https://file.aiquickdraw.com/mathbot/file/1726541858878rcx0yqkw.jpg

To solve this election ranking problem using the **plurality-with-elimination method**, we proceed step by step as follows:

### Step 1: Count the first-choice votes for each candidate
From the preference table, we count how many voters listed each candidate as their first choice:

- **A**: 7 votes (from voters 6+1)
- **B**: 7 votes (from voters 8+4)
- **C**: 6 votes (from voters 6)
- **D**: 12 votes (from voters 6+6)
- **E**: 8 votes (from voters 8)

### Step 2: Eliminate the candidate with the fewest first-choice votes
Candidate **C** has the fewest first-choice votes (6 votes). **C** is eliminated.

### Step 3: Redistribute votes
After eliminating **C**, we redistribute the votes of those who chose **C** as their first choice. These voters' second choice is:

- For 6 voters who chose **C** first: The second choice is **B**.

Now the updated first-choice vote counts are:

- **A**: 7 votes
- **B**: 13 votes (7 + 6 from C voters)
- **D**: 12 votes
- **E**: 8 votes

### Step 4: Eliminate the next candidate with the fewest votes
Now **A** has the fewest first-choice votes (7 votes). **A** is eliminated.

### Step 5: Redistribute votes
After eliminating **A**, we redistribute the votes of those who chose **A** as their first choice. Their second choices are:

- For 7 voters who chose **A**: The second choice is **D**.

Now the updated vote counts are:

- **B**: 13 votes
- **D**: 19 votes (12 + 7 from A voters)
- **E**: 8 votes

### Step 6: Eliminate the next candidate with the fewest votes
**E** now has the fewest votes (8 votes). **E** is eliminated.

### Step 7: Final comparison
We are left with **B** and **D**. The votes of those who originally voted for **E** (8 votes) are redistributed based on their next preferences. These 8 voters chose:

- **B**: 6 voters (from the second choice of the 8 voters who initially picked E)
- **D**: 2 voters.

The final vote count is:

- **B**: 19 votes (13 + 6 from E voters)
- **D**: 21 votes (19 + 2 from E voters).

### Step 8: Final ranking
Since **D** has more votes than **B**, **D** wins the election.

The complete ranking of the candidates is:
1. **D**
2. **B**
3. **E**
4. **C**
5. **A**

Thus, the correct answer is **D, B, E, C, A**.

Would you like further clarification on any step or more details? Here are 5 related questions:

1. How does the plurality method differ from the plurality-with-elimination method?
2. What happens if two candidates tie in the elimination process?
3. How can the plurality-with-elimination method affect voter strategy?
4. Can you explain another example where a candidate wins after multiple eliminations?
5. What are the advantages and disadvantages of the plurality-with-elimination method?

**Tip**: Always verify vote counts after each round of elimination to avoid any confusion!

The given table shows the preference schedule for an election with five candidates (A, B, C, D, and E). Find the complete ranking of the candidates using the plurality-with-elimination method.

Learn how to determine the complete ranking of five candidates (A, B, C, D, and E) using the plurality-with-elimination voting method. Step-by-step guide with examples suitable for Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation