Take a country named Konowland that has an Electoral College system. Suppose there are nine small states in Konowland that each have 1 million peopleinm. For simplicity, we will say that these ten states each have a population of 1. There is also one big state in Konowland that has a population that has a population of 6 (million).
Suppose the states with a population of 1 get a total of 2 votesin electoral college and the bigger state gets 7 votesin electoral college. So there are a total of 25 electoral votes to be won. A candidate needs to get 13 electoral votes to win the election.
Listing the different orderings and coalitions isn't going to work for this problem because there are too many possibilities, but you can use different tools that we have discussed in class.
a)Find the Shapley-Shubik power index for the large state and for the small states. Also find the power for the big state first by taking the position of the other states as given.
b)Find the Banzhaf power index for the large state and for the small states.
Also find the number of coalitions that win with 13 votes that each 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)Divide the Banzhaf power index by the number of votersin state. Are votersin small states or are votersin 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 votersin state. Are votersin small states or are votersin big state more powerful, according to this measure?
f)In Konowland, you should have found that each voterin 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 voterin 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.