This is just one activity topic that you may choose to complete a Supernova award. The activity topic list has many others you may complete, plus information about what's needed for reports. Any resources listed are examples and you might use alternative or additional sources.
A Paradox of Counting: Voting Methods and Fair Decisions
This activity can be done individually or with a group of two to six people, and requires cooperation from about 20 to 30 individuals.
The scenario: Your unit wants to plan a superactivity for next summer but cannot agree on what that activity should be. There are four options under consideration, and your unit decides to vote. Your task is to collect ballots and tabulate results using several different voting methods.
This is not a binding decision on your unit! This is an exercise, but one that will be more meaningful if you use real-life possibilities.
Part 1: Ballot Setup, Gathering, and Tabulating
1.
Decide on four superactivities that your unit would genuinely be interested in doing next summer. Aim for four genuine options, none of which is likely to receive a majority of the votes. Discuss these options with your mentor before doing the following:
A.
Create ballots on which each voter can list his/her first, second, third, and fourth choices from among the four prospective superactivities.
B.
Find 20 to 30 unit members, prospective guests for the superactivity, unit leaders, parents, and so on, to complete one ballot each. Each voter should vote sincerely, without trying to strategize.
C.
Do some research and learn how to tabulate winners using each of the following four voting methods:
3.
Plurality-with-elimination method (sometimes called the instant runoff method)
4.
Pair-wise comparison method (sometimes called Copeland’s method)
Part 2: Analysis and Report
1.
As you tabulate the results using each voting method, evaluate each method and discuss the following with your mentor.
A.
What do you notice? How fair is each method?
B.
How would the results be affected if two or three voters had cast strategic ballots (instead of sincere ballots), in an effort to “not waste their votes”?
C.
Which of the four voting methods do you believe is the right voting method for this decision in your unit? Why?
D.
Consider how we elect the president of the United States of America.
1.
What voting method do we use?
2.
What are its advantages and disadvantages?
3.
Do you believe each voting citizen in the United States has an equal say in the vote tabulation?
4.
Is it possible for citizens to cast strategic votes and influence the outcome of a presidential election?
2.
Create a report that summarizes the results from the various voting methods, outlines your analysis, and comments on voting methods for the U.S. presidency. Share your report with your mentor.
Resources
Donald G. Saari. Chaotic Elections! A Mathematician Looks at Voting (for youth with stronger mathematics backgrounds). American Mathematical Society, 2001.
William Poundstone. Gaming the Vote: Why Elections Aren’t Fair (and What We Can Do About It). Hill and Wang, 2008.
