Distribution of Decision Power among the Parties and Coalitions in the 44th Bulgarian Parliament as a Weighted Voting Game
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.
 Barua R., S. Chakravatry, S. Roy, On the Coleman Indices of Voting Power, European Journal of Operational Research vol. 172 (2006), 273-289.
 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.
 Burgin M., L. Shapley, Enhanced Banzhaf Power Index and its Mathematical Properties, WP-797, Department of Mathematics, UCLA, 2001.
 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.
 Dubey P., L. Shapley, Mathematical Properties of the Banzhaf Power Index, Mathematics of Operations Research vol. 4 no. 2 (1979), 99-151.
 Houy N., W. Zwicker, The Geometry of Voting Power: Weighted Voting and Hyper-Ellipsoids, Games and Economic Behavior vol. 84 (2014), 7-16.
 Laruelle A., F. Valenciano, Voting and Collective Decision-Making: Bargaining and Power, Cambridge University Press, 2008.
 Masser N., Decision-Making in Committees: Game-Theoretic Analysis, Springer, 2010.
 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.
 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.
 Slavov Z., C. Evans, On the Voting Paradox of Luxembourg and Decision Power Indices, Mathematics and Education in Mathematics vol. 43 (2014), 138-144.
 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
 Von Neumann J., O. Morgenstern, Theory of Games and Economic Behavior, Princeton University Press, 1944.
Copyright (c) 2019 Zdravko Dimitrov Slavov
This work is licensed under a Creative Commons Attribution 4.0 International License.
Please find the rights and licenses into Chemistry Journal
All articles published in this journal are licensed under a Creative Commons Attribution 4.0 International License.
2. Author’s Warranties
The author warrants that the article is original, written by stated author(s), has not been published before, contains no unlawful statements, does not infringe the rights of others, is subject to copyright that is vested exclusively in the author and free of any third party rights, and that any necessary written permissions to quote from other sources have been obtained by the author(s).
3. User Rights
To Chemistry Journal's spirit is to disseminate articles published are as free as possible. Under the Creative Commons Attribution 4.0 International License., which permits unrestricted use, distribution, and reproduction in any medium, provided that the original work is properly cited.
4. Rights of Authors
Authors retain the following rights:
- Copyright, and other proprietary rights relating to the article, such as patent rights,
- The right to use the substance of the article in future own works, including lectures and books,
- The right to reproduce the article for own purposes,
- The right to self-archive the article,
- the right to enter into separate, additional contractual arrangements for the non-exclusive distribution of the article's published version (e.g., post it to an institutional repository or publish it in a book), with an acknowledgment of its initial publication in this journal (To Chemistry Journal ).
If the article was jointly prepared by other authors, the signatory of this form warrants that he/she has been authorized by all co-authors to sign this agreement on their behalf, and agrees to inform his/her co-authors of the terms of this agreement.
This agreement entitles the author to no royalties or other fees. To such extent as legally permissible, the author waives his or her right to collect royalties relative to the article in respect of any use of the article by To Chemistry Journal or its sublicensee.
To Chemistry Journal will publish the article (or have it published) in the journal if the article’s editorial process is successfully completed and To Chemistry Journal has become obligated to have the article published. To Chemistry Journal may conform the article to a style of punctuation, spelling, capitalization, referencing and usage that it deems appropriate. The author acknowledges that the article may be published so that it will be publicly accessible and such access will be free of charge for the readers.