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Mathematical aspects of degressive proportionality

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  • Słomczyński, Wojciech
  • Życzkowski, Karol

Abstract

We analyze mathematical properties of apportionment functions in the context of allocating seats in the European Parliament. Some exemplary families of such functions are specified and the corresponding allocations of seats among the Member States of the European Union are presented. We show that the constitutional constraints for the apportionment are so strong that the admissible functions lead to rather similar solutions.

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  • Słomczyński, Wojciech & Życzkowski, Karol, 2012. "Mathematical aspects of degressive proportionality," Mathematical Social Sciences, Elsevier, vol. 63(2), pages 94-101.
    • Handle: RePEc:eee:matsoc:v:63:y:2012:i:2:p:94-101
    DOI: 10.1016/j.mathsocsci.2011.12.002
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    1. Katarzyna Cegielka & Piotr Dniestrzanski & Arkadiusz Maciuk & Maciej Szczecinski, 2022. "The Implications of Possible Enlargements of the European Union for the Configuration of Power in the European Parliament," European Research Studies Journal, European Research Studies Journal, vol. 0(2), pages 145-159.
    2. Janusz Łyko & Radosław Rudek, 2017. "Operations research methods in political decisions: a case study on the European Parliament composition," Computational and Mathematical Organization Theory, Springer, vol. 23(4), pages 572-586, December.
    3. Blanca L Delgado-Márquez & Michael Kaeding & Antonio Palomares, 2013. "A more balanced composition of the European Parliament with degressive proportionality," European Union Politics, , vol. 14(3), pages 458-471, September.
    4. Katarzyna Cegiełka & Piotr Dniestrzański & Janusz Łyko & Arkadiusz Maciuk & Maciej Szczeciński, 2021. "A neutral core of degressively proportional allocations under lexicographic preferences of agents," Eurasian Economic Review, Springer;Eurasia Business and Economics Society, vol. 11(4), pages 667-685, December.
    5. Wenruo Lyu & Liang Zhao, 2023. "Axioms and Divisor Methods for a Generalized Apportionment Problem with Relative Equality," Mathematics, MDPI, vol. 11(15), pages 1-13, July.
    6. Macé, Antonin & Treibich, Rafael, 2012. "Computing the optimal weights in a utilitarian model of apportionment," Mathematical Social Sciences, Elsevier, vol. 63(2), pages 141-151.
    7. Katarzyna Cegiełka & Janusz Łyko & Radosław Rudek, 2019. "Beyond the Cambridge Compromise algorithm towards degressively proportional allocations," Operational Research, Springer, vol. 19(2), pages 317-332, June.

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