The Economics of Partisan Gerrymandering

In the United States, the boundaries of congressional districts are often drawn by political partisans. In the resulting partisan gerrymandering problem, a designer partitions voters into equal-sized districts with the goal of winning as many districts as possible. When the designer can perfectly predict how each individual will vote, the solution is to pack unfavorable voters into homogeneous districts and crack favorable voters across districts that each contain a bare majority of favorable voters. We study the more realistic case where the designer faces both aggregate and individual-level uncertainty, provide conditions under which appropriate generalizations of the pack and crack solution remain optimal, and analyze comparative statics. All districting plans that we find to be optimal are equivalent to special cases of segregate-pair districting, a generalization of pack and crack where all sufficiently unfavorable voter types are segregated in homogeneous districts, and the remaining types are matched in a negatively assortative pattern. Methodologically, we exploit a mathematical connection between gerrymandering—partitioning voters into districts—and information design—partitioning states of the world into signals.