HW11. 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. a. Find the Banzhaf power distribution of this voting system. b. According to Banzhaf’s approach to measuring power, how many times more power does a council member with veto power have than a council member without veto power? c. 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 >