Inertial Hegselmann-Krause Systems

We derive an energy bound for inertial Hegselmann-Krause (HK) systems, which we define as a variant of the classic HK model in which the agents can change their weights arbitrarily at each step. We use the bound to prove the convergence of HK systems with closed-minded agents, which settles a conjecture of long standing. This paper also introduces anchored HK systems and show their equivalence to the symmetric heterogeneous model

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

Modeling limited attention in opinion dynamics by topological interactions

This work explores models of opinion dynamics with opinion-dependent connectivity. Our starting point is that individuals have lim-ited capabilities to engage in interactions with their peers. Motivated bythis observation, we propose a continuous-time opinion dynamics modelsuch that interactions take place with a limited number of peers: we re-fer to these interactions astopological, as opposed tometricinteractionsthat are postulated in classical bounded-confidence models. We observethat topological interactions produce equilibria that arevery robust todisruption

Modeling limited attention in opinion dynamics by topological interactions

This work explores models of opinion dynamics with opinion-dependent connectivity. Our starting point is that individuals have limited capabilities to engage in interactions with their peers. Motivated by this observation, we propose a continuous-time opinion dynamics model such that interactions take place with a limited number of peers: we refer to these interactions as topological, as opposed to metric interactions that are postulated in classical bounded-confidence models. We observe that topological interactions produce equilibria that are very robust to perturbations.Comment: To be presented at NETGCOOP 2020; revised version including simulation