ABSTRACT
I consider the principle of structural balance that is commonly characterized with the aphorisms: “The friend of a friend is a friend, the friend of an enemy is an enemy, the enemy of a friend is an enemy, and the enemy of an enemy is a friend.” I study what patterns of friendship and hostility emerge at the macro-level when actors at the micro-level make friends and enemies in accordance with this principle. Recent studies have drawn attention to configurations that are imbalanced with many triadic relations violating structural balance yet jammed because no change in sentiment in any one relation can accomplish a net reduction in the number of violations of structural balance. The existence of such jammed states suggests that individual behavior consistent with structural balance need not aggregate to system-wide satisfaction of the principle. To investigate this I employ a best-response model of sentiment change on a fixed social network. I show that under a broad set ofmodel conditions only configurations in which all triadic relations satisfy the structural balance principle can emerge. In a close-knit community in which all actors maintain relations with all other actors such a balanced configuration must consist of either one friendship clique or multiple antagonistic groups.
