Back to Examples Labs: Voting and Social Choice. Part 2. Math Alive

Explanation for the Last Example

What is the Banzhaf power index of the following weighted voting system?

[51: 26, 26, 26, 22]

26262622# of votesoutcome
yyyy100Win
yyyn78Win
y(s)y(s)ny74Win
y(s)y(s)nn52Win
y(s)ny(s)y74Win
y(s)ny(s)n52Win
yn(s)n(s)y48Lose
yn(s)n(s)n26Lose
ny(s)y(s)y74Win
ny(s)y(s)n52Win
n(s)yn(s)y48Lose
n(s)yn(s)n26Lose
n(s)n(s)yy48Lose
n(s)n(s)yn26Lose
nnny22Lose
nnnn0Lose

Here are all the possible voting coalitions for the weighted voting system [51: 26, 26, 26, 22]. It should now be clear that the Banzhaf index for this system is (8, 8, 8, 0).


Back to Examples Last Modified: August 2008