Measuring Compactness and the Role of a Compactness Standard in a Test for Partisan and Racial Gerrymandering

Abstract

As we move into the 1990s, compactness of legislative districts is likely to take on greater importance because of its relevance to questions of racial and partisan discrimination. We show that at least two distinct components of shape--dispersion and perimeter length--are necessary elements of any reasonable compactness measure and that compactness may be based on geography or on population. An appropriate strategy, therefore, is simultaneously to consider multiple measures that collectively define compactness. We identify and evaluate multiple operationalizations and compare them both theoretically and empirically. Data from five states provide abundant evidence that the major types of measures sometimes vary widely in their evaluation of the compactness of a given district. There is some support, however, for the hypothesis that multiple measures yield similar assessments of districting plans. We conclude with a discussion of how compactness might be used in legislative districting.