  We study a model of opinion dynamics introduced by Krause: each agent has an
opinion represented by a real number, and updates its opinion by averaging all
agent opinions that differ from its own by less than 1. We give a new proof of
convergence into clusters of agents, with all agents in the same cluster
holding the same opinion. We then introduce a particular notion of equilibrium
stability and provide lower bounds on the inter-cluster distances at a stable
equilibrium. To better understand the behavior of the system when the number of
agents is large, we also introduce and study a variant involving a continuum of
agents, obtaining partial convergence results and lower bounds on inter-cluster
distances, under some mild assumptions.
