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Math Horizons Contents—September 2016

The 2016 election season has been under way for a while, and voters will head to the polls very soon. We look at some of the interesting mathematics behind elections in this special voting-themed issue of Math Horizons:

-A geometric explanation of the aggregation paradox with examples from the 2016 primaries.
-A game theory explanation of why we can't agree on a better way to vote than the plurality method.
-Redistricting in Minnesota.
-The census and congressional apportionment.
-How averaging all positional voting methods leads to an existing, well-known voting method.
-An editorial encouraging mathematicians and other mathematically inclined citizens to become involved in public policy.

Enjoy these articles and more in the September issue ofMath Horizons. And don't forget to vote! -David Richeson, Editor

Volume 24, Issue 1


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Such supplemental information as solutions for contests, contest winners, editorials, and other reader responses to Math Horizons articles is available here.


The Geometry of Adding up Votes (PDF)

Michael A. Jones and Jennifer Wilson

The 2016 Democratic primaries in Arkansas and Alabama exhibited apportionment paradoxes that can be described geometrically. 

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The Mean(est) Voting System

Sam Gutekunst, David Lingenbrink, and Michael Orrison

What happens if we average all the positional voting systems?

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Electing to Disagree

Jim Wiseman and Thomas Wiseman

Game theory tells us why experts can’t agree on the best way to vote.

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Sugihara's Impossible Cylinder

David Richeson

David Richeson shows the mathematics behind one of the Internet's favorite illusion.

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Confidence in the Census

Jeff Suzuki

Jeff Suzuki presents the challenges of using census data to determine congressional apportionment.

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Undergraduate Research: Viewpoints from the Student Side

Alejandro Camacho, Jeffrey Laylon Davis, Sarah Klett, Herbert Medina, Angel R. Pineda, and Samantha VanSchalkwyk

Four students give their recommendations for student-faculty research.

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Rethinking Redistricting

Tommy Ratliff

Tommy Ratliff chats with Karen Saxe about her work on the Minnesota Citizens Redistricting Commission.

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L.A. Math by James D. Stein

Reviewed by Melissa Hoover

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Fluke by Joseph Mazur

Reviewed by Carrie Diaz Eaton

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The Math Horizons problem section, edited by Gary Gordon

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Mathematician Goes to Washington

Katherine Crowley

Katherine Crowley describes her work as a congressional fellow for Senator Al Franken.

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