Skip to contents

Banzhaf (absolute and normalised), Shapley-Shubik, Deegan-Packel, Johnston and Holler (public good) indices of the weighted game with quota q and weights w by exact enumeration, with the minimal winning coalitions.

Usage

PowerIndices(weights, quota = NULL)

Arguments

weights

Player weights (at most 20).

quota

Quota (default: simple majority of the total weight).

Value

list(banzhaf, banzhaf_absolute, shapley_shubik, deegan_packel, johnston, holler, minimal_winning (1-based), min_winning_size, quota).

References

Banzhaf, J. F. (1965). Weighted voting doesn't work. Rutgers Law Review 19, 317-343. Shapley, L. S. and Shubik, M. (1954). A method for evaluating the distribution of power in a committee system. American Political Science Review 48, 787-792. Deegan, J. and Packel, E. W. (1978). A new index of power for simple n-person games. International Journal of Game Theory 7, 113-123. Johnston, R. J. (1978). On the measurement of power. Environment and Planning A 10, 907-914.

Examples

PowerIndices(c(3, 2, 2), 4)$banzhaf
#> [1] 0.3333333 0.3333333 0.3333333