johnstonIndex {CoopGame}

Compute Johnston index

Description

johnstonIndex calculates the Johnston index for a simple game.

Usage

johnstonIndex(v)

Arguments

v

Numeric vector of length 2^n - 1 representing the values of the coalitions of a TU game with n players

Value

Johnston index for a specified simple game

Author(s)

Johannes Anwander [e-mail]

Michael Maerz

Jochen Staudacher [e-mail]

References

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

Chakravarty S.R., Mitra M. and Sarkar P. (2015) A Course on Cooperative Game Theory, Cambridge University Press, p. 124

Examples

library(CoopGame)
johnstonIndex(c(0,0,0,1,0,0,1))


#player 1 has 3 votes
#player 2 has 2 votes
#player 3 has 1 vote
#majority for the decision is 4 (quota)

library(CoopGame)
#function call generating the game vector:
v <- weightedVotingGameVector(n = 3, w = c(3,2,1), q = 4)

johnstonIndex(v)
#[1] 0.6666667 0.1666667 0.1666667