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Voting power in the Council of the European Union: A comprehensive sensitivity analysis

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  • D'ora Gr'eta Petr'oczy
  • L'aszl'o Csat'o

Abstract

The Council of the European Union (EU) is one of the main decision-making bodies of the EU. A number of decisions require a qualified majority, the support of 55% of the member states (currently 15) that represent at least 65% of the total population. We investigate how the power distribution based on the Shapley--Shubik index and the proportion of winning coalitions change if these criteria are modified within reasonable bounds. The power of the two countries, with approximately 4% of the total population each, is found to be almost flat. The decisiveness index decreases if the population criterion is above 68\% or the states criterion is at least 17. Some quota combinations contradict the principles of double majority. The proportion of winning coalitions can be increased from 13.2% to 20.8% (30.1%) such that the maximal relative change in the Shapley--Shubik indices remains below 3.5% (5.5%). Our results are indispensable for evaluating any proposal to reform the qualified majority voting system.

Suggested Citation

  • D'ora Gr'eta Petr'oczy & L'aszl'o Csat'o, 2023. "Voting power in the Council of the European Union: A comprehensive sensitivity analysis," Papers 2312.16878, arXiv.org, revised Jan 2026.
    • Handle: RePEc:arx:papers:2312.16878
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    1. Bilbao, J. M. & Fernandez, J. R. & Jimenez, N. & Lopez, J. J., 2002. "Voting power in the European Union enlargement," European Journal of Operational Research, Elsevier, vol. 143(1), pages 181-196, November.
    2. Bindseil, Ulrich & Hantke, Cordula, 1997. "The power distribution in decision making among EU member states," European Journal of Political Economy, Elsevier, vol. 13(1), pages 171-185, February.
    3. Le Breton, Michel & Montero, Maria & Zaporozhets, Vera, 2012. "Voting power in the EU council of ministers and fair decision making in distributive politics," Mathematical Social Sciences, Elsevier, vol. 63(2), pages 159-173.
    4. Annick Laruelle & Federico Valenciano, 2001. "Shapley-Shubik and Banzhaf Indices Revisited," Mathematics of Operations Research, INFORMS, vol. 26(1), pages 89-104, February.
    5. André Casajus & Frank Huettner, 2019. "The Coleman–Shapley index: being decisive within the coalition of the interested," Public Choice, Springer, vol. 181(3), pages 275-289, December.
    6. Manfred Holler & Stefan Napel, 2005. "Local monotonicity of power: Axiom or just a property?," Quality & Quantity: International Journal of Methodology, Springer, vol. 38(5), pages 637-647, January.
    7. SCHMEIDLER, David, 1969. "The nucleolus of a characteristic function game," LIDAM Reprints CORE 44, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    8. Rana Barua & Satya R. Chakravarty & Sonali Roy, 2009. "A Note On The Carreras-Coleman Decisiveness Index," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 11(02), pages 237-245.
    9. Heikki Kauppi & Mika Widgrén, 2004. "What determines EU decision making? Needs, power or both? [‘Implications of the EC expansion for European agricultural policies, trade and welfare’]," Economic Policy, CEPR, CESifo, Sciences Po;CES;MSH, vol. 19(39), pages 222-266.
    10. Agnieszka Szczypinska, 2018. "Who Gains More Power in the EU after Brexit?," Czech Journal of Economics and Finance (Finance a uver), Charles University Prague, Faculty of Social Sciences, vol. 68(1), pages 18-33, February.
    11. Widgren, Mika, 1994. "Voting power in the EC decision making and the consequences of two different enlargements," European Economic Review, Elsevier, vol. 38(5), pages 1153-1170, May.
    12. Philip Straffin, 1977. "Homogeneity, independence, and power indices," Public Choice, Springer, vol. 30(1), pages 107-118, June.
    13. repec:bla:ecpoli:v:19:y:2004:i:39:p:221-266 is not listed on IDEAS
    14. Philip D. Grech, 2021. "Power in the Council of the EU: organizing theory, a new index, and Brexit," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 56(2), pages 223-258, February.
    15. Dan S. Felsenthal & Moshé Machover, 1998. "The Measurement of Voting Power," Books, Edward Elgar Publishing, number 1489.
    16. Zaporozhets, Vera & García-Valiñas, María & Kurz, Sascha, 2016. "Key drivers of EU budget allocation: Does power matter?," European Journal of Political Economy, Elsevier, vol. 43(C), pages 57-70.
    17. Laruelle, Annick & Widgren, Mika, 1998. "Is the Allocation of Voting Power among EU States Fair?," Public Choice, Springer, vol. 94(3-4), pages 317-339, March.
    18. Stefano Benati & Giuseppe Vittucci Marzetti, 2013. "Probabilistic spatial power indexes," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 40(2), pages 391-410, February.
    19. Ori Haimanko, 2020. "Generalized Coleman-Shapley indices and total-power monotonicity," International Journal of Game Theory, Springer;Game Theory Society, vol. 49(1), pages 299-320, March.
    20. Werner Kirsch, 2022. "The distribution of power within the EU: perspectives on a Ukrainian accession and a Turkish accession," International Economics and Economic Policy, Springer, vol. 19(2), pages 401-409, May.
    21. Werner Kirsch & Wojciech S{l}omczy'nski & Dariusz Stolicki & Karol .Zyczkowski, 2018. "Double Majority and Generalized Brexit: Explaining Counterintuitive Results," Papers 1812.07048, arXiv.org.
    22. Moshé Machover & Dan S. Felsenthal, 2001. "The Treaty of Nice and qualified majority voting," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 18(3), pages 431-464.
    23. Algaba, E. & Bilbao, J.M. & Fernandez, J.R., 2007. "The distribution of power in the European Constitution," European Journal of Operational Research, Elsevier, vol. 176(3), pages 1752-1766, February.
    24. Laruelle, Annick & Valenciano, Federico, 2009. "Cooperative bargaining foundations of the Shapley-Shubik index," Games and Economic Behavior, Elsevier, vol. 65(1), pages 242-255, January.
    25. Stefano Benati & Giuseppe Vittucci Marzetti, 2021. "Voting power on a graph connected political space with an application to decision-making in the Council of the European Union," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 57(4), pages 733-761, November.
    26. Freixas, J., 2004. "The dimension for the European Union Council under the Nice rules," European Journal of Operational Research, Elsevier, vol. 156(2), pages 415-419, July.
    27. Alonso-Meijide, J.M. & Bilbao, J.M. & Casas-Méndez, B. & Fernández, J.R., 2009. "Weighted multiple majority games with unions: Generating functions and applications to the European Union," European Journal of Operational Research, Elsevier, vol. 198(2), pages 530-544, October.
    28. Kóczy, László Á., 2012. "Beyond Lisbon: Demographic trends and voting power in the European Union Council of Ministers," Mathematical Social Sciences, Elsevier, vol. 63(2), pages 152-158.
    29. László Á. Kóczy, 2021. "Brexit and Power in the Council of the European Union," Games, MDPI, vol. 12(2), pages 1-10, June.
    30. Kurz, Sascha & Maaser, Nicola & Napel, Stefan, 2018. "Fair representation and a linear Shapley rule," Games and Economic Behavior, Elsevier, vol. 108(C), pages 152-161.
    31. Shapley, L. S. & Shubik, Martin, 1954. "A Method for Evaluating the Distribution of Power in a Committee System," American Political Science Review, Cambridge University Press, vol. 48(3), pages 787-792, September.
    32. Dan S. Felsenthal & Moshé Machover, 2004. "A Priori Voting Power: What Is It All About?," Political Studies Review, Political Studies Association, vol. 2(1), pages 1-23, January.
    33. Dóra Gréta Petróczy & Mark Francis Rogers & László Á. Kóczy, 2022. "Exits from the European Union and Their Effect on Power Distribution in the Council," Games, MDPI, vol. 13(1), pages 1-25, February.
    34. Carreras, Francesc, 2005. "A decisiveness index for simple games," European Journal of Operational Research, Elsevier, vol. 163(2), pages 370-387, June.
    35. 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.
    36. Fuad Aleskerov & Manfred Holler & Rita Kamalova, 2014. "Power distribution in the Weimar Reichstag in 1919–1933," Annals of Operations Research, Springer, vol. 215(1), pages 25-37, April.
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    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • D72 - Microeconomics - - Analysis of Collective Decision-Making - - - Political Processes: Rent-seeking, Lobbying, Elections, Legislatures, and Voting Behavior

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