Structural indices for potential participation in groups

Abstract

Earlier publications (O'Brien, Biglan, & Penna, 1972; O'Brien & Harary, 1977) defined the potential participation of an individual in a group in terms of the number of connections from the individual to the task system. In order to have an index of potential participation which gives comparable values across groups and organizations varying in size, it is necessary to provide a formula which gives the maximum possible participation value for an individual in a group with a fixed number of persons, positions and tasks. The present paper derives a number of formulae using the notation of structural role theory (Oeser & Harary, 1962, 1964). Different formulae are associated with restrictions in the properties of informal relationships, as well as the length of sequences in the interpersonal and task graphs. The relationship between the indices of potential participation and sociometric indices is discussed briefly.