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Mathematicians and a Political Scientist Use Science to Improve the U.S. Voting System

Three scientists sit before microphones in front of a blue AAAS backdrop
Mathematician Jonathan Mattingly, left, political scientist Matt Barreto and mathematician Moon Duchin discussed the making and unmaking of redistricting maps during a press briefing at the AAAS Annual Meeting. | Andrea Korte/AAAS

The American voting system was never designed to guarantee that a successful party gain seats in direct proportion to the number of votes they receive, even though many voters consider proportional representation fundamental to the fairness of the U.S. electoral system, said election experts.

The panel was in full agreement that proportional representation is a misconception with no standing in the U.S. electoral system, and reached that consensus during a news briefing featuring the role of mathematics and advanced technologies in the study of gerrymandering and racial disparities within the U.S. electoral system on the opening day of the 2020 American Association for the Advancement of Science Annual Meeting in Seattle.

“We don’t have proportional representation,” said Matt Barreto, a political science and Chicana/o Studies professor at the University of California, Los Angeles who assesses racial voting disparities. Consider Wisconsin, he said, where voters won 52% of the vote in a statewide election, but only have 34% of the seats, leaving many to contend that “there must be some sort of mismatch.”

Barreto and two mathematicians joining him reviewed a host of voting issues. They discussed the making of redistricting maps that sometimes are so complex in design that they are given names. A 2011 Pennsylvania map was so mottled it was named the “Goofy kicking Donald Duck” and eventually thrown out by the courts and ordered redrawn. The three discussed emerging voting systems like ranked choice, where voters place candidates in preferential order until a winner emerges. They also examined the political feasibility of compulsory voting.

Jonathan Mattingly, a mathematics professor at Duke University, dismissed compulsory voting, saying it makes things “worse because it gives you greater knowledge of who will vote and so a greater ability to precision engineer to your district.”

Moon Duchin, an associate mathematics professor at Tufts University and the leader of its research laboratory that explores gerrymandering and practices that result in racial voting disparities, called on proponents of proportional representation to work within the U.S. system, propose rule changes and work to have them put to a vote.

Already, Moon said, five states, Utah, Colorado, Missouri, Ohio and Michigan, have voted for redistricting reforms. “It’s better to comport with a deliberative democracy notion of what people are looking for from the system. … That’s also an important perspective to have … rules that entail some structural properties, and if you’re not happy with those, the rules can be changed.”

Such research on how congressional, state and local voting districts are drawn and voting systems established comes in advance of the release of the 2020 Census results that will produce updated population figures that will be used to reapportion seats in the U.S. House of Representatives and state legislatures. Growing attention on the topic demonstrates how the decennial process elevates the importance of mathematics, data and social science in determining the fairness of new voting districts.

The speakers described statistical tools and advanced technologies they use to quantify instances when redistricting leads to gerrymandering, the manipulation of district voting boundaries. Mathematicians and social scientists are increasingly being tapped to bring their knowledge to legal disputes and serve as expert witnesses against partisan and racial gerrymandering.

Random sampling mathematical models through the Markov chain Monte Carlo method, for instance, are used to analyze redistricting plans, the speakers said, in describing how the method can both quantify partisan gerrymandering and help determine whether resulting redistricting proposals provide adequate electoral opportunity for minority groups.

Three maps of North Carolina voting districts
A legal battle over districts in North Carolina went all the way to the U.S. Supreme Court. | Courtesy of Jonathan Mattingly

The statistical tools help produce maps that can define fair districts and be effectively compared against gerrymandered ones. North Carolina, for instance, had kept the opposing party from gaining legislative seats even though the opposing party held the majority of votes. An ensuing legal battle went all the way to the U.S. Supreme Court which punted the case back to the state’s highest court where its judges relied upon such methods to strike down the state legislature’s maps and order them redrawn.

Barreto and Duchin are working on modernizing statistical techniques used to detect racially polarized voting. They also underscored that shifting demographics and case law require new attention be paid to the 1965 Voting Rights Act.

Barreto, who also has advised independent redistricting commissions in California and Arizona and testified as an expert in more than a dozen federal voting rights and redistricting lawsuits, unveiled a statistical package during a later scientific session at the AAAS’ Annual Meeting that provided new methods that greatly expand analysts’ ability to more accurately detect racial voting patterns and as a result draw districts that fairly balance diverse racial interests.

“As we head into the 2021 redistricting, we hope that people are able to build on this work and in our analysis in this paper to understand how and when districts are being drawn to have a very particular eye toward racial vote dilution and how racial gerrymandering is affecting communities of color,” Barreto said.

Outlining the effectiveness of mathematical approaches in legal cases, Duchin added, “We’re bringing ideas from all over science and applied mathematics.”


[Associated image credit: bizoo_n/Adobe Stock]



Anne Q. Hoy

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