Questions: Number of voters: 15, 13, 4 1st choice: B, A, C 2nd choice: C, C, B 3rd choice: A, B, A Condorcet Candidate = none Number of voters: 8, 9, 10, 7 1st choice: A, B, D, C 2nd choice: B, C, A, A 3rd choice: C, D, B, D 4th choice: D, A, C, B Points = Winner =

Solution Steps

To find the Condorcet Candidate, we need to compare each candidate against every other candidate in head-to-head matchups. A Condorcet Candidate is one who would win against every other candidate in these pairwise comparisons. If no such candidate exists, then there is no Condorcet Candidate.

For the second question, using Pairwise Comparison (Copeland's Method), we compare each candidate against every other candidate. A candidate earns 1 point for each head-to-head victory, 0.5 points for a tie, and 0 points for a loss. We calculate the total points for Candidate D and determine the overall winner by comparing the total points of all candidates.

To find the Condorcet Candidate, we compare each candidate in head-to-head matchups based on voter preferences. The results of the pairwise comparisons show the following victories:

• Candidate \( B \) wins against \( A \) (1 victory).
• Candidate \( C \) wins against both \( A \) and \( B \) (2 victories).
• Candidate \( A \) does not win against any candidate (0 victories).

Since Candidate \( C \) wins against both \( A \) and \( B \), it is the Condorcet Candidate.

Using Copeland's Method, we calculate the points for each candidate based on their head-to-head matchups. The scores are as follows:

• Candidate \( A \): 2.0 points
• Candidate \( B \): 1.5 points
• Candidate \( C \): 1.0 points
• Candidate \( D \): 1.5 points

Candidate \( D \) receives \( 1.5 \) points.

The overall winner is determined by the candidate with the highest score. In this case, Candidate \( A \) has the highest score of \( 2.0 \) points.

Final Answer