Our Mission

The MGGG Redistricting Lab is a research group at Tisch College of Tufts University that grew out of an informal research collective called the Metric Geometry and Gerrymandering Group. The Lab is led by PI Moon Duchin. Our staff has expertise and interests spanning mathematics (geometry, topology, discrete math, dynamics), algorithms, software development, geography, STS, and policy. We research data science interventions for civil rights.

Our goals are these:

• to pursue cutting-edge research in the basic science and practically relevant applications of geometry, topology, and computing to the redistricting problem;
• to build open-source tools and resources that create public access and analytical power for better understanding districts and their consequences;
• to partner with civil rights organizations to reexamine and strengthen the quantitative toolkit for protecting voting rights;
• to offer formal and informal expert consulting to stakeholders on all sides.

Highlights

• 

  The (Homological) Persistence of Gerrymandering

  MGGG

  02 October 2020

  We apply persistent homology, the dominant tool from the field of topological data analysis, to study electoral redistricting. Our method combines the geographic information from a political districting plan with election data to produce a persistence diagram. We are then able to visualize and analyze large ensembles of computer-generated districting plans of the type commonly used in modern redistricting research (and court challenges). We set out three applications: zoning a state at each scale of districting, comparing elections, and seeking signals of gerrymandering. Our case studies focus on redistricting in Pennsylvania and North Carolina, two states whose legal challenges to enacted plans have raised considerable public interest in the last few years. To address the question of robustness of the persistence diagrams to perturbations in vote data and in district boundaries, we translate the classical stability theorem of Cohen–Steiner et al. into our setting and find that it can be phrased in a manner that is easy to interpret. We accompany the theoretical bound with an empirical demonstration to illustrate diagram stability in practice.

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  Implementing partisan symmetry: Problems and paradoxes.

  MGGG

  02 October 2020

  We consider the measures of partisan symmetry proposed for practical use in the political science literature, as clarified and developed in Katz-King-Rosenblatt. Elementary mathematical manipulation shows the symmetry metrics derived from uniform partisan swing to have surprising properties. To accompany the general analysis, we study measures of partisan symmetry with respect to recent voting patterns in Utah, Texas, and North Carolina, flagging problems in each case. Taken together, these observations should raise major concerns about using quantitative scores of partisan symmetry – including the mean-median score, the partisan bias score, and the more general “partisan symmetry standard” – as the decennial redistricting approaches.

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  Clustering propensity: A mathematical framework for measuring segregation

  MGGG

  02 October 2020

  We propose a new family of metrics called capy (or clustering propensity) scores, designed to measure the clustering level of one or more subgroups within a population. The intended application is to offer new ways of measuring the segregation of demographic subgroups. We discuss two main capy scores, Edge and HalfEdge (as well as weighted variants of each) and we compare them to existing segregation scores in the political science, geography, and network science literature. To evaluate the scores, we compute and plot values of minority proportion ρ vs. clustering score C for test distributions on large n × n grids, and on actual demographic data from U.S. states and cities. We argue that capy scores successfully discern qualitatively important differences while providing a stabler baseline for interpretation than classic scores like the Dissimilarity Index and Moran’s I.

The MGGG Redistricting Lab is a nonpartisan research organization. MGGG has major support from the Jonathan M. Tisch College of Civic Life at Tufts University and the Amar G. Bose Research Grant Program at MIT and an active partnership with the Lawyers' Committee for Civil Rights Under Law.