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Unformatted text preview: 1 1 1 11 ABCE 1 1 11 1 ABCDE 1 1 1 1 1 TBP 5 5 3 1 1 BI 1 3 1 3 1 5 1 15 1 15 (c) (5 Points) Calculate the ShapleyShubik Index of Power for voter C. Hint: 5!=120. ..Don±t try and do this the long way! 1 Answer: Voter C is pivotal if preceded by a coalition with 14, 15, 16, or 17 votes. Since all individual votes are even, it is impossible to have 15 or 17. There fore we only need to add up the orderings where C is preceded by 14 or 16 votes. There is one coalition to that produces 14 votes: coalition AB. The number of orderings where C is preceded by AB is 2!1!2! = 4 : There are 2 coalitions that yield 16 votes: ABD, ABE. Thus, there are 3!1!1! = 6 orderings where C is preceded by ABD and 3!1!1! = 6 orderings where C is preceded by ABE . The total number of pivotal orderings for C is 16 : Thus, C &s SSI is 16 120 = 2 15 : 2...
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 Spring '12
 Vanessen
 Voting system, Plurality voting system, votes

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