Our Mission

The Metric Geometry and Gerrymandering Group (MGGG) is a Boston-based working group led by Moon Duchin of Tufts University and Justin Solomon of MIT. Our mission is to study applications of geometry and computing to U.S. redistricting. We believe that gerrymandering of all kinds is a fundamental threat to our democracy.

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;

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;

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;

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

Campus Coronavirus Response MGGG At the MGGG Redistricting Lab, our team includes expertise in math modeling, geospatial data, and app development. We have a RAPID grant from the National Science Foundation to support planning related to Campus Coronavirus Response, and have launched several component projects.

Geometry of Graph Partitions via Optimal Transport Tara Abrishami, Nestor Guillen, Parker Rule, Zachary Schutzman, Justin Solomon, Thomas Weighill, and Si Wu We define a distance metric between partitions of a graph using machinery from optimal transport. Our metric is built from a linear assignment problem that matches partition components, with assignment cost proportional to transport distance over graph edges. We show that our distance can be computed using a single linear program without precomputing pairwise assignment costs and derive several theoretical properties of the metric. Finally, we provide experiments demonstrating these properties empirically, specifically focusing on its value for new problems in ensemble-based analysis of political districting plans.

Complexity and Geometry of Sampling Connected Graph Partitions Daryl DeFord, Lorenzo Najt, and Justin Solomon In this paper, we prove intractability results about sampling from the set of partitions of a planar graph into connected components. Our proofs are motivated by a technique introduced by Jerrum, Valiant, and Vazirani. Moreover, we use gadgets inspired by their technique to provide families of graphs where the “flip walk” Markov chain used in practice for this sampling task exhibits exponentially slow mixing. Supporting our theoretical results we present some empirical evidence demonstrating the slow mixing of the flip walk on grid graphs and on real data. Inspired by connections to the statistical physics of self-avoiding walks, we investigate the sensitivity of certain popular sampling algorithms to the graph topology. Finally, we discuss a few cases where the sampling problem is tractable. Applications to political redistricting have recently brought increased attention to this problem, and we articulate open questions about this application that are highlighted by our results.

The Metric Geometry and Gerrymandering Group 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.