Sample Solution from
Excursions in Modern Mathematics (9th Edition)
9th Edition
ISBN: 9780134468372
Chapter 1
Problem 1E
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Textbook Problem
Figure 1-8 shows the preference ballots for an election with 21 voters and 5 candidates. Write out the preference schedule for this election.
Figure 1-8
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Expert Solution
To determine
To find:
The preference schedule for the election with given preference ballots.
Answer
Solution:
The preference schedule for the preference ballots for 21 voters and 5 candidates is,
| Number of Voters | 5 | 5 | 3 | 3 | 3 | 2 |
| 1st Choice | A | C | A | B | D | D |
| 2nd Choice | B | E | D | E | C | C |
| 3rd Choice | C | D | B | A | B | B |
| 4th Choice | D | A | C | C | E | A |
| 5th Choice | E | B | E | D | A | E |
Explanation of Solution
Given:
The preference ballots for 21 voters and 5 candidates are given as,
Calculation:
The ballots of the same preferences are grouped together as,
The preference schedule table for the above ballots is given by,
| Number of Voters | 5 | 5 | 3 | 3 | 3 | 2 |
| 1st Choice | A | C | A | B | D | D |
| 2nd Choice | B | E | D | E | C | C |
| 3rd Choice | C | D | B | A | B | B |
| 4th Choice | D | A | C | C | E | A |
| 5th Choice | E | B | E | D | A | E |
Conclusion:
The preference schedule for the preference ballots for 21 voters and 5 candidates is,
| Number of Voters | 5 | 5 | 3 | 3 | 3 | 2 |
| 1st Choice | A | C | A | B | D | D |
| 2nd Choice | B | E | D | E | C | C |
| 3rd Choice | C | D | B | A | B | B |
| 4th Choice | D | A | C | C | E | A |
| 5th Choice | E | B | E | D | A | E |
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