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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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Mathematical Excursions (MindTap C...
4th Edition
Richard N. Aufmann + 3 others
Publisher: Cengage Learning
ISBN: 9781305965584
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Section
BuyFindarrow_forward
Mathematical Excursions (MindTap C...
4th Edition
Richard N. Aufmann + 3 others
Publisher: Cengage Learning
ISBN: 9781305965584
Chapter 4.2, Problem 37ES
Textbook Problem
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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.
To determine
(a)
Find the winner of the election by the help of Borda count method.
Explanation of Solution
Given:
The given data is
Calculation:
Given:
Use Borda count method.
For each first place
For each second place
For each third place
Vote received by Jhon Lorenz is,
First place vote
Second place vote
Third place vote
Total votes
To determine
(b)
Check whether the majority criteria is violated or not.
To determine
(c)
Find the candidate who wins all head-to-head comparisons.
To determine
(d)
Explain why the Condorcet criterion has been violated.
To determine
(e)
Find the winner of the election by the help of Borda count method.
To determine
(f)
Describe the independence of irrelevant alternatives criterion has been violated.
Chapter 4 Solutions
Mathematical Excursions (MindTap Course List)
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