Opinion evolution in time-varying social influence networks with prejudiced agents

Investigation of social influence dynamics requires mathematical models that are "simple" enough to admit rigorous analysis, and yet sufficiently "rich" to capture salient features of social groups. Thus, the mechanism of iterative opinion pooling from (DeGroot, 1974), which can explain the generation of consensus, was elaborated in (Friedkin and Johnsen, 1999) to take into account individuals' ongoing attachments to their initial opinions, or prejudices. The "anchorage" of individuals to their prejudices may disable reaching consensus and cause disagreement in a social influence network. Further elaboration of this model may be achieved by relaxing its restrictive assumption of a time-invariant influence network. During opinion dynamics on an issue, arcs of interpersonal influence may be added or subtracted from the network, and the influence weights assigned by an individual to his/her neighbors may alter. In this paper, we establish new important properties of the (Friedkin and Johnsen, 1999) opinion formation model, and also examine its extension to time-varying social influence networks.

[1]  Karl Henrik Johansson,et al.  Structural Balance and Opinion Separation in Trust–Mistrust Social Networks , 2016, IEEE Transactions on Control of Network Systems.

[2]  F. R. Gantmakher.  The Theory of Matrices , 1984 .

[3]  Noah E. Friedkin,et al.  Two steps to obfuscation , 2014, Soc. Networks.

[4]  Claudio Altafini,et al.  Consensus Problems on Networks With Antagonistic Interactions , 2013, IEEE Transactions on Automatic Control.

[5]  Károly Takács,et al.  Discrepancy and Disliking Do Not Induce Negative Opinion Shifts , 2016, PloS one.

[6]  E. David,et al.  Networks, Crowds, and Markets: Reasoning about a Highly Connected World , 2010 .

[7]  Roberto Tempo,et al.  Novel Multidimensional Models of Opinion Dynamics in Social Networks , 2015, IEEE Transactions on Automatic Control.

[8]  Chiara Ravazzi,et al.  Distributed randomized algorithms for opinion formation, centrality computation and power systems estimation: A tutorial overview , 2015, Eur. J. Control.

[9]  Charles R. Johnson,et al.  Matrix analysis , 1985, Statistical Inference for Engineers and Data Scientists.

[10]  S. Fortunato,et al.  Statistical physics of social dynamics , 2007, 0710.3256.

[11]  R. Srikant,et al.  Opinion dynamics in social networks with stubborn agents: Equilibrium and convergence rate , 2014, Autom..

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

[13]  Francesco Bullo,et al.  A Theory of the Evolution of Social Power: Natural Trajectories of Interpersonal Influence Systems along Issue Sequences , 2016 .

[14]  Chiara Ravazzi,et al.  Gossips and Prejudices: Ergodic Randomized Dynamics in Social Networks , 2013, ArXiv.

[15]  Hai Lin,et al.  Stability and Stabilizability of Switched Linear Systems: A Survey of Recent Results , 2009, IEEE Transactions on Automatic Control.

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

[17]  Peter Lancaster,et al.  The theory of matrices , 1969 .

[18]  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.

[19]  Chris Arney,et al.  Networks, Crowds, and Markets: Reasoning about a Highly Connected World (Easley, D. and Kleinberg, J.; 2010) [Book Review] , 2013, IEEE Technology and Society Magazine.

[20]  Yongcan Cao,et al.  Distributed Coordination of Multi-agent Networks , 2011 .

[21]  Ming Cao,et al.  Clustering in diffusively coupled networks , 2011, Autom..

[22]  Roberto Tempo,et al.  Network science on belief system dynamics under logic constraints , 2016, Science.

[23]  Francesco Bullo,et al.  Opinion Dynamics and the Evolution of Social Power in Influence Networks , 2015, SIAM Rev..

[24]  John Scott.  What is social network analysis , 2010 .

[25]  Carl D. Meyer,et al.  Matrix Analysis and Applied Linear Algebra , 2000 .

[26]  Mark E. J. Newman,et al.  The Structure and Function of Complex Networks , 2003, SIAM Rev..

[27]  M. Degroot.  Reaching a Consensus , 1974 .

[28]  Chiara Ravazzi,et al.  Ergodic Randomized Algorithms and Dynamics Over Networks , 2013, IEEE Transactions on Control of Network Systems.

[29]  Zhi Xu,et al.  Distributed evaluation and convergence of self-appraisals in social networks , 2015, 2015 54th IEEE Conference on Decision and Control (CDC).

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

[31]  Jon M. Kleinberg,et al.  How Bad is Forming Your Own Opinion? , 2011, 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science.

[32]  Alexey S. Matveev,et al.  Opinion Dynamics in Social Networks With Hostile Camps: Consensus vs. Polarization , 2015, IEEE Transactions on Automatic Control.

[33]  Zhi Xu,et al.  Distributed Evaluation and Convergence of Self-Appraisals in Social Networks , 2017, IEEE Trans. Autom. Control..

[34]  Ming Cao,et al.  Pagerank and opinion dynamics: missing links and extensions , 2016, 2016 IEEE Conference on Norbert Wiener in the 21st Century (21CW).

[35]  Tom A. B. Snijders,et al.  Social Network Analysis , 2011, International Encyclopedia of Statistical Science.

[36]  Noah E. Friedkin.  Social Influence Network Theory , 2006 .

[37]  H. Kowarzyk.  Structure and Function. , 1910, Nature.

[38]  Randal W. Beard,et al.  Distributed Consensus in Multi-vehicle Cooperative Control - Theory and Applications , 2007, Communications and Control Engineering.

[39]  J.N. Tsitsiklis,et al.  Convergence in Multiagent Coordination, Consensus, and Flocking , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[40]  M. Macy,et al.  Small Worlds and Cultural Polarization , 2011 .

[41]  J. Kleinberg,et al.  Networks, Crowds, and Markets , 2010 .

[42]  G. Weisbuch,et al.  Persuasion dynamics , 2004, cond-mat/0410200.