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Network models and biproportional rounding for fair seat allocations in the UK elections

Author

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  • Kerem Akartunalı

    (University of Strathclyde)

  • Philip A. Knight

    (University of Strathclyde)

Abstract

Systems for allocating seats in an election offer a number of socially and mathematically interesting problems. We discuss how to model the allocation process as a network flow problem, and propose a wide choice of objective functions and allocation schemes. Biproportional rounding, which is an instance of the network flow problem, is used in some European countries with multi-seat constituencies. We discuss its application to single seat constituencies and the inevitable consequence that seats are allocated to candidates with little local support. However, we show that variants can be selected, such as regional apportionment, to mitigate this problem. In particular, we introduce a parameter based family of methods, which we call balanced majority voting, that can be tuned to meet the public’s demand for local and global “fairness”. Using data from the 2010 to 2015 UK general elections, we study a variety of network models and implementations of biproportional rounding, and address conditions of existence and uniqueness.

Suggested Citation

  • Kerem Akartunalı & Philip A. Knight, 2017. "Network models and biproportional rounding for fair seat allocations in the UK elections," Annals of Operations Research, Springer, vol. 253(1), pages 1-19, June.
    • Handle: RePEc:spr:annopr:v:253:y:2017:i:1:d:10.1007_s10479-016-2323-0
    DOI: 10.1007/s10479-016-2323-0
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    References listed on IDEAS

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    1. Hannu Nurmi, 2014. "Some remarks on the concept of proportionality," Annals of Operations Research, Springer, vol. 215(1), pages 231-244, April.
    2. 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.
    3. Friedrich Pukelsheim, 2014. "Biproportional scaling of matrices and the iterative proportional fitting procedure," Annals of Operations Research, Springer, vol. 215(1), pages 269-283, April.
    4. 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.
    5. Daniele Pretolani, 2014. "Apportionments with minimum Gini index of disproportionality: a Quadratic Knapsack approach," Annals of Operations Research, Springer, vol. 215(1), pages 257-267, April.
    6. Balinski, M. L. & Young, H. P., 1978. "Stability, Coalitions and Schisms in Proportional Representation Systems," American Political Science Review, Cambridge University Press, vol. 72(3), pages 848-858, September.
    7. 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.
    8. repec:spr:pharme:v:21:y:2003:i:12:p:839-851 is not listed on IDEAS
    9. Federica Ricca & Andrea Scozzari & Paolo Serafini & Bruno Simeone, 2012. "Error minimization methods in biproportional apportionment," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 20(3), pages 547-577, October.
    10. Lamond, B. & Stewart, N. F., 1981. "Bregman's balancing method," Transportation Research Part B: Methodological, Elsevier, vol. 15(4), pages 239-248, August.
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