Math Problem Statement

(c) Who is the winner using the Borda Count Method?

ABC- 4

BAC- 5

CBA- 4

CAB - 2

Vote 1​

​Vote 2

​Vote 3

​Vote 4

​Total

​A

3*4=12

​2*5=10

1*4=4

2*2=4

​B

2*4=8

3*5=15

2*4=8

​1*2=2

​C

​1*4=4

1*5=5

​3*4=12

​3*2=6

Total​

24

30

24

12​

​90 points

therefore the winner is BAC with 30 points

Solution

Using the Borda Count method to determine the winner, the total points for each candidate are calculated by assigning weighted points to their ranking in each voting preference. Here's a detailed breakdown of the computation:

Step-by-Step Calculation:

  1. Point Distribution:

    • 1st place: 3 points
    • 2nd place: 2 points
    • 3rd place: 1 point
  2. Tally by Ranking in Each Ballot:

    • Vote 1 (ABC):
      • A = 3×4=123 \times 4 = 12
      • B = 2×4=82 \times 4 = 8
      • C = 1×4=41 \times 4 = 4
    • Vote 2 (BAC):
      • A = 2×5=102 \times 5 = 10
      • B = 3×5=153 \times 5 = 15
      • C = 1×5=51 \times 5 = 5
    • Vote 3 (CBA):
      • A = 1×4=41 \times 4 = 4
      • B = 2×4=82 \times 4 = 8
      • C = 3×4=123 \times 4 = 12
    • Vote 4 (CAB):
      • A = 2×2=42 \times 2 = 4
      • B = 1×2=21 \times 2 = 2
      • C = 3×2=63 \times 2 = 6
  3. Total Scores:

    • A = 12+10+4+4=3012 + 10 + 4 + 4 = 30
    • B = 8+15+8+2=338 + 15 + 8 + 2 = 33
    • C = 4+5+12+6=274 + 5 + 12 + 6 = 27

Winner:

The candidate with the highest total points is B (BAC) with 33 points.

Would you like me to explain the process further or adjust for any other voting methods?


5 Related Questions:

  1. How does the Borda Count compare to other voting methods, like plurality or Condorcet?
  2. Can the Borda Count method ever result in a tie? How is it resolved?
  3. How does the ranking order impact the final outcome?
  4. What are some advantages and disadvantages of the Borda Count method?
  5. Can this method be manipulated, and if so, how?

Tip: Always double-check your point allocations to ensure accurate calculations in ranked voting systems.

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Math Problem Analysis

Mathematical Concepts

Voting Systems
Borda Count Method
Weighted Scoring

Formulas

Points = Rank Weight × Number of Votes

Theorems

Borda Count Scoring Principle

Suitable Grade Level

Grades 9-12