Using the table (ADBC)= 8 (DACB)=5 (BADC)=3 (BDCA)=1 (DCAB)=2 (it is supposed to be a table but the table won't paste correctly). Deter mine:
a) deter mine the winner using the Borda count
b) deter mine the winner using the Hare method? What round did you find an answer? Explain
is a) D b) not sure
To determine the winner using the Borda count method:
a) First, assign points to each candidate based on their ranking in each preference. In this case, there are 4 candidates: A, B, C, and D.
For (ADBC)= 8:
- Candidate A receives 2 points (8-1)
- Candidate B receives 1 point (8-2)
- Candidate C receives 3 points (8-3)
- Candidate D receives 0 points (8-4)
For (DACB)= 5:
- Candidate A receives 3 points (5-1)
- Candidate B receives 0 points (5-4)
- Candidate C receives 2 points (5-2)
- Candidate D receives 1 point (5-3)
For (BADC)= 3:
- Candidate A receives 1 point (3-2)
- Candidate B receives 3 points (3-3)
- Candidate C receives 2 points (3-1)
- Candidate D receives 0 points (3-4)
For (BDCA)= 1:
- Candidate A receives 3 points (1-1)
- Candidate B receives 2 points (1-3)
- Candidate C receives 1 point (1-2)
- Candidate D receives 0 points (1-4)
For (DCAB)= 2:
- Candidate A receives 1 point (2-3)
- Candidate B receives 0 points (2-4)
- Candidate C receives 3 points (2-1)
- Candidate D receives 2 points (2-2)
Adding up the points for each candidate, we have:
- Candidate A: 10 points
- Candidate B: 6 points
- Candidate C: 11 points
- Candidate D: 3 points
According to the Borda count, the winner is Candidate C.
b) To determine the winner using the Hare method, we need to calculate the total votes received by each candidate in each round until a candidate obtains more than half of the total votes.
First, we calculate the total votes received by each candidate in the initial round:
- Candidate A: 8 + 5 + 1 = 14 votes
- Candidate B: 8 + 3 + 1 = 12 votes
- Candidate C: 5 + 3 + 2 = 10 votes
- Candidate D: 3 + 2 + 5 = 10 votes
Since no candidate has more than half of the total votes (which is 8 votes), we proceed to the next round.
In the second round, we eliminate the candidate with the lowest number of votes, which is Candidate C and Candidate D with 10 votes each (as they have the same number of votes).
In the third round, we calculate the new total votes:
- Candidate A: 8 + 5 = 13 votes
- Candidate B: 8 + 3 = 11 votes
Now, Candidate A has more than half of the total votes, and therefore, the winner using the Hare method is Candidate A. The answer was found in the third round.
To determine the winner using the Borda count method, we assign points to each candidate based on their rank in each preference. The candidate with the highest total points is declared the winner.
a) To calculate the Borda count, we assign points to each candidate for each preference. The highest-ranked candidate receives (N-1) points, the second-highest receives (N-2) points, and so on, where N is the number of candidates. In this case, we have four candidates: A, B, C, D.
Using the given preferences:
(ADBC)=8:
- A receives 3 points (N-1 = 4-1)
- D receives 2 points (N-2 = 4-2)
- B receives 1 point (N-3 = 4-3)
- C receives 0 points
(DACB)=5:
- D receives 3 points
- A receives 2 points
- C receives 1 point
- B receives 0 points
(BADC)=3:
- B receives 3 points
- A receives 2 points
- D receives 1 point
- C receives 0 points
(BDCA)=1:
- B receives 3 points
- D receives 2 points
- C receives 1 point
- A receives 0 points
(DCAB)=2:
- D receives 3 points
- C receives 2 points
- A receives 1 point
- B receives 0 points
Calculating the total points for each candidate:
A: 2 + 2 + 0 + 0 + 1 = 5
B: 1 + 0 + 3 + 3 + 0 = 7
C: 0 + 1 + 0 + 1 + 2 = 4
D: 3 + 3 + 2 + 2 + 3 = 13
Based on the Borda count method, candidate D has the highest total points with 13, making them the winner in this election.
b) The Hare method, also known as the "Instant Runoff" method, is a way to determine the winner through multiple rounds of counting the votes. In each round, the candidate with the fewest first-preference votes is eliminated, and their votes are redistributed to the remaining candidates, based on the voters' second preferences.
To determine the winner using the Hare method, we need to carry out the rounds of counting until a candidate receives over 50% of the votes.
From the given example, we can see that candidate D has the highest Borda count with 13 points. However, to determine the winner using the Hare method, we need to know the percentage of votes each candidate received in the first round. Without the information on the total number of votes or the percentage of each candidate's first-preference votes, we cannot determine the winner or identify the specific round where a candidate achieves over 50% of the votes using the Hare method.