Representation in District-Based Elections

District-based elections must reconcile two objectives: representing each district's electorate and matching the statewide delegation to parties' vote shares. We study seat allocation rules when these objectives conflict. The optimal rules, characterized by a cutoff, form a family ranging from first-past-the-post to proportional representation as the weight on statewide representation increases. Along this path, gaining further seats through gerrymandering becomes increasingly difficult. The characterization yields a measure of the robustness of first-past-the-post to statewide representation concerns, which we compare with established electoral diagnostics. In U.S. House elections from 2002 to 2024, we find that maps drawn by single-party legislatures perform worse than those produced by courts or non-partisan commissions. The efficiency gap, a common measure of partisan gerrymandering, is more strongly associated with litigated maps than the other measures, yet magnifies the extent to which Republican-legislature maps appear worse than Democratic-legislature maps.