  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 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.
