weightedmajoritygame {TUGLab} | R Documentation |
Weighted majority game
Description
This function returns the characteristic function of the described weighted majority game.
Usage
weightedmajoritygame(q, w, binary = FALSE)
Arguments
q |
A quota, as a number between 0 and the sum of player weights. |
w |
The player weights, as a vector of non-negative numbers. |
binary |
A logical value. By default, |
Details
Given a situation in which a number of agents have to vote for or against a certain measure,
let N =\{1,\ldots,n\}
be the set of voters, w
be a non-negative vector of voter weights (the weight of each voter is the number of votes or the proportion of total votes they hold),
and q \in [0,\sum_{i \in N}w_{i}]
be the quota (the minimum number of votes or the minimum proportion of total votes needed to pass the measure).
The corresponding weighted majority game, v
, is defined by
v(S)=1 \text{ if } \sum_{i \in S}w_{i} \geqslant q \text{ and } v(S)=0 \text{ otherwise, for each }S\in 2^N.
Value
The characteristic function of the weighted majority game associated with the described situation, as a vector in binary order if binary=TRUE
and in lexicographic order otherwise.
Examples
q <- 39
w <- c(rep(7,5),rep(1,10))
weightedmajoritygame(q,w)