Balance Theory with Incomplete Awareness

In this paper, we reformulate balance theory by allowing actors to possess incomplete awareness of the evaluations held by other actors, and by adopting balance closure (modified to allow incomplete awareness) as an equilibrium concept. Our treatment highlights psychological mechanisms, maintains a clear distinction between actors and objects, emphasizes the effects of self-awareness and self-evaluations of actors, and permits actors to hold ambivalent (simultaneously positive and negative) evaluations. Our analysis extends previous results linking the imbalance of a signed graph to ambivalence in its balance closure and reveals that an actor's “indirect awareness” of imbalance is necessary but not sufficient for that actor's ambivalence in the balance closure.