A SURVEY OF ALGORITHMS FOR CALCULATING POWER INDICES OF WEIGHTED MAJORITY GAMES

For measuring an individual's voting power of a voting game, some power indices are proposed. In this paper, we discuss the problems for calculating the Shapley-Shubik index, the Banzhaf index and the Deegan-Packel index of weighted majority games.

[1]  F. Frances Yao,et al.  Computational Geometry , 1991, Handbook of Theoretical Computer Science, Volume A: Algorithms and Complexity.

[2]  S. Brams,et al.  Power and size: A new paradox , 1976 .

[3]  Ronald L. Graham,et al.  An Efficient Algorithm for Determining the Convex Hull of a Finite Planar Set , 1972, Inf. Process. Lett..

[4]  J. Neumann,et al.  Theory of games and economic behavior , 1945, 100 Years of Math Milestones.

[5]  Reducibility Among Combinatorial Problems , 1972, Complexity of Computer Computations.

[6]  Martin Shubik,et al.  A Method for Evaluating the Distribution of Power in a Committee System , 1954, American Political Science Review.

[7]  L. Shapley,et al.  VALUES OF LARGE GAMES. 6: EVALUATING THE ELECTORAL COLLEGE EXACTLY , 1962 .

[8]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[9]  L. Shapley A Value for n-person Games , 1988 .

[10]  N. Megiddo Nucleoluses of Compound Simple Games , 1974 .

[11]  R. Bellman Notes on the theory of dynamic programming IV ‐ Maximization over discrete sets , 1955 .

[12]  G. Owen Multilinear Extensions of Games , 1972 .

[13]  Pradeep Dubey,et al.  Mathematical Properties of the Banzhaf Power Index , 1979, Math. Oper. Res..

[14]  H. D. Brunk,et al.  Statistical inference under order restrictions : the theory and application of isotonic regression , 1973 .

[15]  G. Owen Multilinear extensions and the banzhaf value , 1975 .

[16]  J. Deegan,et al.  A new index of power for simplen-person games , 1978 .

[17]  Xiaotie Deng,et al.  On the Complexity of Cooperative Solution Concepts , 1994, Math. Oper. Res..

[18]  Tomomi Matsui,et al.  NP-completeness for calculating power indices of weighted majority games , 2001, Theor. Comput. Sci..

[19]  William F. Lucas,et al.  Measuring Power in Weighted Voting Systems , 1983 .

[20]  P. Dubey On the uniqueness of the Shapley value , 1975 .

[21]  J. M. Bremner,et al.  Statistical Inference under Restrictions , 1973 .