Question

number of voters 2 8 5 1 6 9
1st choice a c b c a d
2nd choice b d d a c a
3rd choice c b c d b b
4th choice d a a b d c

find the borda count for candidate c. use the count that assigns 1 point to last place.

count = .

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Explanation:

Step1: Determine points per place

Since there are 4 choices, last place (4th) gets 1 point, 3rd place gets 2 points, 2nd place gets 3 points, 1st place gets 4 points.

Step2: Analyze each group of voters for Candidate C

• Group 1: 2 voters, 1st choice A, 2nd B, 3rd C, 4th D. So C is 3rd here: \(2 \times 2 = 4\) (wait, no: 3rd place is 2 points? Wait, no: 4 choices, so places are 1st (4 points), 2nd (3), 3rd (2), 4th (1). So for each group:
• Group 1 (2 voters): C is 3rd. Points: \(2 \times 2 = 4\)? Wait no, 3rd place is 2 points? Wait, 4 choices: 1st (4), 2nd (3), 3rd (2), 4th (1). Yes. So:
• Group 1: 2 voters, C is 3rd: \(2 \times 2 = 4\)
• Group 2: 8 voters, 1st C, 2nd D, 3rd B, 4th A. C is 1st: \(8 \times 4 = 32\)
• Group 3: 5 voters, 1st B, 2nd D, 3rd C, 4th A. C is 3rd: \(5 \times 2 = 10\)
• Group 4: 1 voter, 1st C, 2nd A, 3rd D, 4th B. C is 1st: \(1 \times 4 = 4\)
• Group 5: 6 voters, 1st A, 2nd C, 3rd B, 4th D. C is 2nd: \(6 \times 3 = 18\)
• Group 6: 9 voters, 1st D, 2nd A, 3rd B, 4th C. C is 4th: \(9 \times 1 = 9\)

Step3: Sum all points

Now sum these up: \(4 + 32 + 10 + 4 + 18 + 9\)
First, \(4 + 32 = 36\); \(36 + 10 = 46\); \(46 + 4 = 50\); \(50 + 18 = 68\); \(68 + 9 = 77\)

Answer:

77