Effect of Stubborn Agents on Bounded Confidence Opinion Dynamic systems: Unanimity in Presence of Stubborn Agents

In this paper, various bounded confidence opinion dynamic algorithms are examined to illustrate the effect of a stubborn minority groups on opinion dynamics. A notion of variable opinion stubborn agent is defined and it is shown that stubborn minorities are able to fully control the opinions of a Hegselmann-Krause opinion dynamic system through deliberate slow variation in the opinions of stubborn agents. Furthermore, an upper bound for the change rate of stubborn agents to preserve connectivity and control other flexible agents is given. Moreover, a method based on population and growing confidence bound is presented to achieve both unanimity and stubborn opinion rejection. To support the proposed method simulation results are provided.