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Banner image: To draw computer-generated maps of Colorado's potential political districts, Jeanne Clelland's software first pinpoints the hundreds of voting districts in the state, then connects them with lines to form borders. (Credit: Jeanne Clelland)

On the evening of Tuesday, Sept. 28, an voted to approve a new map for Colorado鈥檚 congressional districts鈥撯�揹ividing the state into with roughly equal populations.听

Colorado, like every other state in the Union, undergoes the process of reshaping its local and national voting districts every 10 years. You could fill a picture book with the convoluted, sometimes cartoonish shapes these regions take. Ohio鈥檚 fourth congressional district, for example, looks like a bit like duck, or maybe a dragon. Then there鈥檚 Illinois鈥� fourth, which political commentators often compare to earmuffs.

Which is where Jeanne Clelland, a professor of mathematics at CU Boulder, enters the picture. She鈥檚 one of a growing number of researchers who are drawing on their skills to help inform the process of redistricting, bringing nonpartisan numbers to bear on this politically-fraught endeavor.听

The risks come down to more than just funny shapes: Politicians have historically used redistricting as a chance to cut rivals out of power鈥撯�揳nd, in more insidious cases, to disenfranchise nonwhite voters. That American pastime, gerrymandering, gets its name from Massachusetts governor Elbridge Gerry, known for his cantankerous nature. In 1812, the staunch Democratic-Republican approved a map for his state that kneecapped opponents in the Federalist Party.听

But听math, Clelland said, can help.

鈥淟itigation around redistricting has been going on for a long time, especially when it comes to racial gerrymandering,鈥� Clelland said. 鈥淏ut it鈥檚 only in the last 10 years or so that mathematicians have started getting into the game.鈥�

Clelland doesn鈥檛 advocate for any political party or for any particular redistricting proposal. Instead, she and her colleagues use mathematical models to build a series of redistricting statistics. These numbers give redistricting officials a baseline that they can compare their own maps to, potentially identifying cases of gerrymandering before they鈥檙e inked into law.听

The topic has taken on new relevance this year. Colorado鈥檚 newly drawn congressional map is now off to the state Supreme Court for its final OK. A second independent commission is in the process of setting the borders for Colorado鈥檚 35 General Assembly districts.

The mathematician鈥檚 team has released . And, she said, the findings suggest these maps don鈥檛 seem to give any political party an unfair advantage in the state鈥檚 elections鈥撯�揳t least for now.

鈥淎s far as I can tell, both commissions are acting in good faith and really trying to do the right thing,鈥� she said. 鈥淭here鈥檚 no way that everybody is going to be happy with the outcome, but we鈥檝e got a good process in place, and I think the outcome will be fair.鈥�

Coauthors on the new analyses include Beth Malmskog and Flavia Sancier-Barbosa of Colorado College and Daryl DeFord of Washington State University.

A bevy of maps

Clelland, who joined the CU Boulder faculty in 1998, discovered the field of redistricting math almost by accident at an academic workshop in 2017. She had previously studied more esoteric concepts in math like differential geometry and differential equations.

鈥淚 was looking for ways for me to use my professional skills to make a difference and improve the political landscape a little bit,鈥� Clelland said. 鈥淭his seemed like an opportunity for mathematicians to get involved and do good work.鈥澨�

Here鈥檚 how it works: Clelland and her colleagues use computer software to dice Colorado up into as many potential district maps as possible鈥撯�揾undreds of thousands of maps in all. In doing so, they run through the full gamut of what Colorado鈥檚 voting landscape could theoretically look like in the next decade. They can also tweak those maps to favor some priorities over others.

鈥淵ou can tell the computer, I want districts to be as politically competitive as possible, or I want districts to avoid dividing counties as much as possible,鈥� Clelland said.

Clelland and her colleagues have presented their analyses to both independent commissions. She鈥檚 adamant that none of the team鈥檚 maps can, or should, set Colorado鈥檚 official district boundaries. But, she noted, they can give the independent commission a useful point of reference.

In other words, how do the results from a group of flawed humans stack up against the work of an unfeeling computer?

Keeping things fair

Say, for example, that Colorado voters turned out to the polls in 2022 and voted exactly like they did in recent statewide elections, such as for governor and secretary of state in 2018. In that scenario, Clelland鈥檚 hypothetical maps would produce about three or four Republican representatives and four or five Democratic representatives on average. Plenty of factors, from political scandals to wave elections, could tip those results toward either party. But, the mathematician said, if a redistricting map leaned too much toward a different outcome, it might be a sign that something was fishy.听

鈥淚f somebody wanted to propose a plan that produced seven Democratic representatives, you鈥檇 say that plan may have some partisan bias in it,鈥� Clelland said.

And, she said, the independent commission鈥檚 map seems to align well with her team鈥檚 results. That final proposal, for example, creates four districts that lean Democrat, three that tilt Republican鈥撯�損lus an eighth than is about as close to a toss-up as you can get.听

For Clelland, a member of the League of Women Voters, the project is her chance to help Coloradans make their voices heard.

鈥淎s a pure mathematician, I鈥檝e always enjoyed my research, but it鈥檚 kind of lousy for cocktail parties,鈥� Clelland said. 鈥淪uddenly, I have research that people are excited to hear about.鈥�