Four candidates, Allen (A), Bryant (B), Chula (C) and Ditka (D), are running for president of a club. The club uses a "First/Second/Third" ranking system. After the polls close, votes are tallied and the following results are obtained
ranking 3565 1655 478 3641
first A C C B
second B A B C
third C B D D
a. Using the Borda Count with {3,2,1} assignment, which candidate wins? ? Allen Bryant Chula Ditka ?
b. What total did the winning candidate receive?
To determine the winner using the Borda Count with the {3, 2, 1} assignment, we need to assign points to each candidate based on their ranking. The first-place candidate receives 3 points, the second-place candidate receives 2 points, and the third-place candidate receives 1 point. We will calculate the total points for each candidate and determine the winner.
a. Let's calculate the points for each candidate:
- Allen (A): 3 (from first place in the second column) + 1 (from third place in the first column) = 4 points
- Bryant (B): 2 (from second place in the first column) + 2 (from second place in the third column) = 4 points
- Chula (C): 1 (from third place in the second column) + 3 (from first place in the third column) + 1 (from third place in the second column) = 5 points
- Ditka (D): 1 (from third place in the third column) + 2 (from second place in the third column) = 3 points
Now let's compare the total points:
- Allen (A): 4 points
- Bryant (B): 4 points
- Chula (C): 5 points
- Ditka (D): 3 points
The candidate with the highest total points is Chula (C). Therefore, Chula wins the election.
b. The winning candidate, Chula (C), received a total of 5 points.