#### Consortium for Mathematics and its Applications

Product ID: Modeling Module
Supplementary Print
High School

# Voting Models (Modeling Module)

### Author: Marsha Davis

The context for this module is voting systems. This module begins with a short Preliminary Reading, Electing a Speaker of the U.S. House of Representatives, which focuses on the 2023 election of Kevin McCarthy. Majority and plurality election decisions are discussed. The Preliminary Reading is followed by a brief Preliminary Activity, Majority and Plurality Election Results, in which students analyze situations related to electing a Speaker of the U.S. House of Representatives.

In Activity 1, Plurality Models, students analyze results of elections that are decided using a plurality model, which is the most used method for deciding elections in the United States. Using preference diagrams, students discover a flaw in the model.

In Activity 2, Runoff Models, students analyze data from runoff elections. The expectation is that using runoff elections can avoid the plurality flaw. However, students discover that there are problems with using runoff models as well.

In Activity 3, Rank‑Choice Voting Models, students are introduced to rank‑choice voting (RCV) (also called instant runoff voting (IRV)) models, which are currently in use in some states and cities. But rank‑choice voting models don’t always work perfectly. Activity 3 concludes with a Modeling Alert! focusing on Kenneth Arrow, who proved that no reasonable election model can be entirely free from flaws.

Activity 4 is a project on approval voting models. Students compare the election outcome from approval voting to the outcomes from other voting models covered in this Pull‑ Out. The project ends with students using the Internet to research the pros and cons of approval voting.

Modeling Module
31 Pages

#### Mathematics Topics:

Discrete & Finite Mathematics , Percentages, Basic Math

#### Application Areas:

Social Studies , Political Science, Voting Theory

#### Prerequisites:

Students should be familiar with calculating percentages.

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