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Algorithms for Biproportional Apportionment

In: Mathematics and Democracy

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  • Sebastian Maier

    (Universität Augsburg)

Abstract

For the biproportional apportionment problem two algorithms are discussed, that are implemented in the Augsburg BAZI program, the alternating scaling algorithm and the tie-and-transfer algorithm of Balinski and Demange (1989b). The goal is to determine an integer-valued apportionment matrix that is “proportional to” a matrix of input weights (e.g. vote counts) and that at the same time achieves prespecified row and column marginals. The alternating scaling algorithm finds the solution of most of the practical problems very efficiently. However, it is possible to create examples for which the procedure fails. The tie-and-transfer algorithm converges always, though convergence may be slow. In order to make use of the benefits of both algorithms, a hybrid version is proposed.

Suggested Citation

  • Sebastian Maier, 2006. "Algorithms for Biproportional Apportionment," Studies in Choice and Welfare, in: Bruno Simeone & Friedrich Pukelsheim (ed.), Mathematics and Democracy, pages 105-116, Springer.
    • Handle: RePEc:spr:stcchp:978-3-540-35605-9_8
    DOI: 10.1007/3-540-35605-3_8
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    Citations

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    Cited by:

    1. Sebastian Maier & Petur Zachariassen & Martin Zachariasen, 2010. "Divisor-Based Biproportional Apportionment in Electoral Systems: A Real-Life Benchmark Study," Management Science, INFORMS, vol. 56(2), pages 373-387, February.
    2. V. I. Blanutsa & K. A. Cherepanov, 2019. "Regional Information Flows: Existing and New Approaches to Geographical Study," Regional Research of Russia, Springer, vol. 9(1), pages 97-106, January.
    3. Gaffke, Norbert & Pukelsheim, Friedrich, 2008. "Divisor methods for proportional representation systems: An optimization approach to vector and matrix apportionment problems," Mathematical Social Sciences, Elsevier, vol. 56(2), pages 166-184, September.

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