Socially Optimal Districting

This paper provides a welfare economic analysis of the problem of districting. In the context of a simple micro-founded model intended to capture the salient features of U.S. politics, it studies how a social planner should allocate citizens of different ideologies across districts to maximize aggregate utility. In the model, districting determines the equilibrium seat-vote curve which is the relationship between the aggregate vote share of the political parties and their share of seats in the legislature. To understand optimal districting, the paper first characterizes the optimal seat-vote curve which describes the ideal relationship between votes and seats. It then shows that under rather weak conditions the optimal seat-vote curve is implementable in the sense that there exist districtings which make the equilibrium seat-vote curve equal to the optimal seat-vote curve. The nature of these optimal districtings is described. Finally, the paper provides a full characterization of the constrained optimal seat-vote curve and the districtings that underlie it when the optimal seat-vote curve is not achievable.