EXCURSIONS IN MODERN...(LL)-W/MYMATHLAB
9th Edition
ISBN: 9780134453156
Author: Tannenbaum
Publisher: PEARSON
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Question
Chapter 2, Problem 72E
To determine
To find:
The Banzhaf power distribution of the weighted voting system.
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Given 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: 1/3
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.
. 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.
Chapter 2 Solutions
EXCURSIONS IN MODERN...(LL)-W/MYMATHLAB
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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- 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 youarrow_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_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_forward
- In a randomly selected sample of 500 registered voters in a community, 220 individuals say that they plan to vote for Candidate Y in the upcoming election.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 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_forward
- Find the Banzhaf power distribution of the weighted voting system [26: 16, 14, 10, 2] Give each player's power as a fraction or decimal value Player 1: Player 2: Player 3: Player 4:arrow_forwardA poll is taken in which 349 out of 575 randomly selected voters indicated their preference for a certain candidate.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
- .Consider the weighted voting system [17: 13, 9, 5, 2]. In the sequential coalition <P3,P2,P1,P4> which player is pivotal?arrow_forwardIn voting among four candidates, the outcomes are reported as: (ADBC) (DACB) (BADC) (BDCA) (DCAB) 8 ,6, 4, 3 ,2 How many voters did rank three candidates in the order of A first, D second, B third, and candidate C last?arrow_forward2. A fraternity votes to choose a service project--visiting nursing homes, reading with children in elementary schools, or cleaning up a stretch of highway. Their preference rankings are as follows: Number of Voters 3 1 4 8 2 Visiting nursing homes 1 1 2 3 2 Reading with children 2 3 1 1 3 Cleaning highway 3 2 3 2 1 Is there a Condorcet winner? If there is no Condorcet winner, is there a Weak Condorcet winner? Show the work you do in deciding, including vote totals, and state your conclusion.arrow_forward
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