Each panel shows the estimated probabilities that a representative is a Republican, nonblack Democrat, or black Democrat for all possible levels of BVAP in a given region.
There are important differences across regions, perhaps best summarized by the concentration level of BVAP required to achieve a 50% probability that the elected representative is a black Democrat, that is, the point of equal opportunity for minority voters to elect their candidate of choice.
Yet, the electoral effect of minority voters proved to be much more significant, as the BVAP in a district has a substantial influence on the partisan and racial characteristics of the representative.
To answer this question, we first calculate the expected LCCR score of a representative in each geographic region, depending on the level of BVAP.
E(LCCR [where] BVAP) = [summation over [Theta]] E(LCCR [where] BVAP, [Theta]) [multiplied by] P([Theta] [where] BVAP), (3)
In southern districts, both covered and noncovered, the relationship is positive up to about 25% BVAP, then relatively flat to 35% BVAP, and then rises steeply up to 50% BVAP.
In the Northwest, the relationship increases steadily to about 35% BVAP, when it levels off at 1.
Notice that with only 10% BVAP in a district, the expected support score is nearly 80%.
In general, the total of the BVAPs in all districts will equal the average BVAP in the state times the number of districts.
Given this fact, there is no reason to construct districts with a BVAP in this range, as those voters could be usefully allocated to other districts.
The second and third columns show the number of districts and BVAP in each state.