Excursions in Modern Mathematics (9th Edition)
9th Edition
ISBN: 9780134468372
Author: Peter Tannenbaum
Publisher: PEARSON
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Textbook Question
Chapter 1, Problem 35E
Number of voters |
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B | C | A | D | A | D |
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E | E | B | C | D | B |
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A | D | C | B | E | C |
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C | A | D | B | D | A |
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D | B | E | A | B | E |
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Find the winners of an election with 55 voters whose preference schedule is given below using Plurality Method, Borda Count Method, Method of Pairwise Comparison, and Plurality with Elimination Method. Show the complete output and the winner of each method.
Consider an election with 301 voters cast for 3 candidates. What is the smallest number of first-place votes that a candidate can receive to win by the Plurality method?
Determine which candidate will win using the Borda count method.
Rankings for Club President
Franco
1
4
2
1
3
Jurdan
4
1
3
3
2
Tarshikov
3
2
4
2
1
Vansaghi
2
3
1
4
4
Number of voters:
8
12
4
3
9
Jurdan
Vansaghi
Franco
Tarshikov
Chapter 1 Solutions
Excursions in Modern Mathematics (9th Edition)
Ch. 1 - Figure 1-8 shows the preference ballots for an...Ch. 1 - Figure 1-9 shows the preference ballots for an...Ch. 1 - An election is held to choose the Chair of the...Ch. 1 - The student body at Eureka High School is having...Ch. 1 - An election is held using the printed-names format...Ch. 1 - Prob. 6ECh. 1 - Prob. 7ECh. 1 - Table 1-30 shows a conventional preference...Ch. 1 - The Demublican Party is holding its annual...Ch. 1 - The Epicurean Society is holding its annual...
Ch. 1 - Table 1-31 shows the preference schedule for an...Ch. 1 - Table 1-32 shows the preference schedule for an...Ch. 1 - Table 1-33 shows the preference schedule for an...Ch. 1 - Table 1-34 shows the preference schedule for an...Ch. 1 - Table 1-35 shows the preference schedule for an...Ch. 1 - Table1-36 shows the preference schedule for an...Ch. 1 - Table 1-25 see Exercise 3 shows the preference...Ch. 1 - Table 1-26 see Exercise 4 shows the preference...Ch. 1 - Table 1-25 see Exercise 3 shows the preference...Ch. 1 - Table 1-26 see Exercise 4 shows the preference...Ch. 1 - Table 1-31see Exercise 11 shows the preference...Ch. 1 - Table 1-32 see Exercise 12 shows the preference...Ch. 1 - Table 1-33 see Exercise 13 shows the preference...Ch. 1 - Table 1-34 Number of voters 6 6 5 4 3 3 1st A B B...Ch. 1 - Table 1-35 Percent of voters 24 23 19 14 11 9 1st...Ch. 1 - Table 1-36 Percent of voters 25 21 15 12 10 9 8...Ch. 1 - The Heisman Award. Table 1-37 shows the results...Ch. 1 - The 2014 AL Cy Young Award. Table 1-38 shows the...Ch. 1 - An election was held using the conventional Borda...Ch. 1 - Imagine that in the voting for the American League...Ch. 1 - Table 1-31 see Exercise 11 shows the preference...Ch. 1 - Table 1-32 see Exercise 12 shows the preference...Ch. 1 - Table1-33 Number of voters 6 5 4 2 2 2 2 1st C A B...Ch. 1 - Table 1-34 See Exercise 14 shows the preference...Ch. 1 - Table1-39_ shows the preference schedule for an...Ch. 1 - Table1-40_ shows the preference schedule for an...Ch. 1 - Table 1-35 see Exercise 15 shows the preference...Ch. 1 - Table 1-36 see Exercise 16 shows the preference...Ch. 1 - Top-Two Instant-Runoff Voting. Exercises 39 and 40...Ch. 1 - Top-Two Instant-Runoff Voting. Exercises 39 and 40...Ch. 1 - Table 1-31 see Exercise 11 shows the preference...Ch. 1 - Table 1-32 See Exercise 12 shows the preference...Ch. 1 - Table 1-33 see Exercise 13 shows the preference...Ch. 1 - Table 1-34 see Exercise 14 shows the preference...Ch. 1 - Table 1-35 see Exercise 15 shows the preference...Ch. 1 - Table 1-36 see Exercise 16 shows the preference...Ch. 1 - Table 1-39 see Exercise 35 shows the preference...Ch. 1 - Table1-40 see Exercise36 shows the preference...Ch. 1 - An election with five candidates A, B. C, D, and E...Ch. 1 - An election with six candidates A, B, C, D, E, and...Ch. 1 - Use Table 1-41 to illustrate why the Borda count...Ch. 1 - Use Table 1-32 to illustrate why the...Ch. 1 - Use Table 1-42 to illustrate why the plurality...Ch. 1 - Use the Math Club election Example 1.10 to...Ch. 1 - Use Table 1-43 to illustrate why the...Ch. 1 - Explain why the method of pair wise comparisons...Ch. 1 - Prob. 57ECh. 1 - Explain why the plurality method satisfies the...Ch. 1 - Explain why the Borda count method satisfies the...Ch. 1 - Explain why the method of pairwise comparisons...Ch. 1 - Two-candidate elections. Explain why when there...Ch. 1 - Alternative version of the Borda count. The...Ch. 1 - Reverse Borda count. Another commonly used...Ch. 1 - The average ranking. The average ranking of a...Ch. 1 - The 2006 Associated Press college football poll....Ch. 1 - The Pareto criterion. The following fairness...Ch. 1 - The 2003-2004 NBA Rookie of the Year vote. Each...Ch. 1 - Top-two IRV is a variation of the...Ch. 1 - The Coombs method. This method is just like the...Ch. 1 - Bucklin voting. This method was used in the early...Ch. 1 - The 2016 NBA MVP vote. The National Basketball...Ch. 1 - The Condorcet loser criterion. If there is a...Ch. 1 - Consider the following fairness criterion: If a...Ch. 1 - Suppose that the following was proposed as a...Ch. 1 - Consider a modified Borda count where a...
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Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.Similar questions
determine the (a) winning coalitions; and for each winning coalition, (b) determine the critical voter.
1. Voters A, B, C, and D in the weighted voting system { 31: 19, 15, 12, 10 }.
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determine the (a) winning coalitions; and for each winning coalition, (b) determine the critical voter.
1.Voters A, B, C, and D in the weighted voting system of { 28: 19, 6, 4, 2 }.
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Last year at a certain high school, 11 students sought the nomination for president of the student body. In how many ways could the voters (student body) rank their first 4 choices?
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A campus club needs to elect four officers: a president, a vice president, a secretary, and a treasurer. The club has five volunteers. Rather than vote individually for each position, the club members will rank the candidates in order of preference. The votes will then be tallied using the Borda Count method. The candidate receiving the highest number of points will be president, the candidate receiving the next highest number of points is vice president, the candidate receiving the next highest number of points is secretary, and the candidate receiving the next highest number of points will be treasurer.
Rankings
Cynthia
4
2
5
2
3
Andrew
2
3
1
4
5
Jen
5
1
2
3
2
Hector
1
5
4
1
4
Medin
3
4
3
5
1
Number of votes:
9
12
25
24
23
For the preference schedule shown, determine who wins each position in the club.
president
vice president
secretary
treasurer
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The Science club is selecting its representative for a competition. The members rank the 4 candidates given in the preference table below:
Using the agenda ABCD, who is the pairwise sequential winner?
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explain why when there are only two candidates, the four voting methods discussed give the same winner and the winner is determined by straight majority?
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Consider an election with 589 votesa) If there are 6 candidates, what is the smallest number of first-place votes a candidate could win with under the Plurality method? votesb) If there are 7 candidates, what is the smallest number of first-place votes a candidate could win with under the Plurality method? votes
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One of the voting methods requires voters to rank all candidates from the most favorable to the least favorable. Each last-place vote receives 1 point, each next-to-last place vote 2 points, and so on.
This voting method is called the _________ method. The candidate with the ______ is the winner.
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What is the maximum number of points that a candidate can earn in an election using the pairwise comparison method if there are
nine
candidates?
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1. A local zoo has asked 28 people to rank their preferences for the four names shown below in the table. The zoo will use the pairwise comparison voting method to pick a winning name that will be given to a newborn baby tiger. Use the given information to complete a head-to-head comparison table and determine the winning name.
Rankings for Tiger Cub Name
Apollo
1
4
2
1
3
Bengal
4
1
3
3
2
King
3
2
4
2
1
Prince
2
3
1
4
4
Number of voters:
2
4
8
7
7
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The Science club is selecting its representative for a competition. The members rank the 4 candidates given in the preference table below:
Who is the Hare system winner?
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An organization with branches across the Northeast is trying to decide where it should hold its annual employee picnic. Each branch ranks the locations of Augusta, ME; Boston, MA; and Erie, PA, and the following preference schedule is created:
Number of Votes
36
24
19
16
13
1st Choice
Erie
Augusta
Boston
Augusta
Boston
2nd Choice
Augusta
Erie
Erie
Boston
Augusta
3rd Choice
Boston
Boston
Augusta
Erie
Erie
The organization has chosen to use the Borda Count method to determine which city they will hold their picnic in. Where will the organization’s picnic be held? Make sure to include an explanation along with your answer.
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