Supplementary Appendix: How to Measure Legislative District Compactness If You Only Know it When You See it

To deter gerrymandering, many state constitutions require legislative districts to be “compact.” Yet, the law offers few precise definitions other than “you know it when you see it,” which effectively implies a common understanding of the concept. In contrast, academics have shown that compactness has multiple dimensions and have generated many conflicting measures. We hypothesize that both are correct—that compactness is complex and multidimensional, but a common understanding exists across people. We develop a survey to elicit this understanding, with high reliability (in data where the standard paired comparisons approach fails). We create a statistical model that predicts, with high accuracy, solely from the geometric features of the district, compactness evaluations by judges and public officials responsible for redistricting, among others. We also offer compactness data from our validated measure for 17,896 state legislative and congressional districts, as well as software to compute this measure from any district. Verification Materials: The data and materials required to verify the computational reproducibility of the results, procedures and analyses in this article are available on the American Journal of Political Science Dataverse within the Harvard Dataverse Network, at Kaufman et al. (2021) at https://doi.org/10.7910/DVN/FA8FVF. Compactness is treated in the law as an important legal bulwark against gerrymandering. The Apportionment Act of 1901, many court decisions, and 18 state constitutions require compactness for U.S. House districts, and 37 states require their legislative districts to be compact (see j.mp/aRED). Compactness is also required in federal law as one of the “traditional redistricting principles,” which, when followed, can “defeat a claim that a district has been gerrymandered...” on the basis of race (Shaw v. Reno, 509 U.S. 630, 647 (1993)) or political party (Davis v. Bandemer, 478 U.S. 173, 2815 (1986)).1 Compactness is also important for the academic literature, where scholars seek to help the redistricting and litigation processes, and also to study venerable political science questions such as the causes, consequences, and normative implications of compact districts over American history (e.g., Ansolabehere and Palmer 2016; Ansolabehere and Snyder Jr 2012; Forgette and Platt 2005). Compactness intuitively refers to both how close a legislative district’s boundaries are to its geographic center and how “regular” in shape a district appears to be. But upon deeper study, scholars have shown that in fact compactness is a complicated multidimensional Aaron R. Kaufman is Assistant Professor, New York University Abu Dhabi, Saadiyat Island, Abu Dhabi, UAE (AaronrKaufman.com; aaronkaufman@nyu.edu). Gary King is Albert J. Weatherhead III University Professor, Institute for Quantitative Social Science, 1737 Cambridge Street, Harvard University, Cambridge, MA 02138 (GaryKing.org; King@Harvard.edu). Mayya Komisarchik is Assistant Professor, University of Rochester, Harkness Hall, 333 Hutchinson Road, Rochester, NY 14627 (www.mayyakomisarchik.com; mayya.komisarchik@rochester.edu). Winner of the 2018 Robert H. Durr Award from the Midwest Political Science Association. Our thanks to Steve Ansolabehere, Fred Boehmke, Ryan Enos, Dan Gilbert, Jim Griener, Bernie Grofman, Andrew Ho, Dan Ho, James Honaker, Justin Levitt, Luke Miratrix, Max Palmer, Stephen Pettigrew, Jamie Saxon, Steve Shavell, Anton Strezhnev, Wendy Tam, Rocio Titiunik, Larry Tribe, Robert Ward, participants in “A Causal Lab,” and the audiences at the Society for Political Methodology Meetings, Nuffield College at Oxford University, the Harvard Applied Statistics Workshop, and the ICPSR Summer Program for helpful data or suggestions, and to Stacy Bogan, the Center for Geographic Analysis, and the Institute for Quantitative Social Science at Harvard University for research assistance and support. Claims about most other types of unfairness in redistricting all also seem to depend on a legal finding of noncompactness (Davis v. Bandemer, 478 U.S. 165; Justice Powell in Vieth v. Jubilerer, 541 U.S. 267 (2004) 176–177; Kirkpatrick v. Preisler, supra, at 394 U. S. 526, 538). American Journal of Political Science, Vol. 65, No. 3, July 2021, Pp. 533–550 ©2021, Midwest Political Science Association DOI: 10.1111/ajps.12603