Explanation Procedure used: In Shapley-Shubik method the coalitions are formed sequentially. Players join the coalition and cast their votes in an orderly sequence. The Formula to calculate Shapley-Shubik power distribution is given by, σ i = S S i T Where S S i are the pivotal counts of respective player and T is ∑ S S i . Given: A law firm has N + 1 partners: the senior partner with N votes, and N junior partners with one vote each. The quota is a simple majority of the votes. Calculation: A law firm has N + 1 partners. The senior partners have N votes, and N junior partners have one vote each. While the quota is simple majority of votes, it will always fall between the simple majority and unanimity of votes. Let quota be denoted by q and votes be V . When written mathematically, q > V 2 and q ≤ V ... ( 1 ) The range of quota is, V 2 < q ≤ V The total number of votes is equal to the N votes of senior partners and N votes of junior partners with 1 vote each. The total number of votes is, V = 2 N From equation ( 1 ) and the simple majority of votes, the quota values are, q = V 2 + 1 And q = N + 1 The motion passes when vote of a senior partner and any one vote of a junior partner are in favor of the motion. All the coalition in the first column has senior players in first position, and the coalition in the second column have senior players in the second position and so on. Let P s represent senior players, and P 1 , P 2 , ......... , P N represent N junior players, respectively. The senior player will be pivotal player in the second position and onwards. The number of times the senior player is pivotal is, S S s = N × ( Number of coalition per column ) = N × N ! The Shapley-Shubik power index for Senior partner P S is,

Excursions In Modern Mathematics, 9th Edition

9th Edition

ISBN: 9780134494142

Author: Tannenbaum

Publisher: PEARSON

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Chapter 2, Problem 74E

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The Shapley-Shubik power distribution for given weighted voting system.

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Chapter 2, Problem 73E

Chapter 2, Problem 75E

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Excursions In Modern Mathematics, 9th Edition

Ch. 2 - Five partners (P1,P2,P3,P4, andP5) jointly own the...Ch. 2 - Five partners (P1,P2,P3,P4, andP5) jointly own the...Ch. 2 - Prob. 3E Ch. 2 - Prob. 4E Ch. 2 - In each of the following weighted voting systems,...Ch. 2 - In each of the following weighted voting systems,...Ch. 2 - Consider the weighted voting system[q:7,5,3]. Find...Ch. 2 - Consider the weighted voting system...Ch. 2 - A committee has four members (P1,P2,P3,andP4). In...Ch. 2 - A committee has six members...

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Chapter 2 Solutions

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The Shapley-Shubik power distribution for given weighted voting system.