Question: The Senate of the 112th Congress has 100 members of whom 53 are Democrats and 47 are Republicans. Assume that there are three types of Democrats and three types of Republicans-Liberals, Moderates, Conservatives. Assume that these types vote as a block. For the Democrats, Liberals (1) have 20 votes, Moderates (2) have 25 votes, Conservatives (3) have 8 votes. Also,for Republicans, Liberals (4) have 2 votes, Moderates (5) have 15 votes, and Conservatives (6) have 30 votes. A resolution requires 60 votes to pass.
(a) Find the Shapley-Shubik index and the total power of the Republicans and Democrats.
(b) Find the Banzhaf-Coleman index.
(c) What happens if the Republican Moderate votes becomes 1, while the Republican Conservative votes becomes 44.