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

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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.

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Notes

  1. See the Special Issue ‘Around the Cambridge Compromise: Apportionment in Theory and Practice’, Mathematical Social Sciences, 63(2), 65–192 (March 2012).

  2. Available from http://www.census.gov/population/apportionment/data/.

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Acknowledgements

We are grateful to two anonymous Referees for carefully reading the early versions of this paper and for providing several useful comments.

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  1. DISMI, Università di Modena e Reggio Emilia, Via Amendola 2, 42122, Reggio Emilia, Italy

    Daniele Pretolani

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  1. Daniele Pretolani
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Correspondence to Daniele Pretolani.

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Pretolani, D. Apportionments with minimum Gini index of disproportionality: a Quadratic Knapsack approach. Ann Oper Res 215, 257–267 (2014). https://doi.org/10.1007/s10479-013-1383-7

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