Aaron Montgomery is an assistant professor of mathematics at Baldwin Wallace University.

BEREA, Ohio -- After months of meetings and many rounds of discussion, Ohio legislators have finally reached an elusive compromise on the thorny subject of congressional gerrymandering.

Pending approval from Ohio voters on the May ballot, Ohio's congressional redistricting process will undergo a significant revision designed, among other things, to keep districts compact, limit splits of counties and cities, and to meaningfully involve the minority political party in the redistricting process.

When I make the four-mile trip each morning from my house to my office at Baldwin Wallace University, I cross from Ohio's 16th congressional district into the 9th district. This journey serves as a daily reminder that the redistricting process constitutes a formidable geometry problem. As a math professor, I spend a fair bit of time thinking about geometry problems; as our lawmakers proceed, it will be crucial for them to be careful about exactly which geometry problem they are attempting to solve.

Many use the word "gerrymandered" to refer simply to districts with strange-looking shapes. However, a bizarrely shaped district isn't necessarily a problem. For example, some strangely shaped districts are forced by our nation's natural borders and landscapes. In other cases, odd-looking shapes are used to keep communities together. A truly gerrymandered map is one in which districts have been drawn in a particular way to convey a strong systemic advantage to one political party by wasting the votes of the other party. This is the well-documented reality of the current Ohio district lines.

One way to mathematically analyze voting districts is to consider the "efficiency gap," which is a way to compare each party's wasted votes. The U.S. congressional district efficiency gap is as large now as it has ever been in the last 50 years, which means that more votes than ever are being wasted by the way that congressional boundaries are drawn.

A study from the Brennan Center for Justice at the New York University School of Law indicates that, from 2012 to 2016, the congressional district efficiency gap in Ohio accounted for an average of about 2.5 extra Republican U.S. House members beyond what would be expected from its voting patterns. This GOP bump is the fifth highest in the nation.

Republicans should not applaud these tactics, because they have also given an advantage to Democrats in other states, such as Massachusetts and Maryland, which, respectively, elected an average of around 1.5 and 1 extra Democrats during that same time period.

When a majority party draws shapes in a way that drives the minority party into further irrelevance, it's not only unfair to the voters - it's a crime against geometry.

As our legislators implement the redistricting compromise, they should keep in mind that districts with the fewest wasted votes may not necessarily look like the small, compact shapes we might imagine.

Dustin Mixon, a mathematics professor at Ohio State University, and collaborator Boris Alexeev recently proved a mathematical theorem stating that district maps with the lowest possible efficiency gap may require districts that are not geometrically compact. In other words: For lawmakers to draw politically balanced maps, it may sometimes be necessary to draw districts that have strange, gerrymandered-looking shapes.

The goal of redistricting reform to create compact districts may need to be balanced against the more meaningful goal of achieving fair political representation.

When the next district maps are released, we will need to use more sophisticated analysis than the eyeball test to tell whether the districts have been fairly drawn. Mathematical tools like the efficiency gap can help identify whether new, visually appealing maps have actually made any progress toward reducing gerrymandering.

The current Ohio 9th district - sometimes called the "snake on the lake" - is a famous grotesque-looking district that stretches from Toledo to Cleveland. This district is part of a genuinely politically gerrymandered map, and it is a perfect example of what the new redistricting process should seek to avoid.

But even if this new process does ultimately yield a district with a bizarre shape, it doesn't necessarily indicate a gerrymandering problem. We will need to take a closer look to be sure that any new maps are fair, and that's where math can help.

Aaron Montgomery is an assistant professor of mathematics at Baldwin Wallace University in Berea.

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