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The Mathematics of Voting Systems: Plurality, Runoff and Ranked Choice

Author(s): Tess Hick

Bates College

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Summary:
In this five-day interdisciplinary math and social studies unit, students use math to create informed opinions about the three most common voting systems in the United States: plurality, runoff and ranked choice. The unit ends with a student…

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In this five-day interdisciplinary math and social studies unit, students use math to create informed opinions about the three most common voting systems in the United States: plurality, runoff and ranked choice. The unit ends with a student proposal for how student council elections should be conducted, illustrating how students can use mathematics as a tool to both understand and change their world.

Description

This unit was originally implemented in an eighth-grade math classroom in Maine, but is appropriate for sixth grade and up, and could be used in either math or social studies.

Monday's lesson is about the social context of voting. Students learn about how voting works around the United States and around the world, and consider questions like "what is voting?" and "what should be true in a fair election?" 

Tuesday, Wednesday and Thursday all involve a mock election on the best superpower. On Tuesday, students count the votes using the plurality method, and learn about the difference between plurality and majority. On Wednesday, students count votes using the runoff method, and consider the spoiler effect. On Thursday, students learn about and use ranked choice, and consider the difference between polarizing candidates and candidates with broad support. The math standards involved are going between representations of data (ex. graph to table), calculating percentages, and statistical reasoning.

On Friday, students consider the pros and cons of each system in the context of their school, and create a proposal for which method should be used to count votes in student council elections.

Note that many of the materials have class data filled in as an example. Teachers should replace this data with their own class' votes.

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