00:01
So this question we want to find the bands of power of a distribution.
00:05
So if we have a weighted voting system 18, 158, 311, then we want to find the bands of power distribution.
00:22
So what we do is we want to list the winning coalitions, and then within each winning coalition, we want to highlight the critical voters.
00:46
So these are the ones who, if they switch their vote, the vote would no longer pass.
00:53
So if they switch the vote, it's no longer passes.
01:02
And then the banzaf power is equal to the number of times that a voter is critical, divided by the number of winning coalitions.
01:25
So let's have a look at winning coalitions.
01:28
So if we call this a, b, c and d, we need to get at least 18 votes to pass.
01:34
So a, b, can pass the vote.
01:39
And if a switches their vote, then the vote no longer passes.
01:43
And if b switches their vote, then the vote no longer passes.
01:47
A, c can also pass the vote.
01:51
And if either of them switch, it's still no longer passes.
01:54
A, d can pass the vote.
01:56
And again neither of them can pass it alone.
02:02
Now let's continue with two -person voting coalitions.
02:06
B -c can't pass the vote.
02:09
C -d can't pass the vote, but b -d can pass the vote, and they're both critical...