Explanation Given: The weighted voting system is [ 13 : 6 , 6 , 5 , 3 ] . Definition: In a weighted voting system, the Shapley-Shubik index for a voter is given by the number of times the voter is pivotal in some permutation of the voters the total number of permutations of the voters . Calculation: Initially find the pivotal voter by making a table. In each coalition, find the first voter who makes the coalition a winning one by giving it a voting weight of 13 or more. Consider the voters to be A, B, C and D in that order. List all permutations of these voters and determine in each permutation which voter is pivotal. Sum Weights of Coalition Members until reach Quota of 13 Pivotal Voter ( A, B, C, D ) 6 + 6 + 5 C ( A, B, D, C ) 6 + 6 + 3 D ( A, C, B, D ) 6 + 5 + 6 B ( A, C, D, B ) 6 + 5 + 3 D ( A, D, B, C ) 6 + 3 + 6 B ( A, D, C, B ) 6 + 3 + 5 C ( B, A, C, D ) 6 + 6 + 5 C ( B, A, D, C ) 6 + 6 + 3 D ( B, C, A, D ) 6 + 5 + 6 A ( B, C, D, A ) 6 + 5 + 3 D ( B, D, A, C ) 6 + 3 + 6 A ( B, D, C, A

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ISBN: 9780134434681

Author: Tom Pirnot

Publisher: PEARSON

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Chapter 11.4, Problem 16E

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The Shapley-Shubik index of each voter for weighted voting system [13:6,6,5,3].

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Chapter 11.4, Problem 15E

Chapter 11.4, Problem 17E

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The Shapley-Shubik index of each voter for weighted voting system [ 13 : 6 , 6 , 5 , 3 ] .

Solution Summary: The author explains the Shapley-Shubik index of A, B, C and D in a weighted voting system.

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