The economics of partisan gerrymandering

Abstract

We study the problem of a partisan gerrymanderer who assigns voters to equipopulous districts so as to maximize his party’s expected seat share. The designer faces both aggregate, district-level uncertainty (how many votes his party will receive) and idiosyncratic, voter-level uncertainty (which voters will vote for his party). We argue that pack-and-pair districting, where weaker districts are “packed” with a single type of voter, while stronger districts contain two voter types, is typically optimal for the gerrymanderer. The optimal form of pack-and-pair districting depends on the relative amounts of aggregate and idiosyncratic uncertainty. When idiosyncratic uncertainty dominates, it is optimal to pack opposing voters and pair more favorable voters; this plan resembles traditional “packing-and-cracking.” When aggregate uncertainty dominates, it is optimal to pack moderate voters and pair extreme voters; this “matching slices” plan has received some attention in the literature. Estimating the model using precinct-level returns from recent US House elections indicates that, in practice, idiosyncratic uncertainty dominates and packing opponents is optimal; moreover, traditional pack-and-crack districting is approximately optimal. We discuss implications for redistricting reform and political polarization. Methodologically, we exploit a formal connection between gerrymandering—partitioning voters into districts—and information design—partitioning states of the world into signals.