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Operations research methods in political decisions: a case study on the European Parliament composition

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Abstract

In this paper, we show that operations research methods can be successfully applied to support decision-making in politics on the case study of the apportionment of seats in the European Parliament. The related political constraints and assumptions are quantitatively described and the optimization problem is formulated. On this basis, it is revealed that the current composition of the European Parliament as well as some intuitive propositions do not respect degressive proportionality as far as it was assumed. Nevertheless, our algorithm allows us to find better solutions, and among them, there is only one best allocation, which respects degressive proportionality as far as possible, according to the well known and often applied measures. Namely, over 9 thousands allocations consistent with the political requirement “nobody gains and nobody loses more than one” are referred to over 5.4 millions degressively proportional solutions, and only one allocation is revealed to be the best for all defined criteria under given populations of countries.

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Notes

  1. Following Łyko and Rudek (2013): 28 countries, 6 seats for the least populous country, 96 seats for the most populous country, thereby the number of allocations in general to search for feasible solutions can be estimated by the number of the 26-element multisets with elements from the 91-element set, which is defined by the following binomial coefficients \(\big (\big (~\!^{26}_{91}\big )\big )\!=\!\big (~\!^{116}_{~91}\!~\big )\!>\!10^{25}\).

  2. The proposed algorithm was coded in C++ and calculations were run on PC, CPU Intel\(^{\circledR }\) Core\(^{\mathrm{TM}}\)i7-2600K 3.40 GHz and 8GB RAM.

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Acknowledgements

We are grateful to the Editor and the Referees for their valuable comments on an earlier version of our paper. The results presented in this paper have been supported by the Polish National Science Centre under Grant No. DEC-2013/09/B/HS4/02702.

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Authors and Affiliations

  1. Wrocław University of Economics, Komandorska 118/120, 53-345, Wrocław, Poland

    Janusz Łyko & Radosław Rudek

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  1. Janusz Łyko
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  2. Radosław Rudek
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Correspondence to Radosław Rudek.

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Łyko, J., Rudek, R. Operations research methods in political decisions: a case study on the European Parliament composition. Comput Math Organ Theory 23, 572–586 (2017). https://doi.org/10.1007/s10588-017-9243-7

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