Question

question 5
number of voters 8 5 14 17 11
1st choice c c a d b
2nd choice a b b a c
3rd choice d a d c d
4th choice b d c b a
find the winner under the borda count. use the count that assigns 1 point to last place.
winner =
submit question

Explanation:

Step1: Determine points per rank

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

Step2: Calculate points for A

• Group 1 (8 voters): 2nd choice (3 points) → \(8\times3 = 24\)
• Group 2 (5 voters): 3rd choice (2 points) → \(5\times2 = 10\)
• Group 3 (14 voters): 1st (4) and 2nd (3) → \(14\times4 + 14\times3 = 56 + 42 = 98\)? Wait, no: Group 3 has 1st choice A (14 voters, 4 points) and 2nd choice B. Wait, no: For candidate A, check each group:
• Group 1 (8 voters): 1st: C, 2nd: A → A gets 3 points (2nd) → \(8\times3 = 24\)
• Group 2 (5 voters): 1st: C, 2nd: B, 3rd: A → A gets 2 points (3rd) → \(5\times2 = 10\)
• Group 3 (14 voters): 1st: A → 4 points → \(14\times4 = 56\); 2nd: B → A not here. 3rd: D, 4th: C. So only 1st choice here: 56.
• Group 4 (17 voters): 1st: D, 2nd: A → A gets 3 points → \(17\times3 = 51\)
• Group 5 (11 voters): 1st: B, 2nd: C, 3rd: D, 4th: A → A gets 1 point (4th) → \(11\times1 = 11\)

Total for A: \(24 + 10 + 56 + 51 + 11 = 152\)

Step3: Calculate points for B

• Group 1 (8 voters): 4th choice → 1 point → \(8\times1 = 8\)
• Group 2 (5 voters): 2nd choice → 3 points → \(5\times3 = 15\)
• Group 3 (14 voters): 2nd choice → 3 points → \(14\times3 = 42\)
• Group 4 (17 voters): 4th choice → 1 point → \(17\times1 = 17\)
• Group 5 (11 voters): 1st choice → 4 points → \(11\times4 = 44\)

Total for B: \(8 + 15 + 42 + 17 + 44 = 126\)

Step4: Calculate points for C

• Group 1 (8 voters): 1st choice → 4 points → \(8\times4 = 32\)
• Group 2 (5 voters): 1st choice → 4 points → \(5\times4 = 20\)
• Group 3 (14 voters): 4th choice → 1 point → \(14\times1 = 14\)
• Group 4 (17 voters): 3rd choice → 2 points → \(17\times2 = 34\)
• Group 5 (11 voters): 2nd choice → 3 points → \(11\times3 = 33\)

Total for C: \(32 + 20 + 14 + 34 + 33 = 133\)

Step5: Calculate points for D

• Group 1 (8 voters): 3rd choice → 2 points → \(8\times2 = 16\)
• Group 2 (5 voters): 4th choice → 1 point → \(5\times1 = 5\)
• Group 3 (14 voters): 3rd choice → 2 points → \(14\times2 = 28\)
• Group 4 (17 voters): 1st choice → 4 points → \(17\times4 = 68\)
• Group 5 (11 voters): 3rd choice → 2 points → \(11\times2 = 22\)

Total for D: \(16 + 5 + 28 + 68 + 22 = 139\)

Answer:

A