Twelve people serve on a board and are considering three alternatives: A, B, and C. The choices followed by vote is shown in following table. Determine the winner, if any, using a Borda count.
(ABC) 2
(ACB) 4
(BAC) 2
(BCA) 1
(CAB) 2
(CBA) 1
The winner is _____?
(ABC) 6, 4, 2
(ACB) 12, 4, 8
(BAC) 4, 6, 2
(BCA) 1, 3, 2
(CAB) 4, 2, 6
(CAB) 3, 2, 1
Check my work. Add them up. What do you get?
(ACB)24
You only need to determine the winner.
Thank you Ms. Sue - Happy Holidays to you!
You're welcome, DC. And Happy Holidays to you, too.
To determine the winner using the Borda count method, we assign points to each alternative based on the ranking given by each voter. The alternative ranked first receives the highest number of points, the alternative ranked second receives the second-highest number of points, and so on.
In this case, there are three alternatives, A, B, and C, and a total of 12 people on the board. Therefore, the alternative ranked first by a voter will receive 12 points, the alternative ranked second will receive 11 points, and so on.
Now, let's calculate the Borda count for each alternative:
Alternative A:
ABC: A is ranked second (11 points)
ACB: A is ranked first (12 points)
BAC: A is ranked third (10 points)
BCA: A is ranked third (10 points)
CAB: A is ranked first (12 points)
CBA: A is ranked second (11 points)
Total points for A: 11 + 12 + 10 + 10 + 12 + 11 = 66
Alternative B:
ABC: B is ranked first (12 points)
ACB: B is ranked second (11 points)
BAC: B is ranked first (12 points)
BCA: B is ranked second (11 points)
CAB: B is ranked third (10 points)
CBA: B is ranked third (10 points)
Total points for B: 12 + 11 + 12 + 11 + 10 + 10 = 66
Alternative C:
ABC: C is ranked third (10 points)
ACB: C is ranked third (10 points)
BAC: C is ranked second (11 points)
BCA: C is ranked first (12 points)
CAB: C is ranked second (11 points)
CBA: C is ranked first (12 points)
Total points for C: 10 + 10 + 11 + 12 + 11 + 12 = 66
As we can see, all three alternatives, A, B, and C, have the same total points of 66. Therefore, there is no clear winner using the Borda count method.