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Activity 1: Borda Count Method (Grade Levels: 5-9)

Borda Count Method | Plurality Voting | Pairwise Comparisons | Approval Voting | Career Connections | More Math Concepts

NCTM Standards:

  • Number and Operation
  • Data Analysis, Statistics, and Probability
  • Problem Solving
  • Reasoning and Proof
  • Communication
  • Connections
  • Representation

Objectives:

  • Create a formula for determining the total points for a candidate
  • Use the formula to determine the winner of an election using the Borda Count method

adobe acrobat Student Activity (PDF File)
Answers (PDF File)

voting booth For the Borda Count method, each candidate gets 1 point for each last-place vote received, 2 points for every next-to-last-place vote, etc., all the way up to N points for each first-place vote (where N is the number of candidates). The candidate with the largest point total wins the election. The Borda Count method requires a preference ballot. A preference ballot is an individual voter’s ballot in which the voter lists each candidate in order of preference from first to last.

A. The student council decided to use the Borda Count method of voting to elect their new president. One thousand five hundred students cast their preference ballots for the candidates. The results are summarized in the preference schedule below. The four candidates are: Gail, Twanda, Shawn, and Ricco.

 Number of votes received
Place 390 360 300 450
1st Shawn Gail Gail Ricco
2nd Twanda Twanda Twanda Twanda
3rd Ricco Ricco Shawn Shawn
4th Gail Shawn Ricco Gail

1. Write a formula that can be used to determine the total points awarded by the Borda Count method to an individual candidate.

2. Determine the total number of points Shawn is awarded in this election.

3. Determine the total number of points Gail is awarded in this election.

4. Determine the total number of points Twanda is awarded in this election.

5. Determine the total number of points Ricco is awarded in this election.

6. Who wins the election using the Borda Count method?

B. The preference schedule below represents a ranking of the four football teams in the City of Sportsville by 500 of its most avid football fans.

 Number of votes received
Place 130 120 150 100
1st Grizzlies Indians Broncos Jets
2nd Hoosiers Broncos Hoosiers Grizzlies
3rd Broncos Jets Grizzlies Hoosiers
4th Indians Grizzlies Jets Indians
5th Jets Hoosiers Indians Broncos

1. What is the final ranking using the Borda Count method?