Question 11.83

53. Find the Shapley-Shubik power index for each voter in the system .

53.

Focus on the weight-3 voter, who is singular. This voter is pivot if and only if placed in the third, fourth, or fifth position in a permutation. The permutation has length 7, so the Shapley-Shubik power index for this voter is . The six weight-1 voters share the remaining of the power; thus, each has Shapley-Shubik power index equal to .