Opinion Dynamics Under Heterogenous Bounds of Confidence for the Agents

A group of m agents is to nd a common agreement about a certain issue. An opinion is represented by a real number. We assume that each agent changes his opinion by repeated averaging over the opinions of his agents of condence. An agent i should be an agent of condence for agent j, if the opinion of agent i lies within the condence interval of agent j, which is an interval with the opinion of j in the center. This iterated process is called opinion formation under bounded condence. In this paper we model heterogenity of agents by admitting dierences in the sizes of the condence intervals for each agent. We examine what happens if some of the agents have higher/lower bounds of condence than the other agents. We focus on how the possibility of reaching a consensus among all agents changes through heterogenity. Interestingly there are both, positive and negative eects. Simulations show that the positive eects might be bigger