Abstract
The most important problem in a practical implementation of degressive proportionality is its ambiguity. Therefore, we introduce an order relation on a set of degressively proportional allocations. Its main idea is to define greater allocations such that emerge from other after transferring a certain quantity of goods from smaller to greater entities contending in distribution. Thus, maximal elements in this ordering are indicated as the sought-after solution sanctioning boundary conditions as the only reason of moving away from the fundamental principle of proportionality. In case of several maximal elements the choice of one allocation remains an open issue, but the cardinality of the set from which we make a choice can be reduced significantly. In the best-known example of application of degressive proportionality, which is the apportionment of seats in the European Parliament, the considered set contains a maximal element. Thereby, there exits an allocation that is nearest to the proportional distribution with respect to transfer relation.
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References
Dniestrzański, P., Łyko, J.: Proportionality in the issue of distribution of seats in the European Parliament. In: Proceedings of the 4th International Conference on Computer Science & Computational Mathematics, pp. 542–546 (2015)
Grimmett, G., Laslier, J.-F., Pukelsheim, F., Ramirez-González, V., Rose, R., Słomczyński, W., Zachariasen, M., Życzkowski, K.: The allocation between the EU member states of the seats in the European Parliament. European Parliament, Directorate-General for Internal Policies, Policy Department C: Citizen’s Rights and Constitutional Affairs, PE 432.760 (2011)
Grimmett, G.R.: European apportionment via the Cambridge Compromise. Math. Soc. Sci. 63, 68–73 (2012)
Gualtieri, R., Trzaskowski, R.: Report on the composition of the European Parliament with a view to the 2014 elections. A7–0041/2013 (2013)
Lamassoure, A., Severin, A.: Report on the composition of the European Parliament. A6–0351/2007 (2007)
Łyko, J., Rudek, R.: A fast exact algorithm for the allocation of seats for the EU Parliament. Expert Syst. Appl. 40, 5284–5291 (2013)
Pukelsheim, F.: Proportional Representation. Apportionment Methods and Their Applications. Springer, Cham (2014)
Serafini, P.: Allocation of the EU Parliament seats via integer linear programming and revised quotas. Math. Soc. Sci. 63, 107–113 (2012)
Treaty of Lisbon. Official Journal of the European Union, C 306, 50 (2007)
Acknowledgement
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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Cegiełka, K., Dniestrzański, P., Łyko, J., Maciuk, A., Rudek, R. (2017). On Ordering a Set of Degressively Proportional Apportionments. In: Mercik, J. (eds) Transactions on Computational Collective Intelligence XXVII. Lecture Notes in Computer Science(), vol 10480. Springer, Cham. https://doi.org/10.1007/978-3-319-70647-4_4
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DOI: https://doi.org/10.1007/978-3-319-70647-4_4
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