Excursions In Modern Mathematics, 9th Edition
9th Edition
ISBN: 9780134494142
Author: Tannenbaum
Publisher: PEARSON
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Chapter 2, Problem 74E
To determine
To calculate:
The Shapley-Shubik power distribution for given weighted voting system.
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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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- How many first place votes are needed for a majority?arrow_forwardUse 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 Oarrow_forwardUse 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 4 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 b. Preferential: Jazmine wins with 1370, Plurality: Mary wins with 700 c. Preferential: Jazmine wins with 970, Plurality: Mary wins with 630 d. Preferential: Jazmine wins with 1370, Plurality: Mary wins with 630arrow_forward
- A school is going to offer a new class next year. The school polls the students to see which class they would prefer. 47% respond that they would like East Asian History. 53% respond that they would like Southern African Studies. The margin of error for the poll is +4%. Explain whether the poll clearly indicates the majority's preference.arrow_forwardFour candidates, Lito, Quennie, Kyleigh, and Irish are running for president of the student government. After the polls close, votes are tallied, and the results in the table below are obtained. Candidate Lito Quennie Kyleigh IrishNumber of Votes 314 155 1,052 479 How many votes were cast? Using the plurality method of voting, who wins the election?Did the winner receive a majority of the votes? Why?arrow_forwardSolve the problem. Which voting method always satisfies the head-to- head criterion? Borda count plurality O pairwise comparison plurality with eliminationarrow_forward
- Consider the scenario of three candidates, A, B, and C, who are running for president of the student council. Determine the winner using the Borda count method. Number of Votes 50 65 60 First Choice ACC Second Choice BBA Third Choice CAB The winner is The winner received points.arrow_forwardTwo candidates are running for school president. The two choices are Emilio and Jose. The school's newspaper has been doing some polling. Polling shows Emilio is preferred by a small majority, 52% for Emilio to 48% for Jose. However, before the vote is held, a new candidate has decided to run: Paul. Not a lot of people like Paul, but there are some Emilio supporters who would actually vote for Paul. The results of the vote are below. Jose 48% Emilio 45% Paul 7% What statement below is correct about adding a third candidate to the plurality vote? Paul did not win the vote, but it has no effect on drawing enough support away from Emilio to make Jose the winner, even though a majority of students preferred Emilio over Jose when there were two candidates. Paul did not with the vote, but he draws enough support away from Emilio to make Jose the winner, even though a majority of students preferred Emilio over Jose when there were two candidates. Paul did not win the vote, so because of this,…arrow_forwardSeven students are running for student council. The person with the most votes will be president,Second most votes will be vice president, third most votes will be Secretary. How many different results are there?arrow_forward
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