Resisting Influence: How the Strength of Predispositions to Resist Control Can Change Strategies for Optimal Opinion Control in the Voter Model

In this paper, we investigate influence maximization, or optimal opinion control, in a modified version of the two-state voter dynamics in which a native state and a controlled or influenced state are accounted for. We include agent predispositions to resist influence in the form of a probability q with which agents spontaneously switch back to the native state when in the controlled state. We argue that in contrast to the original voter model, optimal control in this setting depends on q: For low strength of predispositions q, optimal control should focus on hub nodes, but for large q, optimal control can be achieved by focusing on the lowest degree nodes. We investigate this transition between hub and low-degree node control for heterogeneous undirected networks and give analytical and numerical arguments for the existence of two control regimes.

[1]  Vittorio Loreto,et al.  Opinion dynamics: models, extensions and external effects , 2016, Participatory Sensing, Opinions and Collective Awareness.

[2]  Albert-László Barabási,et al.  Statistical mechanics of complex networks , 2001, ArXiv.

[3]  M. Macy,et al.  Complex Contagions and the Weakness of Long Ties1 , 2007, American Journal of Sociology.

[4]  Flávio L. Pinheiro,et al.  When to target hubs? Strategic Diffusion in Complex Networks , 2017, ArXiv.

[5]  M. Mobilia,et al.  Voting and catalytic processes with inhomogeneities. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[6]  Jon M. Kleinberg,et al.  Networks, Crowds, and Markets: Reasoning about a Highly Connected World [Book Review] , 2013, IEEE Technol. Soc. Mag..

[7]  Damon Centola,et al.  The Spread of Behavior in an Online Social Network Experiment , 2010, Science.

[8]  Jon Kleinberg,et al.  Differences in the mechanics of information diffusion across topics: idioms, political hashtags, and complex contagion on twitter , 2011, WWW.

[9]  S. Redner,et al.  Heterogeneous voter models. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[10]  M. Newman,et al.  Mixing patterns in networks. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[11]  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.

[12]  Sidney Redner,et al.  Can partisan voting lead to truth? , 2010, ArXiv.

[13]  Rick Quax,et al.  The diminishing role of hubs in dynamical processes on complex networks , 2011, Journal of The Royal Society Interface.

[14]  M. Mobilia.  Does a single zealot affect an infinite group of voters? , 2003, Physical review letters.

[15]  R. Holley,et al.  Ergodic Theorems for Weakly Interacting Infinite Systems and the Voter Model , 1975 .

[16]  Allan Borodin,et al.  Threshold Models for Competitive Influence in Social Networks , 2010, WINE.

[17]  Mark Newman,et al.  Networks: An Introduction , 2010 .

[18]  Santiago L. Rovere,et al.  Ising-like agent-based technology diffusion model: adoption patterns vs. seeding strategies , 2010, ArXiv.

[19]  Shishir Bharathi,et al.  Competitive Influence Maximization in Social Networks , 2007, WINE.

[20]  Naoki Masuda,et al.  Opinion control in complex networks , 2014, ArXiv.

[21]  S. Redner,et al.  On the role of zealotry in the voter model , 2007 .

[22]  Éva Tardos,et al.  Maximizing the Spread of Influence through a Social Network , 2015, Theory Comput..

[23]  Chen Hongsong,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.

[24]  Mauro Mobilia,et al.  Nonlinear $q$-voter model with inflexible zealots , 2015, Physical review. E, Statistical, nonlinear, and soft matter physics.

[25]  Haibo Hu,et al.  Social networks, mass media and public opinions , 2017 .

[26]  Srinivas Shakkottai,et al.  Influence maximization in social networks: An ising-model-based approach , 2010, 2010 48th Annual Allerton Conference on Communication, Control, and Computing (Allerton).

[27]  Ananthram Swami,et al.  Effect of zealotry in high-dimensional opinion dynamics models. , 2015, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

[29]  Jon Kleinberg,et al.  Maximizing the spread of influence through a social network , 2003, KDD '03.

[30]  Dustin Arendt,et al.  Opinions, influence, and zealotry: a computational study on stubbornness , 2015, Computational and Mathematical Organization Theory.

[31]  S. S. Ravi,et al.  Controlling opinion propagation in online networks , 2013, Comput. Networks.

[32]  Christoph Niemann,et al.  Optimal Opinion Control: The Campaign Problem , 2014, J. Artif. Soc. Soc. Simul..

[33]  Daniel D. Lee,et al.  Maximizing Influence in an Ising Network: A Mean-Field Optimal Solution , 2016, NIPS.

[34]  Martin A. Nowak,et al.  Infectious Disease Modeling of Social Contagion in Networks , 2010, PLoS Comput. Biol..

[35]  Raul Toral,et al.  Zealots in the mean-field noisy voter model. , 2017, Physical review. E.

[36]  P. Clifford,et al.  A model for spatial conflict , 1973 .

[37]  Michael Kearns,et al.  Competitive contagion in networks , 2011, STOC '12.

[38]  Igor M. Sokolov,et al.  Changing Correlations in Networks: Assortativity and Dissortativity , 2005 .

[39]  Spain,et al.  Cascade Dynamics of Complex Propagation , 2005, physics/0504165.

[40]  Mehmet E. Yildiz,et al.  Binary Opinion Dynamics with Stubborn Agents , 2013, TEAC.

[41]  Hernán A. Makse,et al.  Influence maximization in complex networks through optimal percolation , 2015, Nature.