NATIONAL BUREAU OF ECONOMIC RESEARCH
NATIONAL BUREAU OF ECONOMIC RESEARCH

Socially Optimal Districting

Stephen Coate, Brian Knight

NBER Working Paper No. 11462
Issued in July 2005
NBER Program(s):   PE   POL

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.

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Document Object Identifier (DOI): 10.3386/w11462

Published: Coate, Stephen and Brian Knight. “Socially Optimal Districting: A Theoretical and Empirical Exploration” Quarterly Journal of Economics 122, 4 (November 2007): 1409-1471.

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