to receive a particular number of seats. Among the rounding functions with fixed concavity are those based on power means, which include the methods of Adams, Dean, Hill-Huntington, Webster, and Jefferson. The thresholds for Dean's and Hill-Huntington's methods had not been evaluated previously. We use the formulas to analyze the behavior of the thresholds for divisor methods with fixed concavity, and compute and compare threshold values for Hill-Huntington's method (used to apportion the US House of Representatives).
Download InfoIf 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.
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.
Bibliographic InfoArticle provided by Elsevier in its journal Mathematical Social Sciences.
Volume (Year): 59 (2010)
Issue (Month): 3 (May)
Contact details of provider:
Web page: http://www.elsevier.com/locate/inca/505565
Thresholds Divisor methods Power means Hill-Huntington's method Concavity US House of Representatives;
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Friedrich Pukelsheim & Albert W. Marshall & Ingram Olkin, 2002. "A majorization comparison of apportionment methods in proportional representation," Social Choice and Welfare, Springer, vol. 19(4), pages 885-900.
- Balinski, Michel & Ramirez, Victoriano, 1999. "Parametric methods of apportionment, rounding and production," Mathematical Social Sciences, Elsevier, vol. 37(2), pages 107-122, March.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Zhang, Lei).
If references are entirely missing, you can add them using this form.