# Statistics PhD Student and Professor Create Algorithm for Evaluating Redistricting Plans

June 29, 2022

With the mid-term elections coming up this fall, debate has been brewing in states over drawing new congressional district maps, which occurs every 10 years after the completion of the census (also known as “redistricting”).  In multiple court cases, voters have challenged the new maps with claims of gerrymandering (intentionally favoring one political party over another).  In Alabama, voters filed a lawsuit contending that the new plan failed to provide enough majority-minority districts, and thus, hurt black voters. Voters in New York filed a lawsuit claiming Democratic partisan gerrymandering while voters in Ohio filed a lawsuit claiming Republican partisan gerrymandering. With the stakes so high, where could the plaintiffs, defendants, and courts turn to for supporting evidence of bias (or a lack thereof) in a new redistricting plan?

#### 50-State Redistricting Simulation Project

Enter the ALARM (Algorithm-Assisted Redistricting Methodology) Project’s R software package “redist” used to simulate thousands of sample districting plans for all 50 states as part of the 50-State Redistricting Simulation Project.  The ALARM Project is a research group, including graduate and undergraduate students, and one high school student, led by Professor of Statistics and Government Kosuke Imai.  The research group focuses on “redistricting sampling algorithms, best practices and workflows for redistricting analysis, and tools to visualize, explore, and understand redistricting plans,” and receives computational support from the Harvard Data Science Initiative and from Microsoft (ALARM Project website).  To further understand the impact of the ALARM group’s 50-State Project, the Statistics Department spoke with Professor Kosuke Imai and 3rd year Statistics PhD student Cory McCartan, Kosuke’s advisee, who helped develop the simulation algorithms, design the R software package, and introduce the idea of expanding the project to all 50 states and more.  The contents of this article are based on conversations with Kosuke Imai and Cory McCartan.

#### Software Package Addresses Redistricting Problem

According to Kosuke, historically, researchers would consult older districting plans or plans from other states to measure the fairness of their proposed or enacted plan.  However, these methods were not very useful for rating a plan both because demographics and political views often change over time and because states can vary substantially in terms of their demographics, politics, and districting rules.  Instead, researchers needed a method to obtain a random sample of redistricting plans that followed state rules and could be used as a neutral baseline to measure the fairness of an enacted or proposed redistricting plan.

“To address this problem,” explains Kosuke, “Cory and I came up with the new simulation algorithm, called the Sequential Monte Carlo (SMC) algorithm, and implemented a software package  to make these cutting-edge algorithms accessible to a broad audience  - social scientists, policy makers, journalists, etc.” Expanding on Cory’s role in the project, Kosuke says, “Cory is a unique scholar because he brings together both the mathematical and statistical expertise and a passion for politics and the social sciences.  This kind of applied work requires an immense amount of attention to detail while innovating new methods that are actually able to solve real-world problems.  For example, it was important for the algorithm to be able to incorporate criteria such as not splitting county boundaries or not having two incumbents face off.  These details have a significant impact on redistricting and have real-world political implications, even if they might not be math problems that can be easily solved.  Cory understood this and cared about getting this right.”

In recent years, researchers have developed other algorithmic tools to draw proposed districts, but these tools didn’t have a way of measuring bias in the plans.  With our SMC algorithm in the software package, “now, you have a mathematical algorithm, something you can write out on a whiteboard and talk about and study, which helps us to be more confident that the method is fair and doesn’t have bias built in” (Cory McCartan).  The mathematical algorithm that Cory refers to obtains a random sample of plans that incorporate common state redistricting rules, such as that the plans have equal population, follow existing county boundaries, be contiguous, and be geographically compact as much as possible.

To help us visualize the algorithm, Cory describes how the formula starts with a blank map, draws one district that it keeps and then, out of the remaining area in the state, continues to draw a 2nd district, 3rd district, and so on.  This process is completed many times over in parallel, each time starting over with a blank map – “similar to how an etch a sketch works,” explains Cory.  The method that the SMC algorithm follows is an improvement over some other algorithms because it results in a high level of efficiency.  Cory elaborates, “When we talk about the efficiency of the algorithm, it’s about how can I get the most information and explore more possibilities within a given amount of time.  While it’s faster to just change a single border than it is to draw a whole plan from scratch, when we start from scratch each time, we get a whole new map that has a lot more information.”

#### Communicating the Data

While the SMC algorithm excels in efficiently producing a high-quality sample of redistricting plans, this would not be sufficient to make a difference in court cases, in policy, in the real-world in general.  Cory highlights the importance of providing tools that clearly communicate the data: “If you simply make 10,000 plans, that will just show you every single precinct in the state and which district it’s assigned to - for a human that’s completely useless.  We need to think about how to pull information out and visualize the data in one or two helpful charts.  There’s a technical stats side to this project but also a communication side.”  Specifically, the software package helps users communicate data by including graph plotting functions in the code, including graphs that show the geographic compactness and Republican/Democratic vote share by district.

Kosuke shares his thoughts about Cory’s contributions to the project in the area of communication, “Cory is an incredible mathematician and statistician; while he can understand the math and write out the algorithm, he can also make it usable and understandable to others.”  The software package is readily accessible to undergraduate students (and even high school students!), who are now testing out the algorithm for ALARM’s 50 states project to simulate sample plans for all 50 states.  Because the software is open source, it is available to a wide range of researchers, policy makers, journalists, and anyone else interested in the redistricting process.

#### Real-World Impact of 50-State Project

Now that the R software package is accessible to a wide range of stakeholders, it’s easier to hold states accountable for drawing fair, unpartisan voting districts.  The package has been used by many researchers and journalists.  It has also played a significant role in several recent court cases, including Alabama, New York, and Ohio. Cory elaborates on the significance of the project to him: “It’s been great to see how the simulation evidence, either from our team or other teams, has been critical in these court cases to prove that districts are fair or not fair.  This has a big impact on who gets elected and whether voters have a fair chance of electing their preferred candidate.  I’ve been in grad school for 3 years and it’s gone from a very small project to a large team where we get to work on these important cases – it’s been a very cool project to be a part of!”

Regarding the next steps for the Project, Cory expresses his enthusiasm for continuing to learn more: “As the dust settles now, it’s going to be helpful to do a post-mortem to see what things worked (or didn’t).  We are currently working on an analytical framework for looking at the impact of different types of gerrymandering beyond partisan gerrymandering – like racial gerrymandering and gerrymandering at the local level.  We now have a whole other cycle on our hands and that’s going to be very exciting.”  We look forward to seeing what Cory, Kosuke and the rest of the ALARM Project do moving forward and how their work will continue to impact the redistricting process and our society in general.