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Volumn 20, Issue 2, 2010, Pages 105-122

Approximating power indices: Theoretical and empirical analysis

Author keywords

Banzhaf power index; Coalitional games; Power index; Power index approximation; Power indices; Shapley value; Shapley Shubik power index

Indexed keywords


EID: 77953321432     PISSN: 13872532     EISSN: 15737454     Source Type: Journal    
DOI: 10.1007/s10458-009-9078-9     Document Type: Article
Times cited : (126)

References (32)
  • 1
    • 77953322254 scopus 로고    scopus 로고
    • Abramowitz, M., & Stegun, I. A. (1964). Handbook of mathematical functions with formulas, graphs, and mathematical tables (ninth dover printing, tenth gpo printing ed.). New York: Dover.
  • 2
    • 84899967235 scopus 로고    scopus 로고
    • Bachrach, Y., Markakis, V., Procaccia, A. D., Rosenschein, J. S., & Saberi, A. (2008). Approximating power indices. In The seventh international joint conference on autonomous agents and multiagent systems (AAMAS 2008), 12-16 May, Estoril, Portugal (pp. 943-950).
  • 3
    • 77953323642 scopus 로고    scopus 로고
    • Bachrach, Y., & Rosenschein, J. S. (2007). Computing the Banzhaf power index in network flow games. In The sixth international joint conference on autonomous agents and multiagent systems (AAMAS 2007), 14-18 May, Honolulu, Hawaii (pp. 323-329).
  • 4
    • 0000265025 scopus 로고
    • Weighted voting doesn't work: A mathematical analysis
    • Banzhaf J. F. (1965) Weighted voting doesn't work: A mathematical analysis. Rutgers Law Review 19: 317-343.
    • (1965) Rutgers Law Review , vol.19 , pp. 317-343
    • Banzhaf, J.F.1
  • 5
    • 77953323123 scopus 로고    scopus 로고
    • Barua, R., Chakravarty, S. R., & Roy, S. (2007, May). Measuring power in weighted majority games. Staff general research papers, Department of Economics, Iowa State University.
  • 7
    • 0038249934 scopus 로고    scopus 로고
    • Generating functions for computing power indices efficiently
    • Bilbao J. M., Fernandez J. R., Losada A. J., Lopez J. J. (2000) Generating functions for computing power indices efficiently. TOP 8(2): 191-213.
    • (2000) Top , vol.8 , Issue.2 , pp. 191-213
    • Bilbao, J.M.1    Fernandez, J.R.2    Losada, A.J.3    Lopez, J.J.4
  • 11
    • 0002877568 scopus 로고
    • Mathematical properties of the Banzhaf power index
    • Dubey P., Shapley L. (1979) Mathematical properties of the Banzhaf power index. Mathematics of Operations Research 4(2): 99-131.
    • (1979) Mathematics of Operations Research , vol.4 , Issue.2 , pp. 99-131
    • Dubey, P.1    Shapley, L.2
  • 12
    • 77953326898 scopus 로고    scopus 로고
    • Faliszewski, P., & Hemaspaandra, L. A. (2008). The complexity of power-index comparison. CoRR, abs/0801. 4585.
  • 13
    • 77953325095 scopus 로고    scopus 로고
    • Fatima, S. S., Wooldridge, M., & Jennings, N. R. (2007). A randomized method for the Shapley value for the voting game. In The sixth international joint conference on autonomous agents and multiagent systems (AAMAS 2007), 14-18 May, Honolulu, Hawaii (pp. 955-962).
  • 14
    • 47649117256 scopus 로고    scopus 로고
    • A linear approximation method for the shapley value
    • Fatima S. S., Wooldridge M., Jennings N. R. (2008) A linear approximation method for the shapley value. Artificial Intelligence 172(14): 1673-1699.
    • (2008) Artificial Intelligence , vol.172 , Issue.14 , pp. 1673-1699
    • Fatima, S.S.1    Wooldridge, M.2    Jennings, N.R.3
  • 15
    • 77953326401 scopus 로고    scopus 로고
    • The measurement of voting power: Theory and practice, problems and paradoxes
    • Felsenthal D., Machover M. (2000) The measurement of voting power: Theory and practice, problems and paradoxes. Public Choice 102(3-4): 373-376.
    • (2000) Public Choice , vol.102 , Issue.3-4 , pp. 373-376
    • Felsenthal, D.1    Machover, M.2
  • 16
    • 84947403595 scopus 로고
    • Probability inequalities for sums of bounded random variables
    • Hoeffding W. (1963) Probability inequalities for sums of bounded random variables. Journal of the American Statistical Association 58(301): 13-30.
    • (1963) Journal of the American Statistical Association , vol.58 , Issue.301 , pp. 13-30
    • Hoeffding, W.1
  • 17
    • 77953324815 scopus 로고    scopus 로고
    • Laruelle, A. (1999). On the choice of a power index. Papers 99-10. Valencia: Instituto de Investigaciones Económicas.
  • 18
    • 0036522729 scopus 로고    scopus 로고
    • An empirical comparison of the performance of classical power indices
    • Leech D. (2002) An empirical comparison of the performance of classical power indices. Political Studies 50(1): 1-22.
    • (2002) Political Studies , vol.50 , Issue.1 , pp. 1-22
    • Leech, D.1
  • 19
    • 0011506523 scopus 로고    scopus 로고
    • Voting power in the governance of the International Monetary Fund
    • Leech D. (2002) Voting power in the governance of the International Monetary Fund. Annals of Operations Research 109(1-4): 375-397.
    • (2002) Annals of Operations Research , vol.109 , Issue.1-4 , pp. 375-397
    • Leech, D.1
  • 20
    • 0038106592 scopus 로고    scopus 로고
    • Computing power indices for large voting games
    • Leech D. (2003) Computing power indices for large voting games. Journal of Management Science 49(6): 831-837.
    • (2003) Journal of Management Science , vol.49 , Issue.6 , pp. 831-837
    • Leech, D.1
  • 21
    • 0035595830 scopus 로고    scopus 로고
    • The treaty of Nice and qualified majority voting
    • Machover M., Felsenthal D. S. (2001) The treaty of Nice and qualified majority voting. Social Choice and Welfare 18(3): 431-464.
    • (2001) Social Choice and Welfare , vol.18 , Issue.3 , pp. 431-464
    • Machover, M.1    Felsenthal, D.S.2
  • 22
    • 77953323095 scopus 로고    scopus 로고
    • Mann, I., & Shapley, L. S. (1960). Values of large games, IV: Evaluating the Electoral College by Monte-Carlo techniques. Technical report, The Rand Corporation, Santa Monica, CA.
  • 23
    • 77953324939 scopus 로고    scopus 로고
    • Mann, I., & Shapley, L. S. (1962). Values of large games, VI: Evaluating the Electoral College exactly. Technical report, The Rand Corporation, Santa Monica, CA.
  • 24
    • 0034147462 scopus 로고    scopus 로고
    • A survey of algorithms for calculating power indices of weighted majority games
    • Matsui Y., Matsui T. (2000) A survey of algorithms for calculating power indices of weighted majority games. Journal of the Operations Research Society of Japan 43(1): 71-86.
    • (2000) Journal of the Operations Research Society of Japan , vol.43 , Issue.1 , pp. 71-86
    • Matsui, Y.1    Matsui, T.2
  • 25
    • 0034927534 scopus 로고    scopus 로고
    • NP-completeness for calculating power indices of weighted majority games
    • Matsui Y., Matsui T. (2001) NP-completeness for calculating power indices of weighted majority games. Theoretical Computer Science 263(1-2): 305-310.
    • (2001) Theoretical Computer Science , vol.263 , Issue.1-2 , pp. 305-310
    • Matsui, Y.1    Matsui, T.2
  • 26
    • 0016601327 scopus 로고
    • Multilinear extensions and the Banzhaf value
    • Owen G. (1975) Multilinear extensions and the Banzhaf value. Naval Research Logistics Quarterly 22(4): 741-750.
    • (1975) Naval Research Logistics Quarterly , vol.22 , Issue.4 , pp. 741-750
    • Owen, G.1
  • 28
    • 0001255447 scopus 로고
    • A value for n-person games
    • H. W. Kuhn and A. W. Tucker (Eds.), Princeton, NJ: Princeton University Press
    • Shapley L. S. (1953) A value for n-person games. In: Kuhn H. W., Tucker A. W. (eds) Contributions to the theory of games. Princeton University Press, Princeton, NJ, pp 31-40.
    • (1953) Contributions to the Theory of Games , pp. 31-40
    • Shapley, L.S.1
  • 29
    • 84959582296 scopus 로고
    • A method for evaluating the distribution of power in a committee system
    • Shapley L. S., Shubik M. (1954) A method for evaluating the distribution of power in a committee system. American Political Science Review 48: 787-792.
    • (1954) American Political Science Review , vol.48 , pp. 787-792
    • Shapley, L.S.1    Shubik, M.2
  • 30
    • 0000468124 scopus 로고
    • Homogeneity, independence and power indices
    • Straffin P. (1977) Homogeneity, independence and power indices. Public Choice 30: 107-118.
    • (1977) Public Choice , vol.30 , pp. 107-118
    • Straffin, P.1
  • 31
    • 85026748110 scopus 로고    scopus 로고
    • Yao, A. C.-C. (1977). Probabilistic computations: Toward a unified measure of complexity. In Proceedings of the 18th annual symposium on foundations of computer science (FOCS), Providence, RI (pp. 222-227).
  • 32
    • 70350100696 scopus 로고    scopus 로고
    • Young, H. P. (1994). Cost allocation. In R. J. Aumann & S. Hart (Eds.), The handbook of game theory (Vol. II, pp. 1193-1235). Amsterdam: North-Holland.


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.