Contiguity-Based Optimization Models for Political Redistricting Problems

Political redistricting is a process used to redraw political boundaries based on a number of criteria that include population equality, minority representation, contiguity, and compactness. Redistricting plans can be difficult to draw manually and since the 1970s the use of computers in the creation of redistricting plans has increased dramatically. The purpose of this paper is to formulate the problem of finding redistricting plans as optimization problems on the basis of population equality and contiguity. The authors specifically address the problem from the contiguity perspective. They developed two exact optimal models: one based on a minimum spanning tree and one based on network flows. They discuss the spatial representation and the formulation of contiguity for both models and compare the performance of these two models, along with a third model developed in the literature, using a variety of synthetic and real data. The authors' results confirm that such a problem is computationally intensive and more efficient methods are needed for large size problems, but with appropriate formulation approaches they can obtain useful baseline solutions to these problems with relatively small size. They also find that multiple optimal solutions with different spatial configurations may exist for the same problem, which presents a new challenge to the development of solution methods for political redistricting problems.