DIVISION OF THE HUMANITIES AND SOCIAL SCIENCES

Although some judges and political scientists have recently doubted that it is possi­ ble to predict the partisan consequences of redistricting plans, I demonstrate that it is simple to do so with a pair of OLS equations that regress voting percentages on major party registration percentages. I test this model on data for all California Assembly and Congressional elections from 1970 through 1992, and compare it to logit results and to more complicated equations that contain incumbency and socioeconomic variables. Since information on socioeconomic variables is often not available early in a redistricting cy­ cle, and since incumbency in a district is often difficult to determine precisely after a reapportionment, I rely on the simplest equation, which correctly predicts 90% of the re­ sults. I show that analogous equations using registration or votes for minor or even major offices in California, North Carolina, and Texas can predict outcomes with considerable accuracy. Using the party registration equations, I show that the so-called "Burton Gerryman­ der" of 1980 had minimal partisan consequences, while the "nonpartisan" plan instituted by the California Supreme Court's Special Masters in 1992 was nearly as biased in favor of the Republicans as the proposal of the Republican party, which would have insured the GOP a majority of the Congressional seats even if Democrats won a landslide of the votes. I conclude by introducing a new graphical representation of redistricting plans, which strongly implies that in 1991, Republican and Democratic line drawers in Califor­ nia agreed on the registration margins necessary for party control and drew their plans with these in mind. Is it possible to measure partisan gerrymandering directly and reliably? Can it be done even before an election takes place under a proposed redistricting scheme, or even if a plan is never put into effect? Although politicians have generally believed that they could quite accurately determine the partisan consequences of redistricting plans, some judges and political scientists have recently scorned this belief, while others have implicitly cast doubt on it by focusing on the intricacy of lines between districts as an indirect indication of an intent to gerrymander. For example, in 1 992, California Chief Justice Malcolm Lucas, a Republican and former law partner of the Republican governor who appointed him to the state's highest court, curtly rejected extensive evidence that a redistricting plan drawn under the auspices of three judges who had been appointed by Republican governors was meant to damage Democrats: "[P]redictions of future election contests are quite obviously speculative and imprecise; involving the weighing of countless variables. " (Wilson v. Eu, 1992, 727) Similarly, in his provocative analysis of town-level registration and election statistics from Massachusetts and Connecticut, political scientist Mark E. Rush contends that voters' allegiances to parties are too weak and shifting for redistricting to have very determinable consequences. Consequently, Rush concludes, courts should abandon the attempt to adjudicate partisan gerrymandering announced by the U.S. Supreme Court in the Indiana case of Davis v. Bandemer in 1 986: "[I]f we cannot determine a town's partisan profile, we cannot make the claim that a districting system is unfair to one of the parties, because we cannot say with certainty where the parties-in-the-electorate are located. " (Rush 1 993, 96) Finally, legal scholars Daniel Polsby and Robert Popper assert that only a rigid adherence to a test for the geographic compactness of electoral districts can combat partisan gerrymandering, and that the actual partisan consequences of imposing such a test do not matter. Exalting procedures over substance, they view compactness as by definition a politically neutral criterion that should be employed to evaluate competing redistricting plans at least partly because of the difficulty of making substantive decisions about the effects of those plans. (Polsby and Popper 1 991, 336) This paper rejects the contentions of Lucas and Rush and suggests that we do not have to resort to such indirect measures of partisan gerrymandering as compactness, because a simple, unequivocally politically neutral test that uses widely available data is quite reliable. As ever more powerful personal computers and off-the-shelf redistricting software have become available, the number of plans proposed has multiplied and will no doubt expand further in the millennial reapportionments. Consequently, it is more and more important for participants and outside observers to be able to compare the partisan effects of suggested schemes. Unlike other measures of partisan bias (Grofman, 1983; Niemi, 1 985; King and Browning, 1 987; King, 1989; Gelman and King, 1990), the index of party strength presented here may be computed before an election has been held and it offers strong insights into the intentions of the redistricters and into just how those intentions were put into effect. The test is not only more intuitively meaningful and easier to explain to judges and the public than sophisticated variants of seats-votes ratios (Gelman and King, 1990, 1 994a, and 1994b), but the simulations that it suggests are more clearly tied to the specific electoral history in a jurisdiction than are those in more general, abstract schemes. In particular, I suggest ways to project quite easily the consequences of two kinds of possible shifts in voter behavior under proposed plans and to compare plans from one decade to the next. To determine how reliable the test is, I analyze registration and election data from California Congressional and State Assembly districts from 1970 to 1994, as well as unpublished data from various plans proposed in 1991.1 Finally, I introduce a new, revealing, and easy method of graphical representation of redistricting plans. It may be that courts should avoid partisan political thickets, but if so, it is not because they cannot find their way. Justice Byron White was right when he wrote that "It requires no special genius to recognize the political consequences of drawing a district line along one street rather than another. " (Gaffney v. Cummings 1973, 752-53) Ninety percent of _the winners in California Assembly and Congressional contests from 1970 through 1994 can be predicted correctly with two elementary equations estimated by ordinary least squares regression: (1) %D = B01 + (Bn *%Dreg) + (B21 * %Rreg) + u1, (2) %R = B02 + (B1 2 * %Dreg) + (B22 * %Rreg) + u2,. where %R =Republican percentage of the total (not just two-party) vote, by district, 2 %D = Democratic percentage of the total vote, by district, %Rreg =Republican percentage of the total (not just two-party) registration, by district, %Dreg = Democratic percentage of the total registration, by district, the B's are the relevant OLS regression coefficients, and u = an error term. The estimates of the parameters for these equations are given in Table 1 -Panels A and C for the Democrats and Panels B and D for the Republicans.3 (Table 1 about here) The equations fit the data rather well. For one thing, the R2s are fairly high for social science, indicating that party registration generally explains about two-thirds of the variance in the vote, and that the trend in the 1970s toward crossover voting seemed to have reversed in the 1980s.4 For another thing, suppose we apply 'For an extensive discussion of the facts of the California redistrictings from 1971 through 1991, see Kousser, 1995. 2In contemporary California, about 13.5% of the eligibles register with the Libertarian, Peace and Freedom, or Green parties or decline to state a party registration. The percentages vary widely from district to district and over . time with a standard deviation in November, 1992 of 2.7% and a range from 5% to 20%. The number and strength of minority party candidates also diff er considerabiy across space and time. It is also unclear whether a higher registration of Libertarians can be expected to help or hurt Republican candidates, and vice-versa for the other two parties and the Democrats. Because of this theoretical indeterminacy, the effects of all non-major registration are subsumed in the intercept term. 3Since we are trying to predict seats won, the proper unit here is the congressional district. Consequently, the regressions are not weighted. Since in California, but not everywhere, the major parties generally contest nearly every seat, I have made no correction for uncontested seats. For a discussion of how to handle large numbers of uncontested seats, see Gelman and King, 1994a, Appendix A. 4Signs on the Republican coefficients for the Assembly are statistically significant for every year except 1978 and on the D emocratic coefficients for the Assembly, are statistically significant only in 1974. The changes in the signs of the insignificant Democratic coefficients have no substantive importance. The patterns are somewhat more complex in the congressional equations, but the same basic generalizations apply: Coefficients for the Republican registration are significant and in the same directions from 1978 on, with the exception of the quiet 1990 election, while coefficients for the Democratic