Excursions in Modern Mathematics (9th Edition)
9th Edition
ISBN: 9780134468372
Author: Peter Tannenbaum
Publisher: PEARSON
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Question
Chapter 2, Problem 74E
To determine
To calculate:
The Shapley-Shubik power distribution for given weighted voting system.
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The students in a class get to decide on the color of the classroom. The two choices are blue and yellow. Polling shows yellow is preferred by a small
majority, 53% for yellow to 47% for blue. However, before the vote is held, a new color choice is added: red. Not a lot of people like red, but there are
some yellow supporters who would actually vote for red. The results of the vote are below.
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Yellow
Red
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44%
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What statement below is correct about adding a third choice to the plurality vote?
O a
Ob
Oc
d
Red did not win the vote, but it draws enough support away from yellow to make blue the winner, even though a majority of
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Red did not win the vote, but it had no effect on drawing enough support away from yellow to make blue the winner, even though
a majority of students preferred yellow over blue when there were two choices.
Red did not win the vote, so because of this, yellow should win the vote over blue.…
How many first place votes are needed for a majority?
Use the preferential voting method to determine the winner and compare it to the single candidate voting or plurality method. Who wins the
preferential vote and the single candidate vote?
There are 2000 voters and the candidates need 1001 to win. There are
candidates for the house of representatives and you have to rank
them by preference.
Votes
1st
2nd
3rd
4th
630
Mary
Jazmine
Marcos
Henry
600
Jazmine
Marcos
Henry
Mary
400
Henry
Marcos
Jazmine
Mary
370
Marcos
Jazmine
Henry
Mary
a
Preferential: Henry wins with 770, Plurality: Mary wins with 630
Preferential: Jazmine wins with 1370, Plurality: Mary wins with 700
Preferential: Jazmine wins with 970, Plurality: Mary wins with 630
d
Preferential: Jazmine wins with 1370, Plurality: Mary wins with 630
O O O O
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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