Social positions in influence networks

In this article we derive implications about social positions from a formal theory of social influence. The formal theory describes how, in a group of actors with heterogeneous initial opinions, a network of interpersonal influences enters into the formation of actors' settled opinions. We derive the following conclusions about a special form of structural equivalence. If actors are structurally equivalent in the network of interpersonal influences, then any dissimilarity of their initial opinions is reduced by the social influence process. If the social positions of actors are identical, i.e. if they have identical initial opinions and are structurally equivalent in the influence network, then they have identical opinions at equilibrium. If actors are not structurally equivalent in the network of interpersonal influences, then the social influence process does not necessarily reduce dissimilarities of initial opinions. We extend our analysis to consider automorphic equivalence.