From Social Power to Social Importance

In this paper we introduce a method to measure the social importance of an agent in a multiagent system, using a directed graph representing dependencies among agents to achieve their goals, so-called dependence graphs pioneered by Castelfranchi, Conte and Sichman. Our measure is derived from van den Brink and Gilles' β-measure to rank agents, using a directed graph representing an abstract dominance relation among agents. In particular, we show how to define power structures and dependence networks from the goals and skills of individual agents, and how to adapt the β-measure for such dependence networks based on their topological properties. Moreover, we show that our notion of social importance can be given an intuitive meaning: it measures the discontent of the other agents in case the agent would leave the society.