Question 11.39

9. Voters , and use the weighted voting system .

  1. Describe the set of permutations in which Voter is pivotal.
  2. What is the number of permutations that you found in part (a)?
  3. Use the answer that you have given in part (b) to determine the Shapley–Shubik power index of the system.

9.

(a) Voter is pivotal in the third or fourth position of any permutation.

(b)

(c) Voter has a Shapley-Shubik power index of . Each of the five weight-2 voters has a Shapley-Shubik power index equal to of the remaining of the power; that is, .