# PBS Teachers™

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

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?