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Apportionments with minimum Gini index of disproportionality: a Quadratic Knapsack approach

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  • Daniele Pretolani

Abstract

The ultimate goal of proportional apportionment methods is the minimization of disproportionality, i.e., unequal distribution of political representation among voters, or citizens. The Gini index is a well known tool for measuring inequality. In this work we propose a quotient method that minimizes the Gini index of disproportionality. Our method reduces the rounding of quotas to an instance of quadratic knapsack, a widely studied combinatorial optimization problem. Preliminary computational results, including real cases from the EU Parliament and the US House of Representatives, show that the method is effective, since the instances to solve are rather easy. Copyright Springer Science+Business Media New York 2014

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  • 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.
    • Handle: RePEc:spr:annopr:v:215:y:2014:i:1:p:257-267:10.1007/s10479-013-1383-7
    DOI: 10.1007/s10479-013-1383-7
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    1. W. David Pisinger & Anders Bo Rasmussen & Rune Sandvik, 2007. "Solution of Large Quadratic Knapsack Problems Through Aggressive Reduction," INFORMS Journal on Computing, INFORMS, vol. 19(2), pages 280-290, May.
    2. Alberto Caprara & David Pisinger & Paolo Toth, 1999. "Exact Solution of the Quadratic Knapsack Problem," INFORMS Journal on Computing, INFORMS, vol. 11(2), pages 125-137, May.
    3. Grimmett, Geoffrey R., 2012. "European apportionment via the Cambridge Compromise," Mathematical Social Sciences, Elsevier, vol. 63(2), pages 68-73.
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    2. 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.

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