Mathematical Excursions (MindTap Course List)
4th Edition
ISBN: 9781305965584
Author: Richard N. Aufmann, Joanne Lockwood, Richard D. Nation, Daniel K. Clegg
Publisher: Cengage Learning
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Textbook Question
Chapter 4.2, Problem 37ES
Election Three candidates are running for mayor. A vote was taken in which the candidates were ranked in order of preference. The results are shown in the preference schedule below.
a. Use the Borda count method to determine the winner of the election.
b. Verify that the majority criterion has been violated.
c. Identify the candidate who wins all head-to-head comparisons.
d. Explain why the Condorcet criterion has been violated.
e. If Marcia Beasley drops out of there for mayor (and voter preferences remain the same), determine the winner of the election again, using the Borda count method.
f. Explain why the independence of irrelevant alternatives criterion has been violated.
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A Senior High School class held an election for class president. Instead of just voting for one candidate, the students needed to rank all the candidates according to preference. The table presents the results.
RANKINGS
Anton
2
3
1
3
4
2
Maria
4
1
3
4
1
3
Shelly
1
2
2
2
3
4
Troy
3
4
4
1
2
1
Number of Votes
36
53
41
27
31
45
1. Who is the winner by plurality? 2. What is the majority number of votes?
The Rosetown community association plans to meet once each month. The association members are deciding what day of the week to meet by holding a vote.
The choices are Monday (M), Tuesday (T), and Friday (F). Instead of voting for only one day, each member ranks the three days in order of preference. Each
member's ballot gives the member's first, second, and third choice for a monthly meeting day. Here are the ballots submitted.
Baliot 1
Ballot 2
Ballot 3
Ballot 4
Ballot 5
Ballot 6
Balot 7
Ballot 8
Ballot 9
1st
M.
14
M
F.
M.
1st
2n
2n
2nd
2nd
M
M
T.
2nd
2
2nd
2nd
2nd
M.
3rd
3rd
3rd
F
3rd
3rd
M
3rd
3rd
M.
3rd
Ballot 10
Ballot 11
Ballot 12
Ballot 13
Balot 14
Ballot 15
Ballot 16
1st
F
M
1st
T.
M
14
2nd
T.
2nd
T.
2nd
2ne
20
2n M
2nd
F
M
3rd
M
3rd
3rd
M
3rd
3
3rd
Construct a preference table to summarize the ballots. You can add or remove columns in the table as needed. Note: The individual ballots above will highlight
when clicked. (Highlighting the ballots can help you with your…
Voting and Apportionment
Question:
1. Winner by Plurality
2. Winner by Borda Count Method
Chapter 4 Solutions
Mathematical Excursions (MindTap Course List)
Ch. 4.1 - Verify this apportionment using the Jefferson...Ch. 4.1 - Find the apportionment that would have resulted if...Ch. 4.1 - Prob. 3EECh. 4.1 - Find the apportionment that would have resulted if...Ch. 4.1 - Explain how to calculate the standard divisor of...Ch. 4.1 - Teacher Aides A total of 25 teacher aides are to...Ch. 4.1 - In the Hamilton apportionment method, explain how...Ch. 4.1 - Prob. 4ESCh. 4.1 - Governing Boards The following table shows how the...Ch. 4.1 - Forest Rangers The table below shows how the...
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Does the winner in Exercise 12 satisfy the...Ch. 4.2 - Prob. 33ESCh. 4.2 - Prob. 34ESCh. 4.2 - Prob. 35ESCh. 4.2 - Prob. 36ESCh. 4.2 - Election Three candidates are running for mayor. A...Ch. 4.2 - Film Competition Three films have been selected as...Ch. 4.2 - 39. Election A campus club needs to elect four...Ch. 4.2 - Scholarship Awards The members of a scholarship...Ch. 4.2 - Another method of voting is to assign a weight. or...Ch. 4.2 - Prob. 42ESCh. 4.2 - Prob. 43ESCh. 4.3 - Using the data in Example 1 on page 211, list all...Ch. 4.3 - For the data in Example I on page 211, calculate...Ch. 4.3 - Prob. 3EECh. 4.3 - Prob. 4EECh. 4.3 - Create a voting system with three members that is...Ch. 4.3 - Prob. 6EECh. 4.3 - Prob. 7EECh. 4.3 - In the following exercises that involve weighted...Ch. 4.3 - In the following exercises that involve weighted...Ch. 4.3 - Prob. 3ESCh. 4.3 - Calculate, if possible, the l3anzhaf power index...Ch. 4.3 - Calculate, if possible, the l3anzhaf power index...Ch. 4.3 - Calculate, if possible, the l3anzhaf power index...Ch. 4.3 - Calculate, if possible, the l3anzhaf power index...Ch. 4.3 - Prob. 8ESCh. 4.3 - Prob. 9ESCh. 4.3 - Calculate, if possible, the l3anzhaf power index...Ch. 4.3 - Calculate, if possible, the l3anzhaf power index...Ch. 4.3 - Calculate, if possible, the l3anzhaf power index...Ch. 4.3 - Prob. 13ESCh. 4.3 - Prob. 14ESCh. 4.3 - Music Education A music department Consists of a...Ch. 4.3 - Prob. 16ESCh. 4.3 - Criminal Justice In a criminal trial, each of the...Ch. 4.3 - Criminal Justice In California civil court cases,...Ch. 4.3 - Identify any dictator and all dummies for each...Ch. 4.3 - Identify any dictator and all dummies for each...Ch. 4.3 - Prob. 21ESCh. 4.3 - Prob. 22ESCh. 4.3 - Football At the beginning of each football season,...Ch. 4.3 - Prob. 24ESCh. 4.3 - Prob. 25ESCh. 4.3 - Prob. 26ESCh. 4.3 - Consider the weighted voting system { q:8,3,3,2 },...Ch. 4.3 - Prob. 28ESCh. 4.3 - Prob. 29ESCh. 4.3 - UN Security Council The United Nations C Security...Ch. 4 - Education The following table shows the...Ch. 4 - Airline Industry The following table shows the...Ch. 4 - Airline Industry The table below shows how the...Ch. 4 - 4. 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Calculate the Banzhaf power indices for voters...Ch. 4 - Calculate the Banzhaf power indices for voters A,...Ch. 4 - Prob. 27RECh. 4 - Identify any dictator and all dummies for each...Ch. 4 - Four voters. A. B. C. and D. make decisions by...Ch. 4 - Postal Service The table below shows the number of...Ch. 4 - Computer Allocation The following table shows the...Ch. 4 - High School Counselors The following table shows...Ch. 4 - Prob. 4TCh. 4 - Consumer Preference One hundred consumers ranked...Ch. 4 - Prob. 6TCh. 4 - Exam Review A professor is preparing an extra...Ch. 4 - Prob. 8TCh. 4 - Drama Department The four staff members. A, B,C,...Ch. 4 - Three voters. A. B. and C, make decisions by using...
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