Activity IV: Approval Voting (Grades 6-9)

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:

• Apply the definition of Approval Voting to a problem and determine a winner
• Apply the five kinds of voting to an election and determine the winner in a variety of situations

Approval Voting is a procedure in which voters can vote for as many candidates as they wish. Each approved candidate receives one vote, and the candidate with the most votes wins.

Approval Voting has the following advantages over other voting procedures:

• It gives voters more flexible options.
• It helps elect the strongest candidate.
• It reduces negative campaigning.
• It increases voter turnout.
• It gives minority candidates their proper due.
• It is very practical.

A. The participants in a summer school recreation program decided to vote on which activity they preferred, Running Track, Softball, Badminton, or Swimming. The winning activity was determined by Approval Voting.

The following summarizes the responses of the participants:
12 participants voted for Swimming and Badminton.
5 participants voted for Badminton, Running Track, and Softball.
10 participants voted for Running Track and Badminton.
13 participants voted for Softball and Badminton.

5. Which activity is selected by the summer school participants using Approval Voting?

B. Frisbee is a growing sport at Tama High. The Frisbee Club is sponsoring a weekend event, and each participant will receive a T-shirt. Club members decided to let the participants vote on the color of the T-shirt, using Approval Voting. The possible colors are Steel Gray, Robin’s Egg Blue, Eggshell, Candy Apple Red, and Sunflower Yellow. Here is a summary of the results:

12 participants voted for Steel Gray.
7 participants voted for Steel Gray and Sunflower Yellow.
20 participants voted for Eggshell and Candy Apple Red.
18 participants voted for Robin’s Egg Blue, Eggshell, and Candy Apple Red.
23 participants voted for Sunflower Yellow and Robin’s Egg Blue.
25 participants voted for Candy Apple Red.

Use Approval Voting to determine the color of the T-shirt.

C. Summary
Milbourn State University marching band has been invited to march in 5 different parades: the Rose Bowl parade, the Hula Bowl parade, the Cotton Bowl parade, the Orange Bowl parade, and the Sugar Bowl parade. The 100 band members were asked to rank the parades from 1st choice to 5th choice. Then results were summarized in the following preference schedule.

 39 16 45 1st Rose Hula Cotton 2nd Hula Sugar Hula 3rd Cotton Orange Sugar 4th Orange Cotton Orange 5th Sugar Rose Rose

The University now has to decide what to do with this information. 1. Suppose the University decides to choose the parade using Plurality with Elimination. Which parade will be chosen?

 1st Rose Hula Cotton 2nd Hula Cotton Hula 3rd Cotton Rose Rose

The Hula Bowl is eliminated because it has least number of first-place votes.

 1st Rose Cotton Cotton 2nd Cotton Rose Rose

The Cotton Bowl parade is the winner by Plurality with Elimination.

2. Suppose the University decides to choose the parade using Pairwise Comparisons. Which parade will be chosen?

 Cotton Hula Orange Rose Sugar Cotton ----------- Hula Cotton Cotton Cotton Hula ----------- ----------- Hula Hula Hula Orange ----------- ----------- ---------- Orange Sugar Rose ----------- ----------- ---------- ----------- Sugar Sugar ----------- ----------- ---------- ----------- -----------

Now that you know the head-to-head winners, you can total all the scores and determine the winner of the election.
Hula gets four points.
Cotton gets three points.
Sugar gets two points.
Orange gets one point.

The Hula Bowl parade is the winner by Pairwise Comparison.

3. Suppose the University decides to choose the parade using the Borda Count method. Which parade will be chosen?

4. Suppose the University decides to try Approval Voting. Which parade is chosen if, after re-polling, each band member approves only his/her first, second, and third choices?

5. Suppose the University decides to try Approval Voting. Which parade is chosen if, after re-polling, each band member approved only his/her first and second choices?

6. Suppose the University decides to try Approval Voting. Which parade is chosen if, after re-polling, each band member whose first choice was the Cotton Bowl approved only of the Cotton Bowl, but everyone else approved of his/her first three choices?