Gerrymandering and computational redistricting

Partisan gerrymandering poses a threat to democracy. Moreover, the complexity of the districting task may exceed human capacities. One potential solution is using computational models to automate the districting process by optimizing objective and open criteria, such as how spatially compact districts are. We formulated one such model that minimised pairwise distance between voters within a district. Using US Census Bureau data, we confirmed our prediction that the difference in compactness between the computed and actual districts would be greatest for states that are large and, therefore, difficult for humans to properly district given their limited capacities. The computed solutions highlighted differences in how humans and machines solve this task with machine solutions more fully optimised and displaying emergent properties not evident in human solutions. These results suggest a division of labour in which humans debate and formulate districting criteria whereas machines optimise the criteria to draw the district boundaries. We discuss how criteria can be expanded beyond notions of compactness to include other factors, such as respecting municipal boundaries, historic communities, and relevant legislation

The political districting problem: A survey

Computer scientists and social scientists consider the political districting problem from different viewpoints. This paper gives an overview of both strands of the literature on districting in which the connections and the differences between the two approaches are highlighted

Optimal partisan districting on planar geographies

We show that optimal partisan districting in the plane with geographical constraints is an NP-complete problem

Fair redistricting is hard

Gerrymandering is a long-standing issue within the U.S. political system, and it has received scrutiny recently by the U.S. Supreme Court. In this note, we prove that deciding whether there exists a fair redistricting among legal maps is NP-hard. To make this precise, we use simplified notions of "legal" and "fair" that account for desirable traits such as geographic compactness of districts and sufficient representation of voters. The proof of our result is inspired by the work of Mahanjan, Minbhorkar and Varadarajan that proves that planar k-means is NP-hard

Optimal redistricting under geographical constraints: Why "pack and crack" does not work

We show that optimal partisan redistricting with geographical constraints is a computationally intractable (NP-complete) problem. In particular, even when voter's preferences are deterministic, a solution is generally not obtained by concentrating opponent's supporters in \unwinnable" districts ("packing") and spreading one's own supporters evenly among the other districts in order to produce many slight marginal wins ("cracking")