Microsoft Word - 2-Measuring-Power-RU-Version-Jul-13-2015.docx

Consider a simplified version of the UN Security Council in which there are six players (council members) P1, P2, P3, P4, P5, and P6. In order for a resolution to pass, a majority of council members must vote in favor of it. Moreover, P1, P2, and P3 all have veto power while the others do not.

1. -Find the Banzhaf power distribution of this voting system.
2. -According to Banzhafs approach to measuring power, how many times more power does a council member with veto power have than a council member without veto power?
3. -You are not asked to find the Shapley-Shubik power distribution of this voting system, but if you were, the following are just a few of the sequential coalitions you would need to consider. In each of the following sequential coalitions, underline the pivotal player: < P1, P3, P5, P4, P6, P2 > < P2, P5, P3, P4, P1, P6> < P4, P5, P2, P6, P1, P3 > < P6, P5, P4, P3, P2, P1 >