A Consensus Policy for Heterogeneous Opinion Dynamics

A typical emerging behavior in opinion dynamics is the convergence of all agents attitudes to a consensus. In homogeneous networks this situation is a "regression to the mean" of the agents initial conditions. In the presence of heterogeneity more complex behaviors occur. In this paper a strategy for the convergence to a consensus in the bounded confidence Hegselmann-Krause model is proposed. The policy is based on variations of the agents confidence thresholds such that "the richest looks for someone richer and the poorest for someone poorer". Numerical results show the effectiveness of the proposed idea and the effects in the presence of stubborns.

[1]  Haili Liang,et al.  Opinion dynamics in networks with heterogeneous confidence and influence , 2013 .

[2]  D. Kahneman.  Thinking, Fast and Slow , 2011 .

[3]  W. Zheng,et al.  Emergent collective behaviors on coopetition networks , 2014 .

[4]  Francesco Bullo,et al.  Opinion Dynamics in Heterogeneous Networks: Convergence Conjectures and Theorems , 2011, SIAM J. Control. Optim..

[5]  Roberto Tempo,et al.  A Tutorial on Modeling and Analysis of Dynamic Social Networks. Part II , 2018, Annu. Rev. Control..

[6]  Francesco Scafuti,et al.  Heterogeneity induces emergent functional networks for synchronization. , 2015, Physical review. E, Statistical, nonlinear, and soft matter physics.

[7]  Behrouz Touri,et al.  Multi-dimensional Hegselmann-Krause dynamics , 2012, 2012 IEEE 51st IEEE Conference on Decision and Control (CDC).

[8]  Francesco Vasca,et al.  Piecewise quadratic stability of consensus in heterogeneous opinion dynamics , 2016, 2016 European Control Conference (ECC).

[9]  Claudio Altafini,et al.  A bounded confidence model that preserves the signs of the opinions , 2016, 2016 European Control Conference (ECC).

[10]  Zhijun Li,et al.  Opinion dynamics of modified Hegselmann–Krause model in a group-based population with heterogeneous bounded confidence , 2015 .

[11]  Noah E. Friedkin,et al.  The Problem of Social Control and Coordination of Complex Systems in Sociology: A Look at the Community Cleavage Problem , 2015, IEEE Control Systems.

[12]  J. French,et al.  A formal theory of social power. , 1956, Psychological review.

[13]  Xiaoming Hu,et al.  Opinion consensus of modified Hegselmann-Krause models , 2012, CDC.

[14]  Reza Olfati-Saber,et al.  Consensus and Cooperation in Networked Multi-Agent Systems , 2007, Proceedings of the IEEE.

[15]  Bernard Chazelle,et al.  Inertial Hegselmann-Krause Systems , 2015, IEEE Transactions on Automatic Control.

[16]  Jan Lorenz,et al.  A stabilization theorem for dynamics of continuous opinions , 2005, 0708.2981.

[17]  John N. Tsitsiklis,et al.  Continuous-Time Average-Preserving Opinion Dynamics with Opinion-Dependent Communications , 2009, SIAM J. Control. Optim..

[18]  Sébastien Motsch,et al.  Heterophilious Dynamics Enhances Consensus , 2013, SIAM Rev..

[19]  Francesco Vasca,et al.  Consensus Stability in the Hegselmann-Krause Model with Coopetition and Cooperosity , 2017 .

[20]  Rainer Hegselmann,et al.  Opinion dynamics and bounded confidence: models, analysis and simulation , 2002, J. Artif. Soc. Soc. Simul..

[21]  Paolo Frasca,et al.  Continuous and discontinuous opinion dynamics with bounded confidence , 2012 .

[22]  John N. Tsitsiklis,et al.  On Krause's Multi-Agent Consensus Model With State-Dependent Connectivity , 2008, IEEE Transactions on Automatic Control.

[23]  Maria Elena Valcher,et al.  On the consensus and bipartite consensus in high-order multi-agent dynamical systems with antagonistic interactions , 2014, Syst. Control. Lett..

[24]  Ziyang Meng,et al.  Behaviors of networks with antagonistic interactions and switching topologies , 2016, Autom..

[25]  Francesco Vasca,et al.  Coopetition and Cooperosity over Opinion Dynamics , 2016, COMPLEX NETWORKS.