Distribution of Decision Power among the Parties and Coalitions in the 44th Bulgarian Parliament as a Weighted Voting Game

  • Zdravko Dimitrov Slavov Varna Free University
Keywords: Election, Bulgarian Parliament, Weighted Voting Game, swing, Power


Weighted voting games are a class of cooperative games that model group decision making systems in various domains, such as parliaments. One of the main challenges in a weighted voting game is to measure of player influence in decision making. This problem is fundamental in game theory and political science. In this paper we consider the 2017 Bulgarian Election and the distribution of decision power among the parties and coalitions in the 44th Bulgarian Parliament.


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[1] Banzhaf III J., Weighted voting doesn’t work: A mathematical analysis, Rutgers Law Review vol. 19 (1965), 317-343.
[2] Barua R., S. Chakravatry, S. Roy, On the Coleman Indices of Voting Power, European Journal of Operational Research vol. 172 (2006), 273-289.
[3] Barua R., S. Chakravatry, P. Sarkar, Minimal-axiom Characterizations of the Coleman and Banzhaf Indices of Voting Power, Mathematical Social Sciences vol. 58 (2009), 367-375.
[4] Burgin M., L. Shapley, Enhanced Banzhaf Power Index and its Mathematical Properties, WP-797, Department of Mathematics, UCLA, 2001.
[5] Coleman J., Control of collectives and the power of a collectivity to act, in B. Lieberman “Social Choice”, New York, Gordon and Breach, 1971, 269-298.
[6] Dubey P., L. Shapley, Mathematical Properties of the Banzhaf Power Index, Mathematics of Operations Research vol. 4 no. 2 (1979), 99-151.
[7] Houy N., W. Zwicker, The Geometry of Voting Power: Weighted Voting and Hyper-Ellipsoids, Games and Economic Behavior vol. 84 (2014), 7-16.
[8] Laruelle A., F. Valenciano, Voting and Collective Decision-Making: Bargaining and Power, Cambridge University Press, 2008.
[9] Masser N., Decision-Making in Committees: Game-Theoretic Analysis, Springer, 2010.
[10] Nurmi H., T. Meskanen, A. Pajala, Calculus of Consent in the EU Council of Ministers, in M. Holler and H. Nurmi “Power, Voting and Voting Power: 30 Years After”, Springer, 2013, 501-520.
[11] Peleg B., Game-Theoretic Analysis of Voting in Committee, in K. Arrow, A. Sen and K. Suzumura “Handbook of Social Choice and Welfare” vol. 1 chap. 8, Elsevier, 2002, 396-423.
[12] Slavov Z., C. Evans, On the Voting Paradox of Luxembourg and Decision Power Indices, Mathematics and Education in Mathematics vol. 43 (2014), 138-144.
[13] Slavov Z., C. Evans, Voting Games with Positive Weights and Dummy Players: Facts and Theory, Applied Mathematical Sciences vol. 10 no. 53 (2016), 2637-2646. doi:10.12988/ams.2016.67209
[14] Von Neumann J., O. Morgenstern, Theory of Games and Economic Behavior, Princeton University Press, 1944.
How to Cite
Slavov, Z. D. (2019). Distribution of Decision Power among the Parties and Coalitions in the 44th Bulgarian Parliament as a Weighted Voting Game. MathLAB Journal, 2(1), 186-195. Retrieved from http://purkh.com/index.php/mathlab/article/view/356
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