The 2018 Joint Mathematics Meetings were fantastic. One of my favorite talks was — surprise, surprise — the fabulous Saturday afternoon MAA-AMS-SIAM Gerald and Judith Porter Public Lecture, given by Tufts University professor Moon Duchin on Political Geometry: Voting Districts, “Compactness,” and Ideas About Fairness. The audience of – apparently – 953 was enthusiastically engaged. Duchin’s talk focused on the legislative history of redistricting and introduced the mathematical methods and quantitative approaches used to gerrymander and simultaneously to detect gerrymandering.
Her talk was quite timely. The math community is becoming increasingly active in the redistricting process and in court cases challenging particular maps as partisan gerrymanders. Cases under court consideration in which arguments rely on quantitative assessments of partisanship include the Wisconsin case currently in consideration by the U.S. Supreme Court, the North Carolina case just decided, and the Pennsylvania case also just decided. The last one is interesting because, and I believe (if you know otherwise please write me!) it is the first in which mathematical scientists have served as witnesses for both sides.
Professor Duchin spoke about one general approach for detecting partisan gerrymandering that is making its way into legal decisions (e.g., see the discussion on page 91 of the joint decision handed down in North Carolina in the two cases Common Cause v. Rucho, No. 1:16-CV-1026, and League v. Rucho, No. 1:16-CV-1164). The general outline of this approach is to produce — using, for example and as done for the NC case, a Markov chain Monte Carlo method — a large “ensemble” of possible districting plans that comport with traditional principles such as equal population, contiguity, compactness, and simultaneously comply with the Voting Rights Act. After that, we compute some metric(s) that measures partisan outcomes for each of the plans in the ensemble. Finally, one can decide if the proposed plan is an “outlier.” In other words, answer the question: “where does the proposed districting plan lie, in the histogram of the metric, amongst all plans in the ensemble?” A proposed plan is considered to have partisan bias when its value of the fairness measure is highly unusual compared to values for the alternative plans.
On the Tuesday before the Joint Meetings, the AMS Council met and was presented with a statement on gerrymandering; the AMS Committee on Science Policy brought the statement to the Council with a recommendation to endorse. The statement was written by a small team of experts drawn from the membership of the AMS together with colleagues from the American Statistical Association.
I am pleased that the AMS Council voted to endorse this statement, which positions mathematics and statistics in the national conversation on redistricting. In response to the passage of the statement, AMS President Ken Ribet noted
Our community is poised to play a central role in ongoing discussions about methods for creating voting districts and the evaluation of existing and proposed district maps. It has been a pleasure for me to observe the recent explosion in interest in this topic among colleagues and students. I anticipate that the new statement by the ASA and AMS Council will lead to increasing transparency in the evaluation of districting methods.
Every state will begin redistricting as soon as the 2020 Census data are available. We aim to get those charged with drawing maps to incorporate the expertise of AMS and ASA members, with the ultimate goal that every single state has a map that is NOT an outlier in terms of the partisan make-up of the Congressional delegation it elects to the U.S. House of Representatives. Mathematicians and statisticians will be able to do this: immediately after 2020 Census data becomes available, the Metric Geometry and Gerrymandering Group (a Boston-based team led by Moon Duchin) will publicly release a large ensemble of maps for the districted races in each state so that proposed districting plans can be evaluated against a range of viable alternatives.”
While more and more court cases include mathematical and statistical arguments in their proceedings, we have yet to see our expertise brought in adequately in the early, map-drawing stages of the process. The tide may be turning, I know of a few mathematical scientists who have served on citizens’ redistricting committees and as consultants to map-drawers, and Pennsylvania’s Governor has just enlisted the help of a mathematician to draw new maps.
What can you do?
- Learn more!
- Attend one of the regional Geometry of Gerrymandering workshops,
- Look at the great resources by academic research teams, including those posted by:
- Explore legal resources shared by the Brennan Center for Justice.
- Sign-up for the National Academies’ May 8th webinar on redistricting featuring Duke University’s Jonathan Mattingly and yours truly.
- Play with some of the free redistricting software you find via a Google search (e.g., at the Public Mapping project).
- Get yourself a beer, ovaltine, or your drink of choice, sit in a comfy place and try your hand at the Redistricting Game (fun with teens if you have some hanging around your home or classroom).
- Share what you know!
- Write an Op-Ed  for your local paper about the role of mathematics in redistricting (feel free to contact me for specific ideas tailored to your state: firstname.lastname@example.org).
- Get involved with a local civic group (e.g., League of Women Voters) and offer to give a public talk on redistricting.
- If you have kids in school (or even if you don’t) volunteer at the local high school to give a talk on redistricting (contact a math, civics, or AP government teacher, and if you do this I can assure you that the Redistricting Game mentioned above is a big hit).
 Incidentally, I intend to write a post soon on writing op eds; stay tuned!