Find the winner using the Borda count method. Make sure you show all the work clearly to get full points.
\begin{tabular}{lllllll}
Choices: & PQR & PRQ & QPR & QRP & RPQ & RQP \\
Votes: & 10 & 14 & 12 & 21 & 19 & 22
\end{tabular}
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Answer
The Borda count method is a voting system that involves ranking candidates in order of preference. Each position in the ranking is assigned a certain number of points, and the candidate with the most points overall is the winner. In this case, we have three candidates: P, Q, and R. We'll assign points as follows: 3 points for a first-place vote, 2 points for a second-place vote, and 1 point for a third-place vote. Let's calculate the points for each candidate: 1. PQR: P gets 3 points, Q gets 2 points, and R gets 1 point. Multiply these by the number of votes (10), we get P = 30, Q = 20, R = 10. 2. PRQ: P gets 3 points, R gets 2 points, and Q gets 1 point. Multiply these by the number of votes (14), we get P = 42, R = 28, Q = 14. 3. QPR: Q gets 3 points, P gets 2 points, and R gets 1 point. Multiply these by the number of votes (12), we get Q = 36, P = 24, R = 12. 4. QRP: Q gets 3 points, R gets 2 points, and P gets 1 point. Multiply these by the number of votes (21), we get Q = 63, R = 42, P = 21. 5. RPQ: R gets 3 points, P gets 2 points, and Q gets 1 point. Multiply these by the number of votes (19), we get R = 57, P = 38, Q = 19. 6. RQP: R gets 3 points, Q gets 2 points, and P gets 1 point. Multiply these by the number of votes (22), we get R = 66, Q = 44, P = 22. Now, let's add up the points for each candidate: - P: 30 + 42 + 24 + 21 + 38 + 22 = 177 - Q: 20 + 14 + 36 + 63 + 19 + 44 = 196 - R: 10 + 28 + 12 + 42 + 57 + 66 = 215 So, using the Borda count method, the winner is R with 215 points.
Step 1 ：The Borda count method is a voting system that involves ranking candidates in order of preference. Each position in the ranking is assigned a certain number of points, and the candidate with the most points overall is the winner. In this case, we have three candidates: P, Q, and R. We'll assign points as follows: 3 points for a first-place vote, 2 points for a second-place vote, and 1 point for a third-place vote. Let's calculate the points for each candidate: 1. PQR: P gets 3 points, Q gets 2 points, and R gets 1 point. Multiply these by the number of votes (10), we get P = 30, Q = 20, R = 10. 2. PRQ: P gets 3 points, R gets 2 points, and Q gets 1 point. Multiply these by the number of votes (14), we get P = 42, R = 28, Q = 14. 3. QPR: Q gets 3 points, P gets 2 points, and R gets 1 point. Multiply these by the number of votes (12), we get Q = 36, P = 24, R = 12. 4. QRP: Q gets 3 points, R gets 2 points, and P gets 1 point. Multiply these by the number of votes (21), we get Q = 63, R = 42, P = 21. 5. RPQ: R gets 3 points, P gets 2 points, and Q gets 1 point. Multiply these by the number of votes (19), we get R = 57, P = 38, Q = 19. 6. RQP: R gets 3 points, Q gets 2 points, and P gets 1 point. Multiply these by the number of votes (22), we get R = 66, Q = 44, P = 22. Now, let's add up the points for each candidate: - P: 30 + 42 + 24 + 21 + 38 + 22 = 177 - Q: 20 + 14 + 36 + 63 + 19 + 44 = 196 - R: 10 + 28 + 12 + 42 + 57 + 66 = 215 So, using the Borda count method, the winner is R with 215 points.
