Optimal Redistricting Under Geographical Constraints: Why 'Pack and Crack' Does Not Work

Abstract

We show that even when voters’ preferences are deterministic and known optimal partisan redistricting is not generally 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”). More generally, we prove that for districting problems with geographical constraints determining an optimal solution is a computationally intractable (NPcomplete) problem.

Keywords: districting, gerrymandering, NP-complete problems

JEL Classification: D72