Padding and pruning: gerrymandering under turnout heterogeneity

Padding is the practice of adding nonvoters (e.g., noncitizens or disenfranchised prisoners) to an electoral district in order to ensure that the district meets the size quota prescribed by the one man, one vote doctrine without affecting the voting outcome in the district. We show how padding— and its mirror image, pruning—, can lead to arbitrarily large deviations from the socially optimal composition of elected legislatures. We solve the partisan districter’s optimal padding problem.