The Shapley value as a function of the quota in weighted voting games

IJCAI International Joint Conference on Artificial Intelligence

Volumn , Issue , 2011, Pages 490-495

  Zick, Yair ^a   Skopalik, Alexander ^a   Elkind, Edith ^a  

^a NANYANG TECHNOLOGICAL UNIVERSITY   (Singapore)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMIC ISSUES; SHAPLEY; SHAPLEY VALUE; WEIGHT DISTRIBUTIONS; WEIGHTED VOTING GAMES;

ALGORITHMS; ARTIFICIAL INTELLIGENCE;

GAME THEORY;

EID: 80055066194     PISSN: 10450823     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.5591/978-1-57735-516-8/IJCAI11-089     Document Type: Conference Paper

References (20)

1. H. Aziz, Y. Bachrach, E. Elkind, and M. Paterson. False-name manipulations in weighted voting games. Journal of Artificial Intelligence Research, 40:57-93, 2011.
2. Y. Bachrach, E. Markakis, E. Resnick, A.D. Procaccia, J.S. Rosenschein, and A. Saberi. Approximating power indices: theoretical and empirical analysis. AAMAS, 20(2):105-122, 2010.
3. J.F. Banzhaf. Weighted voting doesn't work: a mathematical analysis. Rutgers Law Review, 19:317-343, 1965.
4. X. Deng and C.H. Papadimitriou. On the complexity of cooperative solution concepts. Mathematics of Operations Research, 19(2):257-266, 1994.
5. P. Dubey and L.S. Shapley. Mathematical properties of the Banzhaf power index. Mathematics of Operations Research, 4(2):99-131, 1979.
6. P. Faliszewski and L. Hemaspaandra. The complexity of power-index comparison. Theoretical Computer Science, 410(1):101-107, 2009.
7. S.S. Fatima, M. Wooldridge, and N.R. Jennings. A linear approximation method for the Shapley value. Artificial Intelligence, 172(14):1673-1699, 2008.
8. D. S. Felsenthal and M. Machover. The Measurement of Voting Power: Theory and Practice, Problems and Paradoxes. Edward Elgar Publishing, 1998.
9. M.R. Garey and D.S. Johnson. Computers and Intractibility. W.H. Freeman and Company, 1979.
10. D. Leech and M. Machover. Qualified majority voting: the effect of the quota. LSE Research Online, 2003.
11. D. Leech. Computation of power indices. Warwick Economic Research Papers, 2002.
12. D. Leech. Designing the voting system for the council of the European Union. Public Choice, 113:437-464, 2002. (Pubitemid 37133434)
13. M. Machover. Penrose's square-root rule and the EU council of ministers: Significance of the quota. Distribution of power and voting procedures in the EU, 2007.
14. I. Mann and L.S. Shapley. Values of Large Games VI: Evaluating the Electoral College Exactly. The RAND Corporation, 1962.
15. Y. Matsui and T. Matsui. NPcompleteness for calculating power indices of weighted majority games. Theoretical Computer Science, 263(1-2):305-310, 2001. (Pubitemid 32698602)
16. S. Merrill. Approximations to the Banzhaf index. American Mathematical Monthly, 89:108-110, 1982.
17. K. Prasad and J.S. Kelly. NP-completeness of some problems concerning voting games. International Journal of Game Theory, 19:1-9, 1990.
18. L.S. Shapley and M. Shubik. A method for evaluating the distribution of power in a committee system. Am Polit Sci Rev, 48(3):787-792, 1954.
19. L.S. Shapley. A value for n-person games. In Contributions to the Theory of Games, vol. 2, Annals of Mathematics Studies, no. 28, pages 307-317. PUP, 1953.
20. M. Zuckerman, P. Faliszewski, Y. Bachrach, and E. Elkind. Manipulating the quota in weighted voting games. AAAI, 1:215-220, 2008.