Using Boolean Algebra to Analyze Overlapping Memberships

Abstract

The overlap of membership among groups is often of sociological interest. There has been considerable work, for example, on interlocking directorates among corporations (Allen, 1974; Mariolis, 1975; Levine, 1972; Sonquist and Koenig, 1975; Warner and Unwalla, 1967). This work has focused on three issues. First, the amount of overlap has been used as an index of the degree of centralization in the American economy. Second, the pattern of overlap among boards of directors has been used to discover clusters of corporations that operate as well-connected cliques in the economy. Third, the role of certain types of corporations, such as banks, has been examined by looking at their position in the structure of interlocking directorates. Much of this work has not used very powerful methods.