powerindex {powerindexR}

Obtain several measures of power

Description

This general function allows the determination of several distributions of the power under different approaches in a weighted voting situation.

Usage

powerindex(quota, weights, index = c("S", "B", "J", "CM", "JCM"), 
partition = NULL, quasiminimal = FALSE, minimal = FALSE, normalized = FALSE, 
swing = FALSE)

Arguments

quota

Numerical value that represents the majority in a given voting.

weights

Numerical vector of dimension n that indicates the weights of n agents in a given voting.

index

Character that indicates the used approach. S and B denote the Shapley-Shubik index and the Banzhaf index, and the Owen index and the Banzhaf-Owen index if partition exist. J is used for obtaining the Jonhston index, CM determines the Colomer-Martinez index and JCM is used for obtaining the Jonhston-Colomer-Martinez index.

partition

Numerical vector that indicates the partition of voters. Each component indicates the element of the partition to which such voter belongs.

quasiminimal

Logical option to obtain the Quasi-Minimal Winning Coalitions.

minimal

Logical option to obtain the Minimal Winning Coalitions.

normalized

Logical option to obtain the normalized Banzhaf values.

swing

Logical option to obtain the number of swings of each voter.

Value

See the values of the respective functions.

Author(s)

Livino M. Armijos-Toro, Jose M. Alonso-Meijide, Manuel A. Mosquera, Alejandro Saavedra-Nieves.

References

Alonso-Meijide, J. M., & Bowles, C. (2005). Generating functions for coalitional power indices: An application to the IMF. Annals of Operations Research, 137, 21-44.

Brams, S. J., & Affuso, P. J. (1976). Power and size: A new paradox. Theory and Decision, 7(1-2), 29-56.

Colomer, J. M., & Martinez, F. (1995). The paradox of coalition trading. Journal of Theoretical Politics, 7(1), 41-63.

Johnston, R. J. (1978). On the measurement of power: Some reactions to Laver. Environment and Planning A, 10(8), 907-914.

Lucas, W. F. (1983). Measuring power in weighted voting systems (pp. 183-238). Springer New York.

Examples

weights<-c(137,85,71,32,9,8,5,2,1) 
quota<-176
powerindex(quota,weights,index="S")
powerindex(quota,weights,index="B",swing=TRUE)
powerindex(quota,weights,index="B",partition=c(1,1,2,2,3,3,4,4,4),swing=TRUE)
powerindex(quota,weights,index="J",quasiminimal=TRUE)