Relations, residuals, regular interiors, and relative regular equivalence

Given a relation α (a binary sociogram) and an a priori equivalence relation π, both on the same set of individuals, it is interesting to look for the largest equivalence πo that is contained in and is regular with respect to α. The equivalence relation πo is called the regular interior of π with respect to α. The computation of πo involves the left and right residuals, a concept that generalized group inverses to the algebra of relations. A polynomial-time procedure is presented (Theorem 11) and illustrated with examples. In particular, the regular interior gives meet in the lattice of regular equivalences: the regular meet of regular equivalences is the regular interior of their intersection. Finally, the concept of relative regular equivalence is defined and compared with regular equivalence.

Family, community and politics: the fertile legacy of Michael Young

The Institute of Community Studies was set up by Michael Young in order to carry out research on politically relevant social issues, in a context free from direct political control. A research method was devised for it whereby researchers made their own values and objectives very explicit, while staying as close as possible in their reports to the concerns and language of respondents themselves. This method has often been criticized by professional sociologists: but it reflects quite well the nature of social knowledge. It has produced reports which help to increase public understanding of social processes, and provide useful guidance to policy makers. Professional sociology on the other hand has tried to develop a rigorously value-free method. As a result, though, it often seems to be tied implicitly to values shared among researchers but not more universally. Arguably this makes it harder for the general public to understand, and accept, its findings.