Working Paper: NBER ID: w13456
Authors: Roland G. Fryer Jr.; Richard T. Holden
Abstract: The United States Supreme Court has long recognized compactness as an important principle in assessing the constitutionality of political districting plans. We propose a measure of compactness based on the distance between voters within the same district relative to the minimum distance achievable -- which we coin the relative proximity index. We prove that any compactness measure which satisfies three desirable properties (anonymity of voters, efficient clustering, and invariance to scale, population density, and number of districts) ranks districting plans identically to our index. We then calculate the relative proximity index for the 106th Congress, requiring us to solve for each state's maximal compactness; an NP-hard problem. Using two properties of maximally compact districts, we prove they are power diagrams and develop an algorithm based on these insights. The correlation between our index and the commonly-used measures of dispersion and perimeter is -.22 and -.06, respectively. We conclude by estimating seat-vote curves under maximally compact districts for several large states. The fraction of additional seats a party obtains when their average vote increases is significantly greater under maximally compact districting plans, relative to the existing plans.
Keywords: compactness; districting; political representation; gerrymandering
JEL Codes: H70; K19
Edges that are evidenced by causal inference methods are in orange, and the rest are in light blue.
| Cause | Effect |
|---|---|
| relative proximity index (RPI) (R50) | compactness (R12) |
| compactness (R12) | electoral outcomes (K16) |
| maximally compact districts (D79) | responsiveness of electoral outcomes (D72) |
| 1% increase in vote share for Democrats (D79) | larger increase in seats under maximally compact plans (D72) |
| compact districts (Y80) | larger share of Black voters (K16) |
| compact districts (Y80) | greater difference between Republican and Democratic voting percentages (D72) |
| design of districts (R28) | electoral outcomes (K16) |