Seat Apportionment by Population and Contribution in European Parliament After Brexit

  • Cesarino Bertini
  • Gianfranco Gambarelli
  • Izabella StachEmail author
  • Giuliana Zibetti
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11890)


The problem of apportioning seats to member countries of the European Parliament after Brexit and in view of new accessions/exits is delicate, as countries with strong economies (and their consequent large contributions to the European Union) require that they have greater representative weight in the European Parliament. In this paper, we propose a model for seat apportionment in the European Parliament, which assigns seats taking into account both the percentages of the populations and the percentages of the contributions by each member state to the European Union budget by means of a linear combination of these two quantities. The proposed model is a modification of the approach given by Bertini, Gambarelli, and Stach in 2005. Using the new model, we studied the power position of each European Union member state before and after the exit of the United Kingdom using the Banzhaf power index. A short latest-literature review on this topic is given.


Apportionments Brexit Cooperative game theory European Parliament Power indices 



This research is financed by the funds (No. of AGH University of Science and Technology, MIUR, research grants from the University of Bergamo, and the GNAMPA group of INDAM.

The authors would like to thank the anonymous reviewers for their numerous comments and suggestions that led us to improving this paper.


  1. 1.
    Bertini, C., Gambarelli, G., Stach, I.: Apportionment strategies for the European Parliament. In: Gambarelli, G., Holler, M. (eds.) Power Measures III, a Special Issue of Homo Oeconomicus, vol. 22, pp. 589–604. Accedo Verlagsgesellschaft, München (2005). Reprinted in: Holler, M.J., Nurmi, H. (eds.) Power, Voting, and Voting Power: 30 Years After, pp. 541–552. Springer-Verlag, Heidelberg (2013)Google Scholar
  2. 2.
    Bertini, C., Gambarelli, G., Stach, I.: A method of seat distribution in the European Parliament. In: Łebkowski, P. (ed.) Zarządzanie przedsiębiorstwem. Teoria i praktyka 2014, pp. 271–280. AGH University of Science and Technology Press, Kraków (2014)Google Scholar
  3. 3.
    Bilbao, J.M., Fernández, J.R., Jiménez Losada, A., López, J.J.: Generating functions for computing power indices efficiently. Top 8(2), 191–213 (2000)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Mercik, J., Ramsey, D.M.: The effect of Brexit on the balance of power in the European Union Council: an approach based on pre-coalitions. In: Mercik, J. (ed.) Transactions on Computational Collective Intelligence XXVII. LNCS, vol. 10480, pp. 87–107. Springer, Cham (2017). Scholar
  5. 5.
    Shapley, L.S., Shubik, M.: A method for evaluating the distribution of power in a committee system. Am. Polit. Sci. Rev. 48, 787–792 (1954)CrossRefGoogle Scholar
  6. 6.
    Stach, I.: Shapley-Shubik index. In: Dowding, K. (ed.) Encyclopedia of Power, pp. 603–606. SAGE Publications, Los Angeles (2011)Google Scholar
  7. 7.
    Banzhaf, J.F.: Weighted voting doesn’t work. A mathematical analysis. Rutgers Law Rev. 19, 317–343 (1965)Google Scholar
  8. 8.
    Johnston, R.J.: On the measurement of power: some reactions to Laver. Environ. Plann. A 10, 907–914 (1978)CrossRefGoogle Scholar
  9. 9.
    Gładysz, B., Mercik, J., Ramsey, D.M.: The effect of Brexit on the balance of power in the European Union Council revisited: a fuzzy multicriteria attempt. In: Nguyen, N.T., Kowalczyk, R., Mercik, J., Motylska-Kuźma, A. (eds.) Transactions on Computational Collective Intelligence XXXI. LNCS, vol. 11290, pp. 80–91. Springer, Heidelberg (2018). Scholar
  10. 10.
    Kóczy, L.Á.: How Brexit affects European Union power distribution. Discussion Papers (MTDP-2016/11), Institute of Economics, Centre for Economic and Regional Studies, Hungarian Academy of Sciences, Budapest (2016)Google Scholar
  11. 11.
    Petróczy, D.G., Rogers, M.F., Kóczy, L.Á.: Brexit: the belated threat. arXiv:1808.05142v1 [econ.GN], 14 August 2018
  12. 12.
    Bertini, C., Stach, I.: Banzhaf voting power measure. In: Dowding, K. (ed.) Encyclopedia of Power, pp. 54–55. SAGE Publications, Los Angeles (2011)Google Scholar
  13. 13.
    EU elections: how many MEPs will each country get in 2019, News. European Parliament, EU affairs 01-02-2018 10:21 (2018).
  14. 14.
  15. 15.
    Keep, M.: A guide to the EU budget. Briefing Paper 06455 (2018). Accessed 28 Oct 2018
  16. 16.
  17. 17.
  18. 18.
    Gambarelli, G.: Minimax apportionments. Group Decis. Negot. 8(6), 441–461 (1999)CrossRefGoogle Scholar
  19. 19.
    Holler, M.J.: Forming coalitions and measuring voting power. Polit. Stud. 30, 262–271 (1982)CrossRefGoogle Scholar
  20. 20.
    Holler, M.J., Packel, E.W.: Power, luck and the right index. Zeitschrift für Nationalökonomie, J. Econ. 43, 21–29 (1983)CrossRefGoogle Scholar
  21. 21.
    Bertini, C., Freixas, J., Gambarelli, G., Stach, I.: Comparing power indices. Int. Game Theory Rev. 15(2), 13400041–134000419 (2013)MathSciNetzbMATHGoogle Scholar
  22. 22.
    Stach, I.: Sub-coalitional approach to values. In: Mercik, J. (ed.) Transactions on Computational Collective Intelligence XXVII. LNCS, vol. 10480, pp. 74–86. Springer, Cham (2017). Scholar
  23. 23.
    Owen, G.: Values of games with a priori unions. In: Henn, R., Moeschlin, O. (eds.) Essays in Mathematical Economics and Game Theory, vol. 141, pp. 76–88. Springer, Heidelberg (1977). Scholar
  24. 24.
    Owen, G.: Modification of the Banzhaf-Coleman index for games with a priori unions. In: Holler, M.J. (ed.) Power, Voting, and Voting Power, pp. 232–238. Physica, Würzburg (1982)Google Scholar
  25. 25.
    Życzkowski, K., Słomczyński, W.: Voting in the European Union: the square root system of Penrose and a critical point and optimal quota. arXiv:cond-mat/0405396 [cond-mat.other] (2004)
  26. 26.
    Słomczyński, W., Życzkowski, K.: Penrose voting system and optimal quota. Acta Physica Polonica B37(11), 3133–3143 (2006)Google Scholar
  27. 27.
    Słomczyński, W., Życzkowski, K.: Jagiellonian compromise – an alternative voting system for the council of the European Union. In: Życzkowski, K. (ed.) Institutional Design and Voting Power in the European Union, pp. 43–57. Routledge, London (2011)Google Scholar
  28. 28.
    Penrose, L.S.: The elementary statistics of majority voting. J. Roy. Stat. Soc. 109(1), 53–57 (1946)CrossRefGoogle Scholar
  29. 29.
    Penrose, L.S.: On the Objective Study of Crowd Behaviour. H.K. Lewis, London (1952)Google Scholar
  30. 30.
    Kirsch, W., Życzkowski, K., Słomczyński, W.: Getting the votes right. Eur. Voice 13(17), 12 (2007)Google Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Management, Economics and Quantitative MethodsUniversity of BergamoBergamoItaly
  2. 2.AGH University of Science and TechnologyKrakowPoland
  3. 3.Institute Leonardo da VinciBergamoItaly

Personalised recommendations