The Duality of Persons and Groups

A metaphor of classical social theory concerning the "intersection" of persons within groups and of groups within the individual is translated into a set of techniques to aid in empirical analysis of the interpenetration of networks of interpersonal ties and networks of intergroup ties. These techniques are useful in'the study of director interlocks, clique structures, organizations within community and national power structures, and other collectivities which share members. The "membership network analysis" suggested in this paper is compared to and contrasted with sociometric approaches and is applied to the study by Davis et al. (1941) of the social participation of eighteen women. Consider a metaphor which has often appeared in sociological literature but has remained largely unexploited in empirical work. Individuals come together (or, metaphorically, "intersect" one another) within groups, which are collectivities based on the shared interests, personal affinities, or ascribed status of members who participate regularly in collective activities. At the same time, the particular patterning of an individual's affiliations (or the "intersection" of groups within the person) defines his points of reference and (at least partially) determines his individuality.1 The following discussion consists of a translation of this metaphor into a set of techniques which aid in the empirical analysis of the interpenetration of networks of persons and networks of the groups that they comprise. My usage of the term "group" is restrictive in that I consider only those groups for which membership lists are available-through published sources, reconstruction from field observation or interviews, or by any other means. Such groups include corporation boards of directors (J. Levine, 1972), organizations within a community or national power structure (Lieberson, 1971; Perrucci and Pilisuk, 1970), cliques or organizations in a high school (Bonacich, 1972; Coleman, 1961), and political factions. Donald Levine (1959:19-22) writes that "the concept of dualism" is a key principle "underlying Simmel's social thought." Levine explicates Simmel's dualism as "the assumption . . . that the subsistence of any aspect of human life depends on the coexistence of diametrically opposed elements." My own usage of the comparable term "duality" is specified with respect to Equations 3 and 4 below.2 THE BASIC CONCEPTION Consider a set of individuals and a set of groups such that the value of a tie between any two individuals is defined as the number of groups of which they both are members. The value of a tie between any two groups is de* For their criticism and encouragement, I am indebted to Harrison White, Gregory Heil, Francois Lorrain, and Scott Boorman. For seminars which first introduced me to Simmel's thought, I am indebted to Kurt H. Wolff. Thanks are due Professor White for support through NSF Grant GS-2689. 1 Simmel (1955) entitled one of his essays "The Intersection of Social Circles," but Reinhard Bendix changed the title in translation because "a literal translation of this phrase . . . is almost meaningless . . . Simmel often plays with geometric analogies; it has seemed advisable to me to minimize this play with words ." (Simmel, 1955:125). For an assertion that Simmel's original title is not at all inappropriate, see Walter's essay (1959). For a more complete explication of the "dualism" inherent in Simmel's thought, see the essays by D. Levine, Lipman, and Tenbruck in Wolff (1959). A similar metaphor was put forward in America by Charles H. Cooley (1902:148), who wrote that "A man may be regarded as the point of intersection of an indefinite number of circles representing social groups, having as many arcs passing through him as there are groups." Much later, Sorokin (1947:345) observed that "the individual has as many social egos as there are different social groups and strata with which he is connected." On the "much neglected" development of the concept of "social circle" since Simmel's writings, see Kadushin (1966). 2The "directional duality principle" enunciated by Harary et al. (1965) is to be distinguished from my conception. The former principle consists in reversing the directionality of lines in a graph; in the method of this paper, the lines in one graph are transformed into the points of its dual graph, and vice versa.