Johnson caused several additional 30-50% BVAP districts to be created before the 1996 election.
In 1992, the year of their study, no whites won in districts with more than 50% BVAP, so they cannot tell us how whites elected from majority black districts might have voted on the floor of the House.
In that state the overall BVAP is 29.82%, and the Hispanic voting-age population is less than 1%.
The resulting relationships between black voting-age population and (1) the type of representative elected and (2) substantive representation are illustrated for southern districts in Figure 1.(9) As shown, the same basic functional relationship holds in all three cases, even in the 1970s when a greater number of districts with 30-50% BVAP existed, thus reinforcing our original findings.
Our estimates concerning substantive representation agree almost perfectly with those reported in Table 5.6 of Lublin (1997): Southern Democrats have ideology scores close to those of Congress overall, and they do not change significantly over the relevant 0-40% BVAP region.
Estimating the direct relationship between district composition and the resulting voting behavior of the elected representative captures all the indirect effects, all the factors that may change with the percentage BVAP and affect either electoral outcomes or a representative's roll-call voting decisions.(11) And by calculating overall optimal districting schemes statewide, we automatically account for the fact that adding more minority voters to one district requires their removal from a surrounding district (otherwise, optimal districting would always be 100%!).
We found that in districts below 53.10% BVAP, the decline in the North was greater, while for districts above this mark the southern decline was more pronounced.
In particular, we calculate members' expected LCCR score given the level of BVAP in their district and the subgroup [Theta] from which the representative is drawn:
Figure 3 summarizes the relation between BVAP and LCCR in each subgroup.
The row labeled "Pr(F)" provides the probability value for an F-test of the models LCCR = a + b [multiplied by] BVAP and LCCR = a + b [multiplied by] s(BVAP), where s([center dot]) denotes a nonparametric smoothing spline.(17) Only for Northeast Republicans is the nonlinearity statistically significant, as shown by the loess fit in Figure 3.
The percentage of BVAP may thus have its largest effect by influencing the distribution from which a representative is drawn; that is, in determining whether the elected representative is a Republican, a nonblack Democrat, or a black Democrat.
Final Electoral Equation, Multinomial Logit Category Nonblack Variables Democrats Republicans Constant 12.15 12.44 (4.17) (4.18) BVAP -43.43 -54.01 (14.97) (15.17) BVAP*East 17.38 21.98 (7.31) (7.93) South 5.21 5.86 (2.91) (2.92) Log-likelihood -268.34 [[Chi].sup.2] (6) 262.85 Percentage correctly predicted 61% Percentage Improvement 20% Predicted Black Nonblack Repub- Actual Democrats Democrats licans Total Black Democrats 35 2 0 37 Nonblack Democrats 2 147 73 222 Republicans 0 92 84 176 Total 37 241 157 435 Note: Standard errors are given in parentheses.