Applying Mathematical Concepts to Elections – the “Geometry of Redistricting”

Tommy Ratliff, professor of mathematics, participated in the “Geometry of Redistricting” workshop sponsored by the Metric Geometry and Gerrymandering Group , this past August at Tufts University. Professor Ratliff was also accepted and trained as an expert witness ahead of the 2020 census and its subsequent redistricting.

When it comes to personal involvement and interest, Ratliff refers to his work on voting theory for the past 20 years. He has sought to understand the mathematical structure underlying decision making procedures. His work has relevance to gerrymandering and redistricting since once the districts are drawn, the choice of voting structure can still have a significant impact on the outcome of the election. This is particularly relevant in local elections for city councils and other legislative bodies.

“There are a few different ways to look at redistricting,’ says Ratliff, ‘There is a geometric question. You can look at the shapes of the districts and can either say ‘this is a reasonable shape’ or ‘this is not a reasonable shape.’ That is the purely geometric viewpoint. Then there is the question of looking at the distribution of populations within the districts. Even if a district looks nice, compact, and well formed, it is still possible to draw them to take certain populations and split them among districts so that they have less political influence or to take all the constituents and pack them into one district so that they only have influence in that particular location and not in others.”

When asked about getting involved, Ratliff cited the recent Tufts University conference and workshop where mathematicians, GIS specialists, and law professors came together to address these issues.

“What’s really interesting to me is that there may be questions we can solve from a purely mathematical point of view but if the solutions aren’t compelling in the courts or the legislature it doesn’t matter as much. We may [just] be saying really interesting things about a world we don’t live in.” said Ratliff. “There are these other constraints that come in from what case law is, what you’re actually allowed to challenge and not challenge in court, and it makes it an exciting time to begin to be involved with this especially with the next census coming up in 2020.”

The goal among conference participants is to build a consensus for a type of gold standard against which redistricting efforts can be held. This will indicate whether officials should give a closer look into where and why inequities exist in a redistricting, both before and after the process.

“The math is never going to give an absolute answer. [It] is just going to be a point of reference. It’s going to be one piece of information that helps shape the overall story.” said Ratliff. “The same is true for using sophisticated computing tools. We cannot hope to throw enough computing power to provide a complete answer, but it is another tool to use in an analysis.”