MYMATHLAB ACCESS F/MGF 1107
9th Edition
ISBN: 9781323741658
Author: Tannenbaum
Publisher: PEARSON
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Textbook Question
Chapter 2, Problem 29E
Consider the weighted voting system
a. Write down all the sequential coalitions, and in each sequential coalition identify the pivotal player.
b. Find the Shapley-Shubik power distribution of this weighted voting system.
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Students have asked these similar questions
Consider the weighted voting system [q: 15, 8, 3, 1] Find the Banzhaf power distribution of this weighted voting system,
When the quota is 15
When the quota is 16
When the quota is 18
. Find the Banzhaf Power Distribution of a weighted voting system with four players in which the winning coalitions (with critical players highlighted) are
{P1, P2, P3}, {P1, P2, P4}, {P1, P2, P3, P4}.
Enter your answer as a percentage to two decimal places.
In a weighted voting system with three players the winning coalitions are {P1, P2} and {P1, P2, P3}. List the sequential coalitions and identify the pivotal player in each sequential coalition. Then, find the Shapley-Shubik power distribution of the weighted voting system.
Im pretty sure these are the Coalitions:
P1, P2, P3
P1, P3, P2
P2, P1, P3
P2, P3, P1
P3,P1, P2
P3, P2, P1
My question: How do we find the pivotal players when we have not assigned values to each player? please show me that process in detail and then how to do the Shapley-Shubik power distribution. Thank you
Chapter 2 Solutions
MYMATHLAB ACCESS F/MGF 1107
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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- Consider a weighted voting system with three players. If Players 1 and 2 have veto power, and Player 3 is a dummy, find the Banzhof power distribution.arrow_forwardRefer to the weighted voting system [27: 15, 10, 8, 4]. The Banzhaf power distribution of the weighted voting system is: P1 : ["", "", "", ""] P2 : ["", "", "", ""] P3 : ["", "", "", ""] P4 : ["", "", "", ""]arrow_forwardConsider the weighted voting system [15: 7, 7, 4] and the Shapely-Shubik Power distribution. Listed below are 5 of the 6 sequential coalitions.Find the pivotal player in the missing coalition. <P1, P2, P3> <P1, P3, P2> <P2, P1, P3> <P3, P2, P1> <P3, P1, P2> Group of answer choices P1 P2 P3 none are pivotalarrow_forward
- .Consider the weighted voting system [17: 13, 9, 5, 2]. In the sequential coalition <P3,P2,P1,P4> which player is pivotal?arrow_forwardRefer to the weighted voting system [15: 9,8,7] and the Shapley-Shubik definition of power. A. Which member of the sequential coalition <P2, P3, P1> is pivotal? P2 None of them are pivotal players. P3 P1 B. The Shapley-Shubik power distribution of the weighted voting system is P1: 1/3 P2: 1/3 P3: 1/3 P1: 1/2 P2: 1/2 P3: 0 P1: 2/3 P2: 1/3 P3: 0 P1: 2/3 P2: 1/6 P3: 1/6arrow_forwardConsider the weighted voting system 25:18,14,w_(3). What is the largest possible value for the weight w_(3) which guarantees P_(3) is the only player who is a dummy?arrow_forward
- Consider the weighted voting system [9: 6, 5, 2] and the Shapely-Shubik Power distribution.Listed below are 5 of the 6 sequential coalitions. Find the pivotal player in the missing coalition. <P1, P2, P3> <P1, P3, P2> <P2, P1, P3> <P3, P2, P1> <P3, P1, P2> Group of answer choices P1 P2 P3 none are pivotalarrow_forwardGiven the weighted voting system [11: 9, 5, 4], determine the Shapely-Shubik Power Index for each player. Group of answer choices P1: 2/3, P2: 1/6, P3: 1/6 P1: 2/3, P2: 1/3 P3: 1/3 P1: 3/6, P2: 2/6, P3: 1/6 P1: 1/3, P2: 1/3, P3: 1/3arrow_forwardConsider the weighted voting system [15: 10, 6, 5, 3] and the Banzhaf Power distribution. How many winning coalitions will there be? Group of answer choices 5 7 6 8arrow_forward
- Consider a weighted voting system with three players. If only Player 1 has veto power, and there are no dummies, find the Banzhof power distribution.arrow_forwardConsider a weighted voting system with three players. If only Player 1 has veto power, and there are no dummies, find the Banzhof power distribution.Player 1: Player 2: Player 3:arrow_forwardConsider the weighted voting system [15: 9, 6, 3, 1] and the Banzhaf Power distribution method, which player(s) are critical in the coalition { P1, P2, P3}? Group of answer choices P1 P2 P1 and P2 P1, P2 and P3arrow_forward
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