Excursions In Modern Mathematics, 9th Edition
9th Edition
ISBN: 9780134494142
Author: Tannenbaum
Publisher: PEARSON
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Chapter 2, Problem 78E
Suppose that in a weighted voting system there is a player A who hates another player P so much that he will always vote the opposite way of P, regardless of the issue. We will call A the antagonist of P.
a. Suppose that in the weighted voting system
b. Suppose that in a generic weighted voting system with N players there is a player P who has an antagonist A. How many coalitions are there under these circumstances?
c. Give examples of weighted voting systems where a player A can
i. increase his Banzhaf power index by becoming an antagonist of another player.
ii. decrease his Banzhaf power index by becoming an antagonist of another player.
d. Suppose that the antagonist A has more votes than his enemy P. What is a strategy that P can use to gain power at the expense of A?
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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. 3ECh. 2 - Prob. 4ECh. 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...
Ch. 2 - Consider the weighted voting system [q:7,5,3]. a....Ch. 2 - Consider the weighted voting system...Ch. 2 - Find the Banzhaf power distribution of a weighted...Ch. 2 - Find the Banzhaf power distribution of a weighted...Ch. 2 - Consider the weighted voting system [10:6,5,4,2]....Ch. 2 - Consider the weighted voting system [5:3,2,1,1]....Ch. 2 - a.Find the Banzhaf power distribution of this...Ch. 2 - a. Find the Banzhaf power distribution of the...Ch. 2 - Consider the weighted voting system [q:5,4,3,2,1]....Ch. 2 - Consider the weighted voting system [q:8,4,2,1]....Ch. 2 - In a weighted voting system with three players the...Ch. 2 - In a weighted voting system with four players the...Ch. 2 - The Nassau County N.Y. Board of Supervisors 1960s...Ch. 2 - The Nassau County N.Y. Board of Supervisors 1960s...Ch. 2 - A law firm is run by four partners (A,B,C,andD)....Ch. 2 - A law firm is run by four partners (A,B,C,andD)....Ch. 2 - Table 2-13 shows the 24 sequential coalitions with...Ch. 2 - Table 2-14 shows the 24 sequential coalitions with...Ch. 2 - Consider the weighted voting system [16:9,8,7]. a....Ch. 2 - Consider the weighted voting system [8:7,6,2]. a....Ch. 2 - Find the Shapley-Shubik power distribution of each...Ch. 2 - Find the Shapley-Shubik power distribution of each...Ch. 2 - Find the Shapley-Shubik power distribution of each...Ch. 2 - Find the Shapley-Shubik power distribution of each...Ch. 2 - In a weighted voting system with three players the...Ch. 2 - In a weighted voting system with three players the...Ch. 2 - Table 2-15 shows the 24 sequential coalitions in a...Ch. 2 - Table 2-16 shows the 24 sequential coalitions in a...Ch. 2 - Let A be a set with 10 elements. a. Find the...Ch. 2 - Prob. 40ECh. 2 - For a weighted voting system with 10 players. a....Ch. 2 - Consider a weighted voting system with 12 players....Ch. 2 - Consider a weighted voting system with six players...Ch. 2 - Consider a weighted voting system with five...Ch. 2 - Use a calculator to compute each of the following....Ch. 2 - Prob. 46ECh. 2 - Prob. 47ECh. 2 - Prob. 48ECh. 2 - The purpose of Exercises 49 and 50 is for you to...Ch. 2 - The purpose of Exercises 49 and 50 is for you to...Ch. 2 - Consider a weighted voting system with seven...Ch. 2 - Consider a weighted voting system with seven...Ch. 2 - A law firm has seven partners: a senior partner...Ch. 2 - A law firm has six partners: a senior partner (P1)...Ch. 2 - Prob. 55ECh. 2 - Prob. 56ECh. 2 - Consider the weighted voting system [q:8,4,1]. a....Ch. 2 - Consider the weighted voting system [9:w,5,2,1]....Ch. 2 - Equivalent voting systems. Two weighted voting...Ch. 2 - Veto power. A player P with weight w is said to...Ch. 2 - Consider the generic weighted voting system...Ch. 2 - Prob. 62ECh. 2 - Prob. 63ECh. 2 - The weighted voting system [27:10,8,6,4,2]...Ch. 2 - Prob. 65ECh. 2 - Mergers. Sometimes in a weighted voting system two...Ch. 2 - a.Verify that the weighted voting systems...Ch. 2 - Prob. 68ECh. 2 - Prob. 69ECh. 2 - Prob. 70ECh. 2 - Prob. 71ECh. 2 - Prob. 72ECh. 2 - Prob. 73ECh. 2 - Prob. 74ECh. 2 - Prob. 75ECh. 2 - Prob. 76ECh. 2 - Prob. 77ECh. 2 - Suppose that in a weighted voting system there is...Ch. 2 - a. Give an example of a weighted voting system...Ch. 2 - a. Explain why in any weighted voting system with...
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