The Banzhaf Power Index
Tallying votes when the stakes are high is always going to
be a complicated process. Weighted
voting is one of the better methods for obtaining the fairest outcome. We’ve explored the current method, Shapley-Shubik
index, which measures power by the number of different permutations in which
each voter has the pivotal vote. A previous voting index used was the Banzhaf power index. Instead of looking at the number of permutations, the Banzhaf method looks at the number of coalitions which a voter is critical. A coalition is defined as a group of voters who all agree to vote a certain way to have a motion blocked or passed. The Banzhaf method counted the critical voters – a voter who, if he/she changed their vote from yes to no, would cause the coalition to lose. The voter power is measured as the fraction of all swing votes that voter could cast. To calculate the power of a voter using the Banzhaf index, you would list all the winning coalitions and then count the critical voters in each.
An example of the Banzhaf method was the 2000 election when
Bush-Cheney ran against Gore-Lieberman.
The Bush-Cheney team won with 271 electoral votes – only one vote over
quota. This means that almost every
voter in the Bush-Cheney coalition was a critical voter. This is important
because even the state with the smallest weight would still have a high amount
of power in the 2000 election because they were a critical voter in that coalition.
I found it interesting that, at least in the 2000 Presidential election, even a state with a small weight could determine the outcome of the election. When and why did the Shapley-Shubik index become used instead of the Banzhaf Power Index?
ReplyDeleteThis was a interesting method also. I think it is pretty cool how if the voter changed his vote from yes to no, it would affect the outcome. that is different. I also liked how they measured the voting power on determining the winner.
ReplyDeleteI find the Banzhaf method also very interesting. I find it shocking that the state with a small weight still came out ontop to determine the winner of that election.
ReplyDeleteIt's interesting to think of voting in terms of groups. For the most part, the voting that we have discussed has been about individuals.
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