powerindexR (version 1.6)

pi.banzhaf: Power based on the Banzhaf index.

Description

This function determines the distribution of the power based on the Banzhaf index and the Banzaf-Owen value.

Usage

pi.banzhaf(quota, weights, partition = NULL, normalized = FALSE, swing = FALSE)

Value

Banzhaf value

The Banzhaf value, if partition=NULL.

Banzhaf-Owen value

The Banzhaf-Owen value, if partition!=NULL.

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.

partition

Numerical vector that indicates the partition of voters. Each component indicates the element of the partition to which such voter belongs. If it is not NULL, it provides the distribution of the power based on the Banzhaf-Owen value.

normalized

Logical option to obtain the normalized Banzhaf values.

swing

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

Author

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.

Examples

# Example Banzhaf value
weights<-c(137,85,71,32,9,8,5,2,1) 
quota<-176
pi.banzhaf(quota,weights)
pi.banzhaf(quota,weights,normalized=TRUE)

# Example Banzhaf-Owen value
quota<-30
weights<-c(28, 16, 5, 4, 3, 3)
# Partition={{1},{2,4,6},{3,5}}
pi.banzhaf(quota,weights,partition=c(1,2,3,2,3,2))