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

The US Supreme Court, many state constitutions, and numerous judicial opinions require that legislative districts be “compact,” a concept assumed so simple that no definition is offered other than “you know it when you see it.” Academics, in contrast, have concluded that the concept is so complex that it has multiple theoretical dimensions requiring large numbers of conflicting empirical measures. We hypothesize that both are correct — that the concept is complex and multidimensional, but one particular unidimensional ordering represents a common understanding of compactness in the law and across people. We develop a survey design to elicit this understanding, without bias in favor of one’s own political views, and with high levels of intracoder and intercoder reliability (in data where the standard paired comparisons approach fails). We then create a statistical model that predicts, with high accuracy and solely from the geometric features of the district, compactness evaluations by 96 sitting judges, justices, and public officials responsible for redistricting (and 102 redistricting consultants, expert witnesses, law professors, law students, graduate students, undergraduates, and Mechanical Turk workers). As a companion to this paper, we offer data on compactness from our validated measure for 18,215 US state legislative and congressional districts, as well as software to compute this measure from any district shape. We also discuss what may be the wider applicability of our general methodological approach to measuring important concepts that you only know when you see. ∗The current version of this paper is available at http://j.mp/Compactness. Our thanks to Steve Ansolabehere, 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 2017 Society for Political Methodology Summer Meeting and the Harvard Applied Statistics Workshop 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. †PhD Candidate, Institute for Quantitative Social Science, 1737 Cambridge Street, Harvard University, Cambridge MA 02138; aaronrkaufman.com; [email protected], (818) 263-5583. ‡Albert J. Weatherhead III University Professor, Institute for Quantitative Social Science, 1737 Cambridge Street, Harvard University, Cambridge MA 02138; GaryKing.org, [email protected], (617) 5007570. §PhD Candidate, Institute for Quantitative Social Science, 1737 Cambridge Street, Harvard University, Cambridge MA 02138; scholar.harvard.edu/mkomisarchik; [email protected], (720) 2209328.