Geographic compactness vs. race/ethnic compactness and other criteria in the delineation of legislative districts

Abstract

Several criteria have evolved in law and tradition to constrain the delineation of Congressional and State and local legislative districts, such as population equality, geographic compactness, race/ethnic ‘compactness’, and integrity of political boundaries. Among the various criteria, I focus on compactness, and in particular, the legal and mensural aspects. Following the passage of the Voting Rights Act in 1965, racial ‘compactness’ has been employed more and more frequently as a primary criterion, and with reduced restraint compared with other criteria, except perhaps for population equality. In Thornburg v. Gingles (1986), the Supreme Court recognized racial/ethnic compactness and polarization in voting practices as prerequisites for newly established ‘majority-minority’ districts. In Shaw v. Reno (1993), the Court reaffirmed the principle of geographic compactness as against racial compactness by noting that the shape of Cong. Dist. 12 of North Carolina was ‘bizarre’ and that it was drawn solely on racial grounds. With this decision, race/ethnic compactness and, by extension, the broad interpretation of the Voting Rights Act have been put in conflict with geographic compactness as criteria. More recently, in Miller v. Johnson (1995), use of race as a predominant factor in district delineation, apart from compactness, was rejected. These developments should renew interest in and support for formal statistical guidelines in evaluating geographic compactness in redistricting plans. Many formulas for measuring compactness have been proposed and tested. Here the commonly used perimeter/circle measure and the circumscribed area/circle measure are compared by an examination of some simple geometric figures and 1990-Census-based C.D.'s. Some problems with these measures are noted, and a new measure, the CV/radii measure (the complement of the coefficient of variation of the ‘radii’ of the district), is proposed and illustratively applied.