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A numerical method to determine a degressive proportional distribution of seats in the European Parliament

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  • Florek, Jan

Abstract

Distribution of seats in the European Parliament postulated by the Treaty of Lisbon should be degressively proportional. We propose a numerical method which determines uniquely a distribution of seats in the European Parliament which fulfil the requirements of degressive proportionality. More generally, let li, 1≤i≤n, be any non-increasing sequence of real positive numbers. We say that a sequence of positive integers mi is degressively proportional with respect to the sequence li, if mi and limi are non-increasing sequences. For fixed positive integer M we determine inductively a sequence Mi degressively proportional with respect to li which is smaller, then any other such sequence with the first element ≥M. Moreover, for every integer ∑i=1nMi≤Y≤nM we determine a degressively proportional sequence mi with respect to li, which has the first element m1=M and satisfies inequalities Y−(n−2)≤∑i=1nmi≤Y.

Suggested Citation

  • Florek, Jan, 2012. "A numerical method to determine a degressive proportional distribution of seats in the European Parliament," Mathematical Social Sciences, Elsevier, vol. 63(2), pages 121-129.
    • Handle: RePEc:eee:matsoc:v:63:y:2012:i:2:p:121-129
    DOI: 10.1016/j.mathsocsci.2011.07.003
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    References listed on IDEAS

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    1. Dominique Lepelley & N. Andjiga & F. Chantreuil, 2003. "La mesure du pouvoir de vote," Post-Print halshs-00069255, HAL.
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    4. Victoriano Ramírez & Antonio Palomares & Maria L. Márquez, 2006. "Degressively Proportional Methods for the Allotment of the European Parliament Seats Amongst the EU Member States," Studies in Choice and Welfare, in: Bruno Simeone & Friedrich Pukelsheim (ed.), Mathematics and Democracy, pages 205-220, Springer.
    5. Leech, Dennis, 2002. "Designing the Voting System for the Council of the European Union," Public Choice, Springer, vol. 113(3-4), pages 437-464, December.
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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. Zéphirin Nganmeni & Roland Pongou & Bertrand Tchantcho & Jean‐Baptiste Tondji, 2022. "Vaccine and inclusion," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 24(5), pages 1101-1123, October.
      • Zéphirin Nganmeni & Roland Pongou & Bertrand Tchantcho & Jean‐baptiste Tondji, 2022. "Vaccine and inclusion," Post-Print hal-04257703, HAL.
      • Zéphirin Nganmeni & Roland Pongou & Bertrand Tchantcho & Jean-Baptiste Tondji, 2022. "Vaccine and Inclusion," Working Papers 2202E Classification-C62,, University of Ottawa, Department of Economics.
    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. Słomczyński, Wojciech & Życzkowski, Karol, 2012. "Mathematical aspects of degressive proportionality," Mathematical Social Sciences, Elsevier, vol. 63(2), pages 94-101.
    6. Ramírez-González, Victoriano, 2012. "Seat distribution in the European Parliament according to the Treaty of Lisbon," Mathematical Social Sciences, Elsevier, vol. 63(2), pages 130-135.
    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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