Suppose that there are only three hypothetical states with a distribution of popular and electoral votes as shown in the table below. Find the ordering of the Shapley-Shubik indexes for states using the popular vote. Assume that a simple majority is required.
A)A

Question

Suppose that there are only three hypothetical states with a distribution of popular and electoral votes as shown in the table below. Find the ordering of the Shapley-Shubik indexes for states using the popular vote. Assume that a simple majority is required. 
A)A < B < C 
B)A = B < C 
C)A < B = C 
D)A = B = C

Quizplus · Accepted Answer

The Shapley-Shubik index for each state is calculated by considering every possible order in which the states can vote and determining the marginal contribution of that state to the formation of a winning coalition. In this case, since a simple majority is required, any one state alone cannot form a winning coalition. Therefore, the Shapley-Shubik index for all three states is equal to 0.5. Thus, there is no difference in the ordering of the Shapley-Shubik indexes for states using the popular vote. Therefore, the answer is B, which states that A and B have equal Shapley-Shubik indexes and are both less than C.

Suppose That There Are Only Three Hypothetical States with a Distribution