Group relations, resilience and the I Ching

Abstract

We evaluate the robustness and adaptivity of social groups with heterogeneous agents that are characterized by their binary state, their ability to change this state, their status and their preferred relations to other agents. To define group structures, we operationalize the hexagrams of the \emph{I Ching}. The relations and properties of agents are used to quantify their influence according to the social impact theory. From these influence values we derive a weighted stability measure for triads involving three agents, which is based on the weighted balance theory. It allows to quantify the robustness of groups and to propose a novel measure for group resilience which combines robustness and adaptivity. A stochastic approach determines the probabilities to find robust and adaptive groups. The discussion focuses on the generalization of our approach.