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Apportionment methods

Author

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  • Niemeyer, Horst F.
  • Niemeyer, Alice C.

Abstract

Most democratic countries use apportionment methods to transform election results into whole numbers, which usually give the number of seats in a legislative body that the parties obtained. Which apportionment method does this best can be specified by measuring the error between the allocated result and the ideal proportion. We show how to find an apportionment method which is best suited to a given error function. We also discuss several properties of apportionment methods that have been labelled paradoxa. In particular we explain the highly publicised "Alabama" Paradox for the Hare/Hamilton method and show that other popular apportionment methods come with their very own paradoxa.

Suggested Citation

  • Niemeyer, Horst F. & Niemeyer, Alice C., 2008. "Apportionment methods," Mathematical Social Sciences, Elsevier, vol. 56(2), pages 240-253, September.
    • Handle: RePEc:eee:matsoc:v:56:y:2008:i:2:p:240-253
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    References listed on IDEAS

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    1. Balinski, Michel & Ramirez, Victoriano, 1999. "Parametric methods of apportionment, rounding and production," Mathematical Social Sciences, Elsevier, vol. 37(2), pages 107-122, March.
    2. Udo Schwingenschlögl & Friedrich Pukelsheim, 2006. "Seat Biases in Proportional Representation Systems with Thresholds," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 27(1), pages 189-193, August.
    3. N. Gaffke & F. Pukelsheim, 2008. "Vector and matrix apportionment problems and separable convex integer optimization," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 67(1), pages 133-159, February.
    4. 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(2/2005), pages 117-129, February.
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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. Pajala, Tommi & Korhonen, Pekka & Malo, Pekka & Sinha, Ankur & Wallenius, Jyrki & Dehnokhalaji, Akram, 2018. "Accounting for political opinions, power, and influence: A Voting Advice Application," European Journal of Operational Research, Elsevier, vol. 266(2), pages 702-715.

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