Question

number of voters 12 16 13
1st choice c a b
2nd choice b c c
3rd choice a b a

find the winner of this election under the borda count method.

winner =

Explanation:

Step1: Define Borda Count Points

In Borda Count, 1st choice gets 3 points, 2nd choice gets 2 points, 3rd choice gets 1 point (since there are 3 candidates, \( n = 3 \), points per rank: \( n, n - 1, \dots, 1 \)).

Step2: Calculate Points for Candidate A

• 1st choice: 16 voters, points: \( 16 \times 3 = 48 \)
• 2nd choice: 0 voters (check table), points: \( 0 \times 2 = 0 \)
• 3rd choice: \( 12 + 13 = 25 \) voters, points: \( 25 \times 1 = 25 \)
• Total for A: \( 48 + 0 + 25 = 73 \)

Step3: Calculate Points for Candidate B

• 1st choice: 13 voters, points: \( 13 \times 3 = 39 \)
• 2nd choice: 12 voters, points: \( 12 \times 2 = 24 \)
• 3rd choice: 16 voters, points: \( 16 \times 1 = 16 \)
• Total for B: \( 39 + 24 + 16 = 79 \)

Step4: Calculate Points for Candidate C

• 1st choice: 12 voters, points: \( 12 \times 3 = 36 \)
• 2nd choice: \( 16 + 13 = 29 \) voters, points: \( 29 \times 2 = 58 \)
• 3rd choice: 0 voters, points: \( 0 \times 1 = 0 \)
• Total for C: \( 36 + 58 + 0 = 94 \)

Answer:

C