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Mathematics and Elections
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The 2004 Presidential election has provided an excellent opportunity to get students interested in the American political system and mathematics. Many of us here at the Math Forum have been sharing links to resources and interesting discussions, and would like to give others an opportunity to share more publicly.
What resources have you been using with your students to study and explain the mathematics involved in the election process?
We are compiling this page of resources and will continue to update it as more resources are suggested.
Send suggestions to us using this form.
[Lesson Plans] [Other Resources] [Dr. Math] [PoWs] [Discussions] [Books] [COMAP]
Lesson Plans
By the People: Election 2004: Lesson Plans - PBS
Bring elections into your elementary and secondary classrooms, on topics ranging from the electoral college to campaign finance, political humor and more. The Democracy Project - PBS
The online activities are designed for students in grades three to six, with accompanying lesson plans for language arts (LA), social studies (SS), and math (M) teachers. Included is information about the educational goals for each online activity; lesson plans for each activity; curriculum standards related to this content; and the teachers who wrote the lesson plans. Discrete Mathematics Projects (DMP) - James Arnow
Election Theory, Fair Division, Graph Theory, Counting Techniques, Discrete Probability, Matrix Models, and the Mathematics of Iteration/Recursion. Election 2000: Classroom Activities and Election 2000: Ten More Classroom Activities - Education World
Topics include math, drama, art, role-playing activities, and more. Election 2004 WebQuest: A Classroom WebQuest from Education World - Education World
Topics include math, drama, art, role-playing activities, and more. Election Central
Election Central is an online resource that helps teachers and students explore the electoral process past and present, in the United States and around the world. Election Glossary - PBS
A glossary featuring over 100 terms about elections. The Mathematics of Voting - Dr. Larry Bowen
Mathematical economist Kenneth Arrow proved (in 1952) that there is no consistent method of making a fair choice among three or more candidates. Topics cover Fairness Criteria, Voting Methods, Fairness Criteria applied to Voting Methods, and Ranking Procedures.
Sampling Bias and the California Recall - Ryan Martine
A lesson plan from the NewsHour with Jim Lehrer, the nightly news broadcast on PBS. Students identify and differentiate between various types of political samples, including polls and petitions. Vote 2008: The Primaries - Education World
The Online NewsHour: Presidential Election Coverage from PBS. Will the Best Candidate Win? - Illuminations
This lesson plan appeared in the January 2000 edition of Mathematics Teacher Journal. Activities allow students to explore alternative voting methods. Students discover what advantages and disadvantages each method offers and also see that each fails, in some way, to satisfy some desirable properties.
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Other Resources
The 1996 elections, a book, and voting by Donald G Saari
Includes a description of a "voting paradox," a summary of the author's book, "Basic Geometry of Voting," an overview of presenting this material in a fourth grade classroom, and a link to the article, "The symmetry and complexity of elections." Center for Voting and Democracy - Robert Loring, webmaster
Examining how voting systems affect participation, representation and governance. Copernicus Election Watch - USA TODAY
News, special activities, historical timelines, interactive polls, and recommendations for election-related sites and lesson plans. How to Fix an Election - Ivars Peterson's MathTrek (MAA Online)
"Voting sounds like a simple matter. Just pick a candidate, then count the ballots and announce the tally. When there are three or more candidates (or choices), however, the results may not actually reflect the true preferences of the voters..." How to Split Your Vote - Frank Morgan's Math Chat (MAA Online)
"Suppose all that any voter in the U.S. cares about is that different parties control the Presidency and the Congress. If there is no communication, how should each voter vote?" Is Democracy Fair? The mathematics of voting and apportionment
This book published by Key Curriculum Press offers activities for grades 7-12 that explore different types of election decision procedures with mathematical methods. Opensecrets.org - Money in Politics - Center for Responsive Politics
A site for researching campaign finance statistics. The perplexing mathematics of presidential elections - Devlin's Angle (MAA Online)
"...It's not the idea of one person one vote that's the problem, it's that math that is used to turn those votes into a final decision. Ideally, that math should reflect the wishes of the electorate. But does it?" Rock the Vote
Rock the Vote is a non-profit, non-partisan organization, founded in 1990 in response to a wave of attacks on freedom of speech and artistic expression.
Statistics - Cast Your Vote! - Annenberg/CPB
What's Your Opinion On Polling? Voting and Elections by Joseph Malkevitch
The March 2002 essay featured in the What's New in Mathematics Feature Column Archive of the American Mathematical Society (AMS)
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From the Ask Dr. Math Archives:
From the Math Forum's Problems of the Week: [requires membership to access]
Algebra Problem of the Week
Discrete Math Problem of the Week
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Discussion Group Postings
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Books
Mathematics: Modeling Our World, Course 1:
(New York: WH Freeman, 2000)
The first unit is on voting methods and fairness.
Contemporary Mathematics In Context ("Core-Plus" Math Project), Course 3:
Arthur F. Coxford (Editor)
(Chicago: Everyday Learning, 1999)
Unit 3 includes voting methods and statistical interpretation.
Discrete Mathematics Through Applications
Nancy Crisler, Patience Fisher, and Gary Froelich
(New York: WH Freeman, 2000)
For All Practical Purposes
by COMAP
(New York: WH Freeman, 1999)
Excursions in Modern Mathematics
Peter Tannenbaum, Robert Arnold
(New Jersey: Prentice-Hall, 2000)
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The Consortium for Mathematics and its Applications (COMAP)
Membership in COMAP is required to download these PDF files
Decision Analysis for Multi-Candidate Voting Systems
Fair Voting - Weighted Votes for Unequal Constituencies
Math TV - Computer Science and Social Choice: When is a Vote Not a Vote?
The Mathematical Theory of Elections
Measures of Voting Unit I: The Rice Index
Probability in Contested Election
Voting Games, Power Indices, and Presidential Elections
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