Question 11.37

7. Voters use the weighted voting system .

  1. List all permutations in which is pivotal.
  2. List all permutations in which is pivotal.
  3. Calculate the Shapley–Shubik power index of the system.

7.

(a) is pivotal in these permutations: , , , , , , , , , , , and .

(b) is pivotal in these permutations: , , , and .

(c) The Shapley-Shubik index of , which is pivot in 12 permutations, is . Each of the other voters has four pivots and a Shapley-Shubik power index of .