Q. Listing different orderings and coalitions is not going to work for this problem because there are too many possibilities, excluding you can use different tools which we have discussed in class.
a) Find Shapley-Shubik power indicator for the large state as well as for small states. You can discover the power for the big state 1st by taking position of other states as given.
b) Find the Banzhaf power index for large state and for small states. You can find number of coalitions which win with 13 votes that each one small state and the large state are critical for. Then find the number of coalitions that win with 14 votes that the different states are critical for, and so on.
c) Separate the Banzhaf power index by the number of voters in state. Are voters in small states or are voters in big state more powerful, according to this measure?
Now suppose we're in a different country (the United States of Earley (USE) where there are nine small states (population 1) and one big state with a population of 3. The big state has 4 electoral votes and the small states each have 2 electoral votes. So now there are a total of 22 electoral votes. Suppose that 12 electoral votes are needed to win election.
d) Find the Banzhaf power index for the large state and for the small states now.
e) Divide the Banzhaf power index by the number of voters in state. Are voters in small states or are voters in big state more powerful, according to this measure?
f) In Know land, you should have found that each voter in big state has more power than each voter in a small state. In USE, you should have found that a voter in a small state has more power than a voter in big state. Explain the two forces that explain why in some circumstances, the big state can be more powerful, while in another circumstance, the big state is less powerful.