https://file.aiquickdraw.com/mathbot/file/1725720578192870usrje.jpg

I have displayed the image. Let me extract the content and solve the problem based on the provided table and questions.

The table presents voter preferences, and the problem asks for answers based on these preferences using various methods such as:
1. Majority rule
2. Borda count
3. Condorcet method

I'll analyze each method and provide the solutions. Let's break down each question step by step.

### The problem asks:
**a) How many total voters?**
From the table, the voter profile counts are listed in the top row. We can find the total number of voters by adding these values.

**b) Who would win by majority rule?**
Majority rule means a candidate wins if they have more than half of the votes in the first position.

**c) Use the Borda method.**
The Borda count assigns points to each rank (e.g., 3 points for 1st, 2 points for 2nd, 1 point for 3rd in a 3-candidate election).

**d) The Hare method**
In the Hare method (instant-runoff voting), candidates are eliminated one by one until one has a majority.

**e) Would the Borda count yield the same result as Condorcet?**
The Condorcet method compares every candidate head-to-head. If one candidate wins all pairwise comparisons, they are the Condorcet winner.

I'll begin by calculating the total number of voters and then proceed to the remaining parts.**a) Total number of voters: 50**

Now, let's proceed to the next question.

### **b) Who would win by majority rule?**
A candidate needs more than half of the total votes (which is 50/2 = 25 votes) in the first position to win by majority rule. I'll now check the number of votes each candidate received as the top preference.**b) Majority Rule Winner:**
No candidate received more than 25 votes (half of 50) as their first choice, so **no candidate wins by majority rule**.

### **c) Borda Method**
The Borda count assigns points based on rankings. In this case, we have 4 candidates, so:
- 1st place gets 4 points,
- 2nd place gets 3 points,
- 3rd place gets 2 points,
- 4th place gets 1 point.

I'll calculate the total Borda points for each candidate now.

How many total voters? Who wins by majority rule, Borda method, Hare method, and Condorcet?

Solve a voting theory problem using the majority rule, Borda count, Hare method, and Condorcet method. This detailed solution explains how to calculate the winner in each case. Suitable for students in Grades 10-12.

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