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Explanation for the Last Example
What is the Banzhaf power index of the following
weighted voting system?
[51: 26, 26, 26, 22]
| 26 | 26 | 26 | 22 | # of votes | outcome |
| y | y | y | y | 100 | Win |
| y | y | y | n | 78 | Win |
| y(s) | y(s) | n | y | 74 | Win |
| y(s) | y(s) | n | n | 52 | Win |
| y(s) | n | y(s) | y | 74 | Win |
| y(s) | n | y(s) | n | 52 | Win |
| y | n(s) | n(s) | y | 48 | Lose |
| y | n(s) | n(s) | n | 26 | Lose |
| n | y(s) | y(s) | y | 74 | Win |
| n | y(s) | y(s) | n | 52 | Win |
| n(s) | y | n(s) | y | 48 | Lose |
| n(s) | y | n(s) | n | 26 | Lose |
| n(s) | n(s) | y | y | 48 | Lose |
| n(s) | n(s) | y | n | 26 | Lose |
| n | n | n | y | 22 | Lose |
| n | n | n | n | 0 | Lose |
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).
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