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Evaluation of thresholds for power mean-based and other divisor methods of apportionment


  • Jones, Michael A.
  • Wilson, Jennifer M.


For 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).

Suggested Citation

  • Jones, Michael A. & Wilson, Jennifer M., 2010. "Evaluation of thresholds for power mean-based and other divisor methods of apportionment," Mathematical Social Sciences, Elsevier, vol. 59(3), pages 343-348, May.
  • Handle: RePEc:eee:matsoc:v:59:y:2010:i:3:p:343-348

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    References listed on IDEAS

    1. Gallagher, Michael, 1992. "Comparing Proportional Representation Electoral Systems: Quotas, Thresholds, Paradoxes and Majorities," British Journal of Political Science, Cambridge University Press, vol. 22(04), pages 469-496, October.
    2. Balinski, Michel & Ramirez, Victoriano, 1999. "Parametric methods of apportionment, rounding and production," Mathematical Social Sciences, Elsevier, vol. 37(2), pages 107-122, March.
    3. Friedrich Pukelsheim & Albert W. Marshall & Ingram Olkin, 2002. "A majorization comparison of apportionment methods in proportional representation," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 19(4), pages 885-900.
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