Mathematicians implement algorithms to stop fraud

For decades, one such user was Thomas Hofeller, “Michelangelo of Modern Jerrimander. ”Long-time official director of the Republican National Committee for Redistribution of Districts, who died in 2018.

Gerrymandering schemes involve hacking and packaging – scattering votes for one party across constituencies, thereby weakening their power, and driving like-minded people into one constituency, wasting power they would have had elsewhere. The city of Austin, Texas, is split, divided into six boroughs (the largest city in the United States with no boroughs).

In 2010, the full force of the threat materialized with the Republican Majority Redistribution Project, or REDMAP. He spent $ 30 million on state secret ballot elections, with victorious results in Florida, North Carolina, Wisconsin, Michigan and Ohio. “The victories in 2010 gave them the opportunity to draw maps in 2011,” says David Daly, author of the book Ratf ** ked: the true story of a secret plan to steal American democracy

“What used to be dark art has now become dark science.”


The fact that the technology has advanced by leaps and bounds compared to the previous cycle of redistribution of areas only strengthened the result. “This made the Jerrimanders painted this year much more durable and durable than any other Jerrimanders in our country’s history,” he says. “It’s the complexity of the computer software, the speed of computers, the amount of data available that allows guerrilla cartographers to subject their maps to 60 or 70 different iterations and really improve and optimize the guerrilla performance of those maps. … “

As Michael Lee, a district redeployment expert at the Brennan Justice Center at NYU Law School, said, “What used to be dark art is now dark science.” And when manipulated cards are used in elections, he says, they almost impossible to overcome

Mathematical microscope

Mattingly and his Duke’s team staying up late, writing code that they expect will bring “huge benefits, algorithmically” – preparing to actually use their latest tool, which debuted in a (currently pending) article with the technically heady title “Multiscale Markov Chains with Split and Merge Monte Carlo for Boundary Redistribution… “

However, promoting technical discourse is not a top priority. Mattingly and his colleagues hope to educate politicians and the public, as well as lawyers, judges, mathematicians, scientists – anyone interested in the cause of democracy. In July, Mattingly gave a public lecture with a more accessible title, summarized: “Do you hear the will of the people when they vote?

Deformed areas are often considered a sign of Jerrimander. On a 2012 map of North Carolina, the congressional districts were “very strange looking beasts,” says Mattingly, who (along with his key collaborator, Greg Hershlag) provided expert testimony in some of the lawsuits that followed. Over the past decade, legal problems have arisen across the country – in Illinois, Maryland, Ohio, Pennsylvania, Wisconsin.

But while such disfigured neighborhoods “make really pretty posters, coffee cups and T-shirts,” Mattingly says, “the truth is, giving up the weird geometry won’t stop gerrymandering.” In fact, with all the technologically sophisticated hand techniques, a distorted map can be difficult to detect.

These maps of North Carolina counties show that geometry is not a reliable indicator of fraud. The 2012 NC map, with its quirky neighborhood boundaries, has been judged to be a racial game by the court. The replacement, the NC 2016 card, looks very different and tame compared to it, but has been deemed an unconstitutional political game. Analysis by Duke’s Jonathan Mattingly and his team found that the 2012 and 2016 maps were politically equivalent in their party results. A court-appointed expert drew a map of NC 2020.


Instruments developed simultaneously by several mathematicians provide the so-called “extreme emissions test”. Each researcher’s approach is slightly different, but the result is this: a suspected counterfeit card is compared to a large collection or “ensemble” of impartial neutral cards. Mathematical method in action – based on what is called Markov chain Monte Carlo algorithms– generates a random sample of maps from many possible maps and reflects the likelihood that any map drawn will satisfy various political considerations.

The ensemble maps are coded to reflect the different principles used to draw areas, taking into account how these principles interact with the geopolitical geometry of the state. Principles (which vary from state to state) include criteria such as keeping counties relatively compact and interconnected, making them roughly equal in population size, and preserving counties, municipalities, and communities with a common interest. District maps must comply with the U.S. Constitution and the Voting Rights Act of 1965.

Following the 2020 Census Bureau’s release, Mattingly and his team will load the dataset, run their algorithm, and generate a set of typical non-partisan neighborhood plans for North Carolina. From this vast distribution of maps and historical voting patterns, they will be able to identify landmarks that should serve as a fence. For example, they will assess the relative likelihood that these cards will lead to different election results – say, the number of seats won by Democrats and Republicans – and with what difference: when the vote is 50-50 and there is a plausible vote. As with the 2012 card, a neutral card is unlikely to give Republicans 10 seats and Democrats only three.

“We use computational mathematics to figure out what we expect from objective maps, and then we can compare them to a specific map,” says Mattingly.

They will announce their findings by mid-September and then hope that state legislators will heed the restrictions. Once new district maps are proposed later in the fall, they will analyze the results and participate in the public and political discussions that follow – and if the maps are again suspected of tampering with maps, there will be more lawsuits in which mathematicians will play again. central role.

“I don’t want to just convince someone that something is wrong,” says Mattingly. “I want to give them a microscope so they can look at the map and understand its properties, and then draw their own conclusions.”

Jonathan Mattingly
Jonathan Mattingly is an applied mathematician at Duke University.


When Mattingly testified in 2017 and 2019, analyzing two subsequent versions of maps of North Carolina counties, the court agreed that the maps in question were overly biased Jerrimanders discriminating against Democrats. Wes Pegden, a mathematician at Carnegie Mellon University, testified using a similar method in the Pennsylvania case; The court agreed that the card discriminated against Republicans.

“The courts have been trying for a long time to determine how the guerrilla maneuver can be measured,” says Lee. “But then there seemed to be a breakthrough when court after court destroyed the cards using some of these new tools.”

When the North Carolina case made it to the US Supreme Court in 2019 (along with the Maryland case), mathematician and geneticist Eric Lander, a Harvard and MIT professor who is currently chief scientific adviser to President Biden, briefly noted that “Computer technology has faced the problem that it has given rise to.” He considered the standard to be highly non-standard – a test that simply asks, “What proportion of border redistribution plans are less extreme than the proposed plan?” – “a direct quantitative mathematical question to which there is an answer. right answer.”

Most judges concluded otherwise

“The five justices on the Supreme Court are the only ones who seem to have problems understanding how mathematics and models work,” says Lee. “State and other federal courts were able to enforce it – it did not go beyond the intellectual ability of the courts to handle, like a complex sex discrimination case or a complex securities fraud case. But five Supreme Court justices said, “This is too difficult for us.”

“They also said, ‘It’s not for us to fix it – the states have to do it; This Congress to correct; it’s not up to us to fix it, ”says Lee.

Will it matter?

Daly said the Supreme Court ruling gives state legislators “the green light and no speed limit when it comes to guerrilla Jerrimanders they can put in place when they map out later this month.” At the same time, he said, “the technology has improved to the point that we can now use [it] to see through and through the technological gerrimanders created by legislators. “

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