Explanation Consider committee {A, B, C, D} has chairperson A. For a resolution to be passed, the chairperson and at least one other member of the committee must support the resolution. Definition: Weighted voting system: A voting situation where voters are not necessarily equal in the number of voters they control. Weight: The number of votes a player controls. A weighted voting system with n voters is described by a set of numbers that are listed in the following format: [quota: weight of voter 1, weight of voter 2,…, weight of voter n]. Quota: The smallest number of votes required to pass a motion. Winning coalition: Any set of voters who vote the same way is called coalition. The sum of the weights of the voters in a coalition is called the weight of the coalition. If a coalition has a weight that is greater than or equal to the quota, then that coalition is called a winning coalition. Banzhaf Power Index: In a weighted voting system, voter’s Banzhaf power index is defined as follows, the number of times the voter is critical in winning coalitions the total number of times voters are critical in winning coalitions Approach: From the given condiiton winning coalision must the contain chairperson A. The following table represetn the winning coalition, Coalition winning coalition {P 1 } L {P 2 } L { P 1 , P 2 } W {P 3 } L { P 1 , P 3 } W {P 2 , P 3 } L { P 1 , P 2 , P 3 }

Mathematics All Around, Books a la carte edition (6th Edition)

6th Edition

ISBN: 9780134462448

Author: Pirnot, Tom

Publisher: PEARSON

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Question

Chapter 11.CR, Problem 13CR

To determine

The Banzhaf power index for each committee.

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Chapter 11.CR, Problem 12CR

Chapter 11.CR, Problem 14CR

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Chapter 11 Solutions

Mathematics All Around, Books a la carte edition (6th Edition)

Ch. 11.1 - Four candidates running for a vacant seat on the...Ch. 11.1 - Five candidates running for mayor receive votes as...Ch. 11.1 - The university administration has asked a group of...Ch. 11.1 - The university administration has asked a group of...Ch. 11.1 - The university administration has asked a group of...Ch. 11.1 - The university administration has asked a group of...Ch. 11.1 - The drama society members are voting for the type...Ch. 11.1 - The drama society members are voting for the type...Ch. 11.1 - The drama society members are voting for the type...Ch. 11.1 - The drama society members are voting for the type...

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