Explanation Given: A partnership has four partners ( P 1 , P 2 , P 3 , and P 4 ) . In this partnership P 1 has twice as many votes as P 2 , P 2 , has twice as many votes a P 3 ; P 3 has twice as many votes as P 4 . The quota is a simple majority of the votes. Approach: A given number of votes are controlled by each player in a formal voting arrangement, it is said to be weighted voting system. A player is a dictator if and only if the player’s weight is bigger than or equal to the quota. Calculation: Let the votes be represented as x then the number of votes P 4 has is x and P 3 has twice as many votes as P 4 . The number of votes P 3 has, P 3 = 2 × P 4 = 2 x The number of votes P 3 has is 2 x . Number of votes for P 2 is twice as many votes as P 3 , P 2 = 2 × P 3 = 2 × 2 x = 4 x The number of votes P 2 has is 4 x . Number of votes for P 1 is twice as many votes as P 2 , P 1 = 2 × P 2 = 2 × 4 x = 8 x The number of votes P 1 has is 8 x

Excursions in Modern Mathematics (9th Edition)

9th Edition

ISBN: 9780134468372

Author: Peter Tannenbaum

Publisher: PEARSON

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Chapter 2, Problem 71E

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The player P1 is always a dictator.

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Chapter 2, Problem 70E

Chapter 2, Problem 72E

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Chapter 2 Solutions

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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The player P 1 is always a dictator.

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The player P 1 is always a dictator.

Solution Summary: The author explains that the player P_1 is always a dictator.

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The player P1 is always a dictator.