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Seat allocation distributions and seat biases of stationary apportionment methods for proportional representation

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  • Udo Schwingenschlögl
  • Mathias Drton

Abstract

In a proportional representation system, apportionment methods are used to round the vote proportion of a party to an integer number of seats in parliament. Assuming uniformly distributed vote proportions, we derive the seat allocation distributions for stationary divisor methods. An important characteristic of apportionment methods are seat biases, that is, expected differences between actual seat numbers and ideal shares of seats, when the parties are ordered from largest to smallest. We obtain seat bias formulas for the stationary divisor methods and for the quota method of greatest remainders. Copyright Springer-Verlag 2004

Suggested Citation

  • Udo Schwingenschlögl & Mathias Drton, 2004. "Seat allocation distributions and seat biases of stationary apportionment methods for proportional representation," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 60(2), pages 191-202, September.
    • Handle: RePEc:spr:metrik:v:60:y:2004:i:2:p:191-202
    DOI: 10.1007/s001840400347
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    Citations

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    Cited by:

    1. Svante Janson, 2014. "Asymptotic bias of some election methods," Annals of Operations Research, Springer, vol. 215(1), pages 89-136, April.
    2. Heinrich Lothar & Pukelsheim Friedrich & Schwingenschlögl Udo, 2005. "On stationary multiplier methods for the rounding of probabilities and the limiting law of the Sainte-Laguë divergence," Statistics & Risk Modeling, De Gruyter, vol. 23(2), pages 117-129, February.
    3. Schwingenschlögl, Udo & Drton, Mathias, 2006. "Seat excess variances of apportionment methods for proportional representation," Statistics & Probability Letters, Elsevier, vol. 76(16), pages 1723-1730, October.
    4. Schwingenschlögl, Udo, 2007. "Probabilities of majority and minority violation in proportional representation," Statistics & Probability Letters, Elsevier, vol. 77(17), pages 1690-1695, November.
    5. Luc Lauwers & Tom Van Puyenbroeck, 2006. "The Hamilton Apportionment Method Is Between the Adams Method and the Jefferson Method," Mathematics of Operations Research, INFORMS, vol. 31(2), pages 390-397, May.

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