08:44 AM

The answer to gerrymandering? Have Democrats and Republicans play a game

Mathematician combines game theory and politics to draw better electoral maps

A new method of drawing electoral districts that combines game theory and the word game “Ghost” could result in maps that are more demographically representative, according to two mathematicians.

In the game “Ghost,” players take turns saying letters, with each letter building on the last letter played. 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, said Dustin Mixon, assistant professor of mathematics at The Ohio State University.

Mixon’s work focuses on geometric clustering, though he 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 more fair electoral districts.

“The effect we want is that we get a vote that reflects the will of the people,” Mixon said. “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 his study co-author, Soledad Villar of New York University’s Center for Data Science, composed the theorem and posted it on a mathematics preprint server, arXiv.org, 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, Mixon theorizes, 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,” he said. “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 example, 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 doesn’t take into account a third or fourth political party, or a back-room handshake that could protect one incumbent or another.

But it is, Mixon believes, a better system than the one in play right now.

As they ran through the possible outcomes in their proposed game, the mathematicians saw again and again that the number of seats each party won ended up reflecting the population of a given state—something that has come under scrutiny in recent elections, including in Ohio.



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.
Dustin Mixon

Gerrymandered districts have caused issues for elections for nearly 200 years, since the first gerrymandered district—drawn by Massachusetts Gov. Elbridge Gerry—created districts that tipped the balance of power in the state government to his party. The Boston Globe compared the district’s shape to a salamander; the combination of Gerry’s name and that description stuck, and the term “gerrymandering” was born.

Since then, the Supreme Court has weighed in on gerrymandering, going so far as to rule partisan gerrymandering unconstitutional in 1986. But determining if a district has been politically gerrymandered can be tricky—even districts that take wonky shapes can actually be more representative of the electorate than those drawn with clean, neat lines.

Ohio’s own electoral districts have come under fire: After the November election, Republicans won 52 percent of the overall votes for U.S. Congress, but will serve in about 69 percent of Ohio’s Congressional seats. But Ohio voters also voted overwhelmingly last year to put stronger controls in place to prevent gerrymandering, and to require buy-in from both Democrats and Republicans before district lines can be drawn.

That two-party planning is the foundation for Mixon’s theorem: If both parties are operating in their individual best interests, the resulting electoral map will be more fair than one drawn with just one party operating in its best interest.

“Twenty-one states have some sort of redistricting commission that they appoint to draw these maps, and those appointees are made by the party in power,” he said. “This improves on what we currently have.”