Optimal Gerrymandering in a Competitive Environment

We analyze a model of optimal gerrymandering where two parties simulaneously redistrict in a competition for influence in a legislature. Parties allocate geographic blocks to districts, in which the median voter determines the winner. The form of the optimal gerrymander involves “slices ” of extreme right-wing blocks that are paired with “slices ” of left-wing blocks, as in Friedman and Holden (2008). We also show that, as one party controls the redistricting process in more states, that party designs districts so as to spread out the distribution of district median voters from a given state, thus leading to increased polarization in the legislature. We show that this comparative static holds for a broad class of objective functions