Gerrymandering's Potential for Applied Mathematics.

Author:Arenschield, Laura

A new method of drawing electoral districts that combines game theory and "Ghost" could result in maps that are more-demographically representative, according to a pair of mathematicians.

In the word game "Ghost," players take turns saying letters, with each letter building on the last letter employed. Players create word fragments, ultimately trying to get their opponents to complete the word. Whoever completes the word loses. At its core, though, Ghost is a game of collaboration--two players working together to build a word, even as they try to outsmart and outmaneuver each other, says Dustin Mixon, assistant professor of mathematics at Ohio State University. His study coauthor is Soledad Villar of New York University's Center for Data Science.

Their work focuses on geometric clustering, though Mixon dabbles in game theory, and he has created theorems around gerrymandering in the past. He wondered if the same theory--two players with opposing goals working together to build a map--might make for fairer electoral districts.

The effect we want is that we get a vote that reflects the will of the people, and just intuitively, if both sides have a role in drawing the map, it will be better than if only one side calls the shots. Any two-party game where two parties have a voice is going to be more equitable than a system where only one party has a voice."

Mixon and Villar composed the theorem and posted it on a mathematics preprint server, where other mathematicians can review it and weigh in on its validity before it is submitted to an academic journal.

To build a more-equitable electoral map, the pair theorize, the two political parties simply need to play a game. "In each round, a player assigns a precinct or a county to a voting district--and they take turns," explains Mixon. "The theoretical result is that, if you have half the votes, you'll end up with half of the districts, no matter whether you are the first player or the second player."

The theorem takes a few things for granted: it assumes, for instance, that both parties are playing to win the maximum number of seats; it also assumes that the parties have perfect knowledge of how every voter would vote. It does not take into account a third or...

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