Approaches to Voting
A themed collection from the MAA and Taylor & Francis
Ahead of the 2020 US Election, we have put together this themed collection of articles from the Mathematical Association of America, detailing the mathematical Approaches to Voting. Each featured article is free to view until August 31st, 2021, exclusively via this page.
|The American Mathematical Monthly|
|Voting, the Symmetric Group, and Representation Theory||Z. Daugherty, A. K. Eustis, G. Minton and M. E. Orrison|
|Voting in Agreeable Societies||D. E. Berg, S. Norine, F. E. Su, R. Thomas, and P. Wollan,|
|Approval Voting in Product Societies||Mazur, M. Sondjaja, M. Wright, C. Yarnall|
|An Impossibility Theorem for Gerrymandering||B. Alexeev and D. Mixon|
|Measuring Political Gerrymandering||K. Tapp|
|The College Mathematics Journal|
|Gerrymandering and Convexity||J. K. Hodge, E. Marshall & G. Patterson|
|The Self-Limiting Partisan Gerrymander: An Optimization Approach||J. Suzuki|
|Lewis Carroll, Voting, and the Taxicab Metric||T. C. Ratliff|
|Two-Person Pie-Cutting: The Fairest Cuts||J. B. Barbanel & S. J. Brams|
|Apportionment and the 2000 Election||M. G. Neubauer & J. Zeitlin|
|Paradoxes of Preferential Voting||P. C. Fishburn & S. J. Brams|
|Geometry, Voting, and Paradoxes||D. G. Saari & F. Valognes|
|Spectral Analysis of the Supreme Court||B. L. Lawson, M. E. Orrison & D. T. Uminsky|
|The Geometry behind Paradoxes of Voting Power||M. A. Jones|
|What Do We Know at 7 PM on Election Night?||A. Gelman & N. Silver|
|The Mean(est) Voting System||S. Gutekunst, D. Lingenbrink, and M. E. Orrison,|
|Suppose You Want to Vote Strategically||D. Saari|
|270: How to Win the Presidency With Just 17.56% of the Popular Vote||C. Wessell|
|The Geometry of Adding Up Votes||M. A. Jones & J. Wilson|
|Aftermath: The Ensemble Approach to Political Redistricting||J. Clelland, D. DeFord & M. Duchin|
In addition to the Taylor & Francis published journals, peruse these discussions in MAA's own periodical, Convergence.
Michael J. Caulfield
The history of apportionment of representatives in the U.S. Congress, from the 1790s until today, along with a discussion of the mathematics involved in the various methods.
Sidney J. Kolpas
Images related to and brief history of a 19th-century technological advance in tabulating the national census data required to carry out congressional reapportionment.
Frank Swetz and Janet Heine Barnett
Images from and summary of the contents of a pioneering 18th-century book on the application of probability theory to voting theory.
A self-contained project suitable for individual or group work, inside or outside the classroom, that uses US Census data from 1790 to guide students through an exploration of what it means for each state to get its fair share of congresspersons, and of how different methods of apportionment might have altered the course of American history.
An overview of the mathematical content of two eighteenth-century texts on voting theory and the historical context in which they were written, accompanied by a classroom-ready project based on those texts suitable for use as a stand-alone unit on voting theory in a Liberal Arts or high school mathematics course.