GEOGRAPHIC COMPACTNESS VS RACE ETHNIC COMPACTNESS AND OTHER CRITERIA IN THE DELINEATION OF LEGISLATIVE DISTRICTS

Several criteria have evolved in law and tradition to constrain the de lineation of Congressional and State and local legislative districts, such as population equality, geographic compactness, race/ethnic 'comp actness', and integrity of political boundaries. Among the various cri teria, I focus on compactness, and in particular, the legal and mensur al aspects. Following the passage of the Voting Rights Act in 1965, ra cial 'compactness' has been employed more and more frequently as a pri mary criterion, and with reduced restraint compared with other criteri a, except perhaps for population equality. In Thornburg v. Gingles (19 86), the Supreme Court recognized racial/ethnic compactness ana polari zation in voting practices as prerequisites for newly established 'maj ority-minority' districts. In Shaw v. Reno (1993), the Court reaffirme d the principle of geographic compactness as against racial compactnes s by noting that the shape of Gong. Dist. 12 of North Carolina was 'bi zarre' and that it was drawn solely on racial grounds. With this decis ion, race/ethnic compactness and, by extension, the broad interpretati on of the Voting Rights Act have been put in conflict with geographic compactness as criteria. More recently, in Miller v. Johnson (1995), u se of race as a predominant factor in district delineation, apart from compactness, was rejected. These developments should renew interest i n and support for formal statistical guidelines in evaluating geograph ic compactness in redistricting plans. Many formulas for measuring com pactness have been proposed and tested. Here the commonly used perimet er/circle measure and the circumscribed area/circle measure are compar ed 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 m easure, the CV/radii measure (the complement of the coefficient of var iation of the 'radii' of the district), is proposed and illustratively applied.