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Activity II: Plurality Voting (Grades 4-8)

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:

  • Use the Plurality and Plurality with Elimination methods to determine the winner of an election and to rank a series of four football teams.

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

voting booth The Plurality method is the method with which you are most familiar. For the Plurality method, voters vote for one candidate, and the candidate with the most first place votes wins. The winner does not have to receive a majority of the first place votes.

1. The high school student council president is being chosen in an election using the Plurality method. The four candidates for the office are: Shawn, Twanda, Ricco, and Gail. One thousand five hundred students cast their ballots, and the results are summarized in the schedule below.

  Number of votes received
Place 390 360 300 450
1st Shawn Gail Gail Ricco

a. How many first place votes are needed for a majority?

b. Did any candidate receive a majority of first place votes?

c. Who is the winner by the Plurality method?

d. How many first place votes did the winning candidate receive?

Plurality with Elimination

This preferential method is a variation of the Plurality method. Plurality with Elimination requires a preference ballot, and it is carried out in rounds. After each round of voting, the candidate with the fewest number of first place votes is eliminated, and a new round of voting is done with the remaining candidates. If two candidates both have the fewest number of first place votes--or no first place votes--both are eliminated. When only two candidates remain in a round, the candidate with the most votes wins the election.

1. How many rounds are required using the Plurality with Elimination method when you have N candidates?

2. The preference schedule below represents an election among George, Holly, James, and Inez.

  Number of votes received
Place 130 120 100
1st George Inez James
2nd Holly Holly George
3rd James James Holly
4th Inez George Inez

a. How many rounds will it take to determine a winner using the Plurality with Elimination method?

b. Using the Plurality with Elimination method, which candidate is eliminated in the first round?

Note: Since the results of each voter’s preference ballot are summarized in the table, students do not need to hold a new election. They simply remove the eliminated candidate from the preference schedule and adjust the remaining candidates’ scores appropriately.

Here is the adjusted preference schedule for round two. Note that Holly has been eliminated and how the table has been adjusted.

 Number of votes received
Place 130 120 100
1st George Inez James
2nd James James George
3rd Inez George Inez

c. Which candidate is eliminated in round two, and why?

d. Write out the preference schedule for round three.

e. Which candidate is eliminated in round three and why?

f. Who wins the election using Plurality with Elimination? Why?

3. Consider this preference schedule from the student council election in Part A.

 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

a. Using Plurality with Elimination, identify which candidate wins.