July 27, 2011

Contact:   Bill Giduz

Politics involves a lot more math than just counting the final votes.

Mossinghoff's MJM1 Redistricting Proposal

Davidson College Associate Professor Michael Mossinghoff teaches a whole semester-long course in math and politics.

One of the cases he’ll be discussing in the future comes from work he’s done recently in his own back yard. Mossinghoff was involved over the summer in developing new software to help Mecklenburg County redraw the lines for its six electoral districts.

Redistricting is one of the most important—and frequently contentious— mathematical exercises in politics because it can practically determine the winner of an election before a single vote is cast. A Democrat running in a district where Republicans are a majority of the voters may stand very little chance of winning.

The Constitutionally mandated exercise of redistricting occurs on statewide and countywide levels every 10 years, based on new census data about population distribution. The legal goal is to create voting districts that are contiguous and have about the same number of voters – differing no more than 10 percent. But local boards often also establish other parameters for a district’s makeup. The “wish list” for Mecklenburg County Commissioners this year included:

1)    Districts needed to be created from the county’s existing 195 precincts. New precincts could not be created.
2)    Small towns like Davidson that include two or more precincts should not be split between districts.
3)    Two of the six districts should include a majority of minority voters.
4)    To maintain the political balance on the County Commission, three districts should have a history of voting Republican and three should have a history of Democratic votes.
5)    Districts should be as compact in shape as possible.

“Redistricting has historically been shrouded in secrecy,” explained Brian Francis ’96, who lead the team of Mecklenburg County employees charged with the redistricting task. “It used to be commissioners poring over paper maps and spreadsheets, and members of the public never had any more input than a three-minute appeal at a county commission meeting.”

Francis and his staff sought a means of opening the process to more public input this year. “People complain about the process without understanding that it’s not all that easy to do,” he said. “We wanted to give them a way to try it at home for themselves so they could understand the difficulty of the process, and contribute to it if they wish.”

They were able to achieve their goal by developing in-house software called Online Redistricting Tool. The Online Redistricting Tool displays a county map overlaid with boundaries of the 195 election precincts and six districts. (Six of the county’s nine commissioners each represent one of the districts, while three more commissioners are elected at large by all voters.)

Visitors to the online tool site could simply click on the precincts to assign them to any district. A spreadsheet instantly calculated how that assignment affected the goals of equal population, ethnic composition and political tendency.

Francis said, “The process is both art and science, balancing communities of interest and partisan interests. But at its core it’s a math exercise to figure out the optimal configuration.”

With that in mind, Francis decided he should seek input specifically from academicians in the county. He sent an inquiry to faculty members at several area colleges, and received an enthusiastic response from Mossinghoff, an associate professor of mathematics at Davidson.

Mossinghoff said, “I was excited to have the opportunity to work on this problem, in part from my interest in the mathematical aspects of politics, but especially because it wasn’t at all clear that any solution existed that would satisfy all of the board’s desired conditions.”

Mossinghoff determined that it’s a problem best tackled with a branch of math called “combinatorial optimization.” He developed his own computer program to run the data on precinct makeup, and calculated at least 30,000 different possible configurations that satisfied both the legal requirements and the board’s first four desirable properties—all but the “most compact” requirement. Most configurations, however, were very ugly and not at all compact. “There are an almost limitless number of solutions,” Mossinghoff said, “but the good ones are so rare that it’s like looking for a needle in a haystack.”

To find that needle, Mossinghoff wrote another piece of code that assigned values to districts based on their compactness, and ran the 30,000 possibilities against that new criteria. That computation indicated that Mossinghoff’s possibility #24,062 best met all criteria. After a few additional adjustments to improve the district shapes further, Mossinghoff submitted it to the Online Redistricting Tool site as entry MJM1, along with about 100 others that have been submitted.

A citizens’ commission assigned to oversee redistricting reviewed the possibilities in mid July and submitted four of the best ones to the county commission. Mossinghoff’s MJM1 was not among them. Following a few weeks for public review and input, the county commission will adopt a final plan in September.

Michael Mossinghoff

Though Mossinghoff’s proposed districts didn’t make the final cut, he was satisfied that his time working on the issue was well spent. “I’ve learned that certain optimization techniques work very nicely in redistricting problems,” he said. “But more importantly, it’s very satisfying to see mathematics assisting with knotty problems for the public’s benefit.

“It will make for some interesting discussion in my “Math & Politics” class, and will make an appealing topic at the right sort of professional conference. I may write an article about it, too, and who knows? There may be a future opportunity to use my software in another environment.”

Francis was delighted with the public participation in the process, and sees it as the wave of the future of redistricting. He doesn’t believe objective mathematics can ever de-politicize the process, but he thinks it can help. “I’m hoping it will create a greater opportunity to work out the politics as we go through the process. We can hopefully come to greater consensus earlier, rather than having the pressure of politics build and build until it blows up.”
 
Davidson is a highly selective independent liberal arts college for 1,900 students located 20 minutes north of Charlotte in Davidson, N.C. Since its establishment in 1837 by Presbyterians, the college has graduated 23 Rhodes Scholars and is consistently regarded as one of the top liberal arts colleges in the country. Through The Davidson Trust, the college became the first liberal arts institution in the nation to replace loans with grants in all financial aid packages, giving all students the opportunity to graduate debt-free. Davidson competes in NCAA athletics at the Division I level, and a longstanding Honor Code is central to student life at the college.
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