The geo-graph in practice: creating United States Congressional Districts from census blocks

Abstract

Every 10 years, United States Congressional Districts must be redesigned in response to a national census. While the size of practical political districting problems is typically too large for exact optimization approaches, heuristics such as local search can help stakeholders quickly identify good (but suboptimal) plans that suit their objectives. However, enforcing a district contiguity constraint during local search can require significant computation; tools that can reduce contiguity-based computations in large practical districting problems are needed. This paper applies the geo-graph framework to the creation of United States Congressional Districts from census blocks in four states—Arizona, Massachusetts, New Mexico, and New York—and finds that (a) geo-graph contiguity assessment algorithms reduce the average number of edges visited during contiguity assessments by at least three orders of magnitude in every problem instance when compared with simple graph search, and (b) the assumptions of the geo-graph model are easily adapted to the sometimes-irregular census block geography with only superficial impact on the solution space. These results show that the geo-graph model and its associated contiguity algorithms provide a powerful constraint assessment tool to political districting stakeholders.