Candidates A, B, C, and D are competing to win an award. There are 5 voters in this election. The chart below shows the preference schedule. Voter 1 1st choice A B BC 2nd choice 3rd choice C 4th choice D Voter 2 Voter 3 Voter 4 B C B D A D A D B C A Voter 5 A D C B 6. With the previous example, what is the outcome if you use the Borda count method?
Candidates A, B, C, and D are competing to win an award. There are 5 voters in this election. The chart below shows the preference schedule. Voter 1 1st choice A B BC 2nd choice 3rd choice C 4th choice D Voter 2 Voter 3 Voter 4 B C B D A D A D B C A Voter 5 A D C B 6. With the previous example, what is the outcome if you use the Borda count method?
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
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Question

Transcribed Image Text:Candidates A, B, C, and D are competing to win an award. There are 5 voters in this election. The chart below shows the preference schedule.
| | Voter 1 | Voter 2 | Voter 3 | Voter 4 | Voter 5 |
|---------|---------|---------|---------|---------|---------|
| 1st choice | A | B | C | D | A |
| 2nd choice | B | C | B | B | D |
| 3rd choice | C | D | D | C | C |
| 4th choice | D | A | A | A | B |
6. With the previous example, what is the outcome if you use the Borda count method?
### Explanation of the Borda Count Method:
The Borda count method assigns points to each rank, with the top choice receiving the most points and descending in order. For example, if there are 4 candidates, the first choice receives 3 points, the second choice 2 points, the third choice 1 point, and the last choice 0 points.
To calculate the total points for each candidate:
- **Candidate A**
- 1st choice: 2 votes x 3 points = 6 points
- 2nd choice: 0 votes x 2 points = 0 points
- 3rd choice: 0 votes x 1 point = 0 points
- 4th choice: 3 votes x 0 points = 0 points
- **Total points: 6**
- **Candidate B**
- 1st choice: 1 vote x 3 points = 3 points
- 2nd choice: 3 votes x 2 points = 6 points
- 3rd choice: 0 votes x 1 point = 0 points
- 4th choice: 1 vote x 0 points = 0 points
- **Total points: 9**
- **Candidate C**
- 1st choice: 1 vote x 3 points = 3 points
- 2nd choice: 0 votes x 2 points = 0 points
- 3rd choice: 3 votes x 1 point =
Expert Solution

Step 1: Determine the given information
The given preference schedule for the candidates
Voter 1 | Voter 2 | Voter 3 | Voter 4 | Voter 5 | |
1st choice | A | B | C | D | A |
2nd choice | B | C | B | B | D |
3rd choice | C | D | D | C | C |
4th choice | D | A | A | A | B |
The objective is to obtain the winner based on the Borda count method.
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