An Optimization Based Heuristic for Political Districting

Abstract

Redistricting, the redrawing of congressional district boundaries within the states, may occur every 10 years on the basis of the population census. Many redistricting plans are designed with partisan politics in mind, resulting in disputes and forcing judges to intervene. We address this problem from a nonpolitical viewpoint and present an optimization based heuristic incorporating universally agreed upon characteristics. We model the problem as a constrained graph partitioning problem and develop a specialized branch-and-price based solution methodology. We demonstrate the feasibility of our methodology by showing how to satisfy the one-person, one-vote principle with compact and contiguous districts for the state of South Carolina.Graph Partitioning, Branch-and-Price, Column Generation, Clustering, Districting

Extending the automated zoning procedure to reconcile incompatible zoning systems

“…Openshaw (1984) argues strongly that the most appropriate response to the MAUP is to design purpose-specific zonal systems. There is a long history of the modification of electoral geographies in order to achieve approximately equal political representation, and the automated partitioning of geographical space in this context is discussed by Horn (1995) and Mehrotra et al (1998). Openshaw's (1977) Automated Zoning Procedure (AZP) provides a means to automate the process of designing a zonal system in order to maximise the value of some objective function.…”

Spatial Aspects of Census Districting

“…If the original space is composed of a large number of basic spatial units (BSU), then spatial partitioning is aggregating or grouping of these units into larger zones (Figure 1) (Bozkaya et al, 2003;Macmillan, 2001;Salazar-Aguilar et al, 2010;Shirabe, 2005;Yamada, 2009). Spatial partitioning is a multi-objective optimization problem, for which several methods have been proposed based on heuristic and meta-heuristic algorithms (Bação et al, 2005;Bozkaya et al, 2003;Mehrotra, 1998;Wei, 2004) as well as the data structures used in computational geometry (Moreno-Regidor et al, 2012;Mu, 2004;Novaes et al, 2009;Salazar-Aguilar et al, 2010;Svec et al, 2007;Torpelund-Bruin and Lee, 2009;Yamada, 2009 …”

“…Therefore, explicit deployment of their impact on the problem may improve the efficiency of existing districting systems. A variety of applications of urban districting have been the subject of many studies, including political districting (Alt et al, 1996;Bozkaya et al, 2003;Garfinkel and Nemhauser, 1970;Helbig et al, 1972;Hess et al, 1965;Mehrotra, 1998;Yamada, 2009), census districting (Martin, 1998;Openshaw, 1995;Ralphs et al, 2009) and commercial districting (Salazar-Aguilar et al, 2010;SalazarAguilar et al, 2011). Census districting, the case study of this paper, is an urban districting whose goal is providing a fair distribution of the workload to census officers.…”

Network-Based Dissolution

“…Our main inspiration comes from the area of political districting, and in particular from gerrymandering [8,11,12] and from supervised regionalization methods [5]. Of course, graph-theoretic models have been employed before for political districting; for instance Mehrota et al [10] draws a connection to graph partitioning, and Duque [4] and Maravalle and Simeone [9] use graphs to model geographic information in the regionalization problem. These models are tailored towards very specific applications and are mainly used for the purpose of developing efficient heuristic algorithms, often relying on mathematical programming techniques.…”