6 March 2006
One goal of school desegregation is to promote racial understanding by fostering interracial contact. In an article in the American Journal of Sociology (1998, Vol. 103), Scott Feld and William Carter develop a simple combinatorial argument about a surprising potential consequence of school desegregation.
They argue that under certain (not so outlandish) circumstances, school desegregation may actually decrease rather than increase opportunities for interracial contact.
Here is their argument by way of a stylized example. Suppose there are four schools, one with capacity C1=400, and three schools with capacities C2=C3=C4=200 students. Under segregation, all 100 black students in the district attend the big school. The 900 other students are white. Assuming that students only interact with students in their own school, there are thus 300*100=30,000 possible interracial, intra-school ties. Now desegregate such that the percentage of black students is the same in all four schools. Then there are 360*40 potential interracial, intra-school friendships in the big school, and 180*20 potential interracial, intra-school friendships in each of the three small schools. Hence, the total number of potential interracial friendships post-desegregation is 25,200, as compared to 30,000 pre-desegregation.
Whether this decrease in potential ties will actually result in a decrease in realized ties is an empirical question, dependent on factors spelled out in the article. Feld and Carter go on to show that this particularly instance is an example of the so-called Class Size Paradox, known from various applications in sociology.