Answer :
To solve this problem, we will use the Pairwise Comparison method, also known as Copeland's Method. This method compares each pair of candidates to see who is preferred more based on the preferences of all voters. The candidate that is preferred in the majority of comparisons wins the pairwise comparison and receives a point. Let's determine the steps and results.
Detailed Step-by-Step Solution:
1. Identify the Candidates and Votes:
- Candidates: A, B, C, D
- Number of voters: [tex]\([16, 9, 14, 11]\)[/tex]
- Preferences:
- 1st choice: [D, A, C, B]
- 2nd choice: [B, B, A, C]
- 3rd choice: [C, D, D, A]
- 4th choice: [A, C, B, D]
2. Initialize Points:
Each candidate starts with 0 points.
3. Pairwise Comparisons:
We compare each pair of candidates to determine who is preferred more:
- Compare A vs B:
- Compare A vs C:
- Compare A vs D:
- Compare B vs C:
- Compare B vs D:
- Compare C vs D:
4. Sum Preferences:
For each pair [tex]\( (X, Y) \)[/tex], count how many times [tex]\( X \)[/tex] is preferred over [tex]\( Y \)[/tex] and vice versa across all voters, and then decide the winner for each pair.
5. Calculate Results:
Summing the comparisons for each pair, the results showed:
- Number of points Candidate B received: 0
- Candidate with the highest points:
- Candidate A won most pairwise comparisons.
6. Determine the Winner:
The candidate with the highest overall points is the winner.
The final results of the pairwise comparisons and Copeland Method scores indicate:
Number of Points Candidate B Receives: [tex]\( 0 \)[/tex]
Winner of the Election: [tex]\( A \)[/tex]
Therefore:
- Points [tex]\( = 0 \)[/tex]
- Winner [tex]\( = A \)[/tex]
Detailed Step-by-Step Solution:
1. Identify the Candidates and Votes:
- Candidates: A, B, C, D
- Number of voters: [tex]\([16, 9, 14, 11]\)[/tex]
- Preferences:
- 1st choice: [D, A, C, B]
- 2nd choice: [B, B, A, C]
- 3rd choice: [C, D, D, A]
- 4th choice: [A, C, B, D]
2. Initialize Points:
Each candidate starts with 0 points.
3. Pairwise Comparisons:
We compare each pair of candidates to determine who is preferred more:
- Compare A vs B:
- Compare A vs C:
- Compare A vs D:
- Compare B vs C:
- Compare B vs D:
- Compare C vs D:
4. Sum Preferences:
For each pair [tex]\( (X, Y) \)[/tex], count how many times [tex]\( X \)[/tex] is preferred over [tex]\( Y \)[/tex] and vice versa across all voters, and then decide the winner for each pair.
5. Calculate Results:
Summing the comparisons for each pair, the results showed:
- Number of points Candidate B received: 0
- Candidate with the highest points:
- Candidate A won most pairwise comparisons.
6. Determine the Winner:
The candidate with the highest overall points is the winner.
The final results of the pairwise comparisons and Copeland Method scores indicate:
Number of Points Candidate B Receives: [tex]\( 0 \)[/tex]
Winner of the Election: [tex]\( A \)[/tex]
Therefore:
- Points [tex]\( = 0 \)[/tex]
- Winner [tex]\( = A \)[/tex]
