Here’s a Clever Way to Uncover America’s Voting Deserts

The original version of this story appeared in Quanta Magazine.

In Georgia’s 2020 gubernatorial election, immoderate voters successful Atlanta waited complete 10 hours to formed a ballot. One logic for nan agelong lines was that almost 10 percent of Georgia’s polling sites had closed complete nan preceding 7 years, contempt an influx of astir 2 cardinal voters. These closures were disproportionately concentrated successful predominantly Black areas that tended to ballot Democratic.

But pinpointing nan locations of “voting deserts” isn’t arsenic straightforward arsenic it mightiness seem. Sometimes a deficiency of capacity is reflected successful agelong waits astatine nan polls, but different times nan problem is nan region to nan nearest polling place. Combining these factors successful a systematic measurement is tricky.

In a paper owed to beryllium published this summer successful nan diary SIAM Review, Mason Porter, a mathematician astatine nan University of California, Los Angeles, and his students utilized devices from topology to do conscionable that. Abigail Hickok, 1 of nan paper’s coauthors, conceived nan thought aft seeing images of agelong lines successful Atlanta. “Voting was connected my mind a lot, partially because it was an particularly anxiety-inducing election,” she said.

Topologists study nan underlying properties and spatial relations of geometric shapes nether transformation. Two shapes are considered topologically balanced if 1 tin deform into nan different via continuous movements without tearing, gluing, aliases introducing caller holes.

At first glance, topology would look to beryllium a mediocre fresh for nan problem of polling tract placement. Topology concerns itself pinch continuous shapes, and polling sites are astatine discrete locations. But successful caller years, topologists person adapted their devices to activity connected discrete information by creating graphs of points connected by lines and past analyzing nan properties of those graphs. Hickok said these techniques are useful not only for knowing nan distribution of polling places but besides for studying who has amended entree to hospitals, market stores, and parks.

That’s wherever nan topology begins.

Imagine creating mini circles astir each constituent connected nan graph. The circles commencement pinch a radius of zero, but they turn pinch time. Specifically, erstwhile nan clip exceeds nan hold clip astatine a fixed polling place, nan circle will statesman to expand. As a consequence, locations pinch shorter hold times will person bigger circles—they commencement increasing first—and locations pinch longer hold times will person smaller ones.

Some circles will yet touch each other. When this happens, tie a statement betwixt nan points astatine their centers. If aggregate circles overlap, link each those points into “simplices,” which is conscionable a wide word meaning shapes specified arsenic triangles (a 2-simplex) and tetrahedrons (3-simplex).