Number of voters	14	12	17
1st choice	B	C	A
2nd choice	C	B	C
3rd choice	A	A	B


Find the winner of this election under the Borda Count method.

To find the winner of the election under the **Borda Count** method, we assign points to each candidate based on their ranking in each voter's preferences. The points are distributed as follows:

- A candidate receives 2 points for every first-place vote,
- 1 point for every second-place vote,
- 0 points for every third-place vote.

We have three candidates: A, B, and C, and the preferences of voters are distributed as follows:

| Number of voters | 14  | 12  | 17  |
|------------------|-----|-----|-----|
| **1st choice**    | B   | C   | A   |
| **2nd choice**    | C   | B   | C   |
| **3rd choice**    | A   | A   | B   |

### Step 1: Calculate points for each candidate based on the Borda Count rules

1. **Candidate A:**
   - 17 voters ranked A 1st: \( 17 \times 2 = 34 \) points.
   - 14 voters ranked A 3rd: \( 14 \times 0 = 0 \) points.
   - 12 voters ranked A 3rd: \( 12 \times 0 = 0 \) points.
   - **Total points for A = 34 + 0 + 0 = 34 points.**

2. **Candidate B:**
   - 14 voters ranked B 1st: \( 14 \times 2 = 28 \) points.
   - 12 voters ranked B 2nd: \( 12 \times 1 = 12 \) points.
   - 17 voters ranked B 3rd: \( 17 \times 0 = 0 \) points.
   - **Total points for B = 28 + 12 + 0 = 40 points.**

3. **Candidate C:**
   - 12 voters ranked C 1st: \( 12 \times 2 = 24 \) points.
   - 17 voters ranked C 2nd: \( 17 \times 1 = 17 \) points.
   - 14 voters ranked C 2nd: \( 14 \times 1 = 14 \) points.
   - **Total points for C = 24 + 17 + 14 = 55 points.**

### Step 2: Compare the total points
- A: 34 points
- B: 40 points
- C: 55 points

### Conclusion:
**Candidate C** is the winner under the Borda Count method with 55 points.

Would you like more details on the process, or have any questions?

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Here are 5 related questions to explore:
1. How would the result change if the number of voters was different?
2. What would happen if we used a different voting method, like Plurality or Instant Runoff?
3. How does the Borda Count method handle ties between candidates?
4. Can a candidate win under the Borda Count method even if they have the fewest first-place votes?
5. How does strategic voting affect the outcome under the Borda Count method?

**Tip:** In Borda Count, ranking lower-preferred candidates can still affect the final outcome, making it more reflective of overall preferences than Plurality.

Find the winner of this election under the Borda Count method.

Calculate the winner of an election using the Borda Count method with three candidates: A, B, and C. Learn how points are assigned based on voters' rankings and find out why Candidate C wins with 55 points. Suitable for students in Grades 9-12.

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