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

To prevent gerrymandering and to encourage a form of democratic representation, many state constitutions and judicial opinions require US legislative districts be "compact." Yet, few precise definitions are offered other than "you know it when you see it," effectively assuming the existence of a common understanding of the concept. In contrast, academics have concluded that the concept has multiple theoretical dimensions requiring large numbers of conflicting empirical measures. This has proved extremely challenging for courts tasked with adjudicating compactness. We hypothesize that both are correct -- that compactness is complex and multidimensional, but a common understanding exists 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 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). We also offer data on compactness from our validated measure for 18,215 state legislative and congressional districts, as well as software to compute this measure from any district. 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. See this paper: j.mp/Compactness