Our Work

Basics

• Gerrymandering v. Geometry

  Moon Duchin

  01 November 2018

  The mathematics of gerrymandering is surprisingly rich, and computing power is arguably just catching up with the scale and complexity of the redistricting problem. (Related interactive and some supporting numerology.)

  Scientific American, November 2018.

• Gerrymandering metrics: How to measure? What’s the baseline?

  Moon Duchin

  08 November 2017

  Bulletin of the American Academy for Arts and Sciences, Winter 2018.

• Rebooting the mathematics behind gerrymandering

  Moon Duchin and Peter Levine

  01 October 2017

  The Conversation, October 2017.

Research

• 

  Ranked Choice Voting and ‘Structural Democracy’

  MGGG

  14 November 2024

  Since 2019, we’ve pursued a major research theme in structural democracy, meaning the study of voting rules and electoral systems in terms of their properties. For example, ranked choice voting is a reform to move away from first-past-the-post voting that’s being debated around the country– but there’s far too little work that models its effects on representation.

  Our work is both theoretical and practical, from building new statistical models of ranking to testing fairness properties across election systems to writing public-facing reports for communities considering a change of election system.

  Here is a selection of projects that the lab has been involved in…

• 

  Recombination and other samplers

  MGGG

  07 November 2024

  Redistricting is the problem of partitioning a set of geographical units into a fixed number of districts, subject to a list of often-vague rules and priorities. In recent years, the use of randomized methods to sample from the vast space of districting plans has been gaining traction in courts of law for identifying partisan gerrymanders, and it was used as an analytical tool by several legislatures and independent commissions.

  The mathematics of sampling graph partitions is interesting in its own right, and there has been enormous progress in recent years. Most of the new methods use an idea that comes from this research group: that spanning trees provide a computationally efficient way to partition a graph, because deleting a single edge cuts the graph into two pieces. We introduced the idea in 2018 and released a supporting software package called GerryChain the same year. Now the spanning tree partition step can be found in several different kinds of samplers, including those introduced by Jonathan Mattingly’s group at Duke and Kosuke Imai’s group at Harvard.

  Here are a few key papers from the lab on samping graph partitions…

• 

  Voting Rights Act Research

  MGGG

  30 November 2022

  The Voting Rights Act of 1965 (or simply the “VRA”) is a landmark law in the United States that centers on ensuring electoral opportunity for minority groups, including those defined by race or by a common language. A key element in bringing a VRA lawsuit is a demonstration of racial polarization in elections — does a minority group tend to vote cohesively for certain “candidates of choice,” but see their choices blocked from election by an also-cohesive majority? Due to the secret ballot, making claims about the racial breakdown of voting patterns requires techniques for statistical inference. Another key element is geography, where plaintiffs must show that the minority group could have made up more than half of a district in a reasonably configured districting plan.

  In the Roberts Court, there has been a steady erosion of VRA precedent and a ratcheting upwards of the burden on plaintiffs to bring a case. We have a research direction looking at possible futures for the VRA, and racial fairness in political representation more broadly.

Reports

• Election Reform in Lowell, MA

  MGGG

  21 October 2019

  Two years ago, the City of Lowell was sued because its system of election was said to prevent minority communities from being represented in city government. For example, even though there are 9 members of the City Council—and nearly half of Lowell’s population is Asian or Hispanic—there have only been 2 people of color elected to the City Council in 20 years!

• 

  Study of Reform Proposals for Chicago City Council

  MGGG

  15 April 2019

  Many observers agree that the Chicago City Council ward system suffers from problems of gerrymandering, intense segregation, vestiges of machine politics, and inefficiency. In our latest report, we apply mathematical models to analyze Chicago’s current ward plan and compare several reform proposals to address its problems. Our findings strongly support a transition to multimember wards with ranked choice voting to secure and sustain fair representation.

• The Mathematicians' Brief in Rucho v. Common Cause

  MGGG

  18 March 2019

  MGGG has organized a collaborative effort of mathematical and legal experts to file an amicus brief for the upcoming Supreme Court gerrymandering cases. An amicus brief is a “friend of the court” filing, where outside parties try to help supply the court with useful information.

Data

• How Geocoded Voterfiles Can Inform the Collection of Precinct Boundary Data

  MGGG

  08 April 2020

  Our research at the MGGG Redistricting Lab requires election data at the finest spatial resolutions possible. This generally is the voting precinct, also sometimes called voting tabulation districts (VTDs), wards, and election districts. Unfortunately for our research purposes, many states either do not keep track of their precinct boundaries at all or have significant discrepancies between their precinct boundary data and tabular election results. While we can contact individual municipalities to collect data or clear up these discrepancies, this is incredibly time consuming and sometimes local election administrators are unable or unwilling to help. In these instances, a geocoded voterfile can be used to help determine precinct boundaries. Voterfiles are lists kept by state elections officials of registered voters. The information in them varies state by state, but generally they include address information and precinct assignments for all registered voters.

• 

  Election Geodata

  Ruth Buck and MGGG

  09 December 2019

  In most cases, the finest level of geography election results are reported at is the precinct. However, the frequency with which precincts change and the absence in many states of strong data transparency laws can prove to be a significant barrier in compiling election data for redistricting research. Hosted on the GitHub organization mggg-states are the precinct-level election geodata MGGG has compiled for its research and for the open-source web app Districtr.

• The Known Sizes of Grid Metagraphs

  Zach Schutzman and MGGG

  01 October 2018

  One of the reasons that redistricting is hard to study is that the space of possibilities is so huge it’s unthinkable by humans. As a simplified warmup problem, we can ask: how many ways can you district a small grid?

Code

• GerryChain.jl

  Parker Rule, Matthew Sun, Bhushan Suwal, and MGGG

  29 September 2020

  A high-performance implementation of GerryChain in Julia, for running very long chains.

• maup: the geospatial toolkit for redistricting data

  Max Hully and MGGG

  15 June 2019

  maup is our attempt to make working with redistricting data easier for everyone. It is a Python package that streamlines the basic workflows that arise when working with blocks, precincts, and district shapefiles.

• The Known Sizes of Grid Metagraphs

  Zach Schutzman and MGGG

  01 October 2018

  One of the reasons that redistricting is hard to study is that the space of possibilities is so huge it’s unthinkable by humans. As a simplified warmup problem, we can ask: how many ways can you district a small grid?

Interactives

• Districtr

  MGGG

  10 June 2025

  Districtr is our open-source browser-based mapping app. Our goal for Districtr is to put the tools of redistricting in the hands of the public, with an emphasis on meeting the needs of civil rights organizations, community groups, and researchers.

  First conceived as part of a student summer project in 2018, Districtr launched as a public mapping app in 2019 and has grown to be a prominent part of the redistricting landscape in the years since then. We offer affordable mapping support for localities, either working directly with local government and organizers, or through redistricting consulting companies who serve those localities. Districtr is always free to use for members of the public.

  Some highlights from the 2020 census cycle include:

  • offical mapping tool of the People’s Maps Commission in Wisconsin;
  • official mapping tool of cities and localities across the country, from New York City, Los Angeles, San Diego, and Minneapolis to Grand County, Utah (population 9,669);
  • contracted by Michigan Department of State to collect communities-of-interest data (and other public feedback) for the Michigan Independent Citizens’ Redistricting Commission.

  In 2025, we are preparing an ambitious rewrite of Districtr, now available in beta release. We plan a wide public release of Districtr 2.0 by the end of Summer 2025. New features include:

  • ability to split/break precincts down to census blocks;
  • improved contiguity check and zoom to unassigned units;
  • improved import/export options for working with block assignment files;
  • many small feature upgrades, like changing colors on your districts and keyboard shortcuts for super-users.
• 

  District-Shortening Flow

  Zachary I. Schutzman

  08 July 2019

  Use curve-shortening flow to analyze the geometric shape of electoral districts, with interactive widgets and visualizations.

• MIT student project: Visualizing Gerrymandering

  MGGG

  14 June 2019

  As a part of the MIT EECS course 6.894: Interactive Data Visualization, MIT students Chuyan Millie Huang, Wenwei Vicky Liu, and Kim-Anh-Nhi Nguyen created an interactive tool that analyzes ensembles of districting plans for Virginia and Pennsylvania. They were mentored by MGGG’s Daryl R. DeFord and Justin Solomon. Try it out yourself here.