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September  2015, 10(3): 477-509. doi: 10.3934/nhm.2015.10.477

Opinion dynamics under the influence of radical groups, charismatic leaders, and other constant signals: A simple unifying model

Rainer Hegselmann 1, and  Ulrich Krause 2,

1. 

Bayreuth University, Universitaetsstrasse 30, 95440 Bayreuth, Germany
2. 

Bremen University, Bibliotheksstrasse 1, 28359 Bremen, Germany

Received  December 2014 Revised  March 2015 Published  July 2015

By a simple extension of the bounded confidence model, it is possible to model the influence of a radical group, or a charismatic leader on the opinion dynamics of `normal' agents that update their opinions under both, the influence of their normal peers, and the additional influence of the radical group or a charismatic leader. From a more abstract point of view, we model the influence of a signal, that is constant, may have different intensities, and is `heard' only by agents with opinions, that are not too far away. For such a dynamic a Constant Signal Theorem is proven. In the model we get a lot of surprising effects. For instance, the more intensive signal may have less effect; more radicals may lead to less radicalization of normal agents. The model is an extremely simple conceptual model. Under some assumptions the whole parameter space can be analyzed. The model inspires new possible explanations, new perspectives for empirical studies, and new ideas for prevention or intervention policies.
Keywords: Opinion dynamics, constant signals., bounded confidence.
Mathematics Subject Classification: Primary: 90B10, 90B18, 91D30, 37N40; Secondary: 15B51, 39A2.
Citation: Rainer Hegselmann, Ulrich Krause. Opinion dynamics under the influence of radical groups, charismatic leaders, and other constant signals: A simple unifying model. Networks & Heterogeneous Media, 2015, 10 (3) : 477-509. doi: 10.3934/nhm.2015.10.477
References:
[1]

D. Acemoglu and A. Ozdaglar, Opinion dynamics and learning in social networks,, Dynamic Games and Applications, 1 (2011), 3.  doi: 10.1007/s13235-010-0004-1.  Google Scholar

[2]

M. Baurmann, G. Betz and R. Cramm, Meinungsdynamiken in fundamentalistischen Gruppen - Erklärungshypothesen auf der Basis von Simulationsmodellen,, Analyse and Kritik, 36 (2014), 61.   Google Scholar

[3]

V. D. Blondel, J. M. Hendrickx and J. N. Tsitsiklis, Continuous-time average-preserving opinion dynamics with opinion-dependent communications,, SIAM Journal on Control and Optimization, 48 (2010), 5214.  doi: 10.1137/090766188.  Google Scholar

[4]

B. Chazelle, The total s-energy of a multiagent system,, SIAM Journal of Control and Optimization, 49 (2011), 1680.  doi: 10.1137/100791671.  Google Scholar

[5]

G. Deffuant, F. Amblard, G. Weisbuch and T. Faure, How can extremism prevail? A study based on the relative agreement interaction model,, Journal of Artificial Societies and Social Simulation, 5 (2002).   Google Scholar

[6]

G. Deffuant, D. Neau, F. Amblard and G. Weisbuch, Mixing beliefs among interacting agents,, Advances in Complex Systems, 3 (2000), 87.  doi: 10.1142/S0219525900000078.  Google Scholar

[7]

M. H. DeGroot, Reaching a consensus,, Journal of the American Statistical Association, 69 (1974), 118.  doi: 10.1080/01621459.1974.10480137.  Google Scholar

[8]

R. Hegselmann, Bounded confidence, radical groups, and charismatic leaders,, in Advances in Computational Social Science and Social Simulation. Proceedings of the Social Simulation Conference 2014 Barcelona, (2014), 217.   Google Scholar

[9]

R. Hegselmann, S. König, S. Kurz, C. Niemann and J. Rambau, Optimal opinion control: The campaign problem,, Journal of Artificial Societies and Social Simulation (JASSS), (2015).  doi: 10.2139/ssrn.2516866.  Google Scholar

[10]

R. Hegselmann and U. Krause, Opinion dynamics and bounded confidence: Models, analysis and simulation,, Journal of Artificial Societies and Social Simulation, 5 (2002).   Google Scholar

[11]

R. Hegselmann and U. Krause, Truth and cognitive division of labour: First steps towards a computer aided social epistemology,, Journal of Artificial Societies and Social Simulation, 9 (2006).   Google Scholar

[12]

S. Huet, G. Deffuant and W. Jager, Rejection mechanism in 2d bounded confidence provides more conformity,, Advances in Complex Systems, 11 (2008), 529.  doi: 10.1142/S0219525908001799.  Google Scholar

[13]

U. Krause, Positive Dynamical Systems in Discrete Time. Theory, Models, and Applications,, De Gruyter, (2015).  doi: 10.1515/9783110365696.  Google Scholar

[14]

S. Kurz and J. Rambau, On the Hegselmann-Krause conjecture in opinion dynamics,, Journal of Difference Equations and Applications, 17 (2011), 859.  doi: 10.1080/10236190903443129.  Google Scholar

[15]

J. Lorenz, Continuous opinion dynamics under bounded confidence: A survey,, International Journal of Modern Physics C, 18 (2007), 1819.  doi: 10.1142/S0129183107011789.  Google Scholar

[16]

N. Oreskes and E. M. Conway, Merchants of Doubt - How a Handful of Scientists Obscured the Truth on Issues from Tobacco Smoke to Global Warming,, Bloomsbury Press, (2010).   Google Scholar

[17]

G. G. Polhill, L. R. Izquierdo and N. M. Gotts, The ghost in the model (and other effects of floating point arithmetic),, Journal of Artificial Societies and Social Simulation, 8 (2005).   Google Scholar

[18]

S. Wongkaew, M. Caponigro and A. Borzí, On the control through leadership of the Hegselmann-Krause opinion formation model,, Mathematical Models and Methods in Applied Sciences, 25 (2015), 565.  doi: 10.1142/S0218202515400060.  Google Scholar

[19]

H. Xia, H. Wang and Z. Xuan, Opinion dynamics: A multidisciplinary review and perspective on future research,, International Journal of Knowledge and Systems Science, 2 (2011), 72.  doi: 10.4018/978-1-4666-3998-0.ch021.  Google Scholar

show all references

References:
[1]

D. Acemoglu and A. Ozdaglar, Opinion dynamics and learning in social networks,, Dynamic Games and Applications, 1 (2011), 3.  doi: 10.1007/s13235-010-0004-1.  Google Scholar

[2]

M. Baurmann, G. Betz and R. Cramm, Meinungsdynamiken in fundamentalistischen Gruppen - Erklärungshypothesen auf der Basis von Simulationsmodellen,, Analyse and Kritik, 36 (2014), 61.   Google Scholar

[3]

V. D. Blondel, J. M. Hendrickx and J. N. Tsitsiklis, Continuous-time average-preserving opinion dynamics with opinion-dependent communications,, SIAM Journal on Control and Optimization, 48 (2010), 5214.  doi: 10.1137/090766188.  Google Scholar

[4]

B. Chazelle, The total s-energy of a multiagent system,, SIAM Journal of Control and Optimization, 49 (2011), 1680.  doi: 10.1137/100791671.  Google Scholar

[5]

G. Deffuant, F. Amblard, G. Weisbuch and T. Faure, How can extremism prevail? A study based on the relative agreement interaction model,, Journal of Artificial Societies and Social Simulation, 5 (2002).   Google Scholar

[6]

G. Deffuant, D. Neau, F. Amblard and G. Weisbuch, Mixing beliefs among interacting agents,, Advances in Complex Systems, 3 (2000), 87.  doi: 10.1142/S0219525900000078.  Google Scholar

[7]

M. H. DeGroot, Reaching a consensus,, Journal of the American Statistical Association, 69 (1974), 118.  doi: 10.1080/01621459.1974.10480137.  Google Scholar

[8]

R. Hegselmann, Bounded confidence, radical groups, and charismatic leaders,, in Advances in Computational Social Science and Social Simulation. Proceedings of the Social Simulation Conference 2014 Barcelona, (2014), 217.   Google Scholar

[9]

R. Hegselmann, S. König, S. Kurz, C. Niemann and J. Rambau, Optimal opinion control: The campaign problem,, Journal of Artificial Societies and Social Simulation (JASSS), (2015).  doi: 10.2139/ssrn.2516866.  Google Scholar

[10]

R. Hegselmann and U. Krause, Opinion dynamics and bounded confidence: Models, analysis and simulation,, Journal of Artificial Societies and Social Simulation, 5 (2002).   Google Scholar

[11]

R. Hegselmann and U. Krause, Truth and cognitive division of labour: First steps towards a computer aided social epistemology,, Journal of Artificial Societies and Social Simulation, 9 (2006).   Google Scholar

[12]

S. Huet, G. Deffuant and W. Jager, Rejection mechanism in 2d bounded confidence provides more conformity,, Advances in Complex Systems, 11 (2008), 529.  doi: 10.1142/S0219525908001799.  Google Scholar

[13]

U. Krause, Positive Dynamical Systems in Discrete Time. Theory, Models, and Applications,, De Gruyter, (2015).  doi: 10.1515/9783110365696.  Google Scholar

[14]

S. Kurz and J. Rambau, On the Hegselmann-Krause conjecture in opinion dynamics,, Journal of Difference Equations and Applications, 17 (2011), 859.  doi: 10.1080/10236190903443129.  Google Scholar

[15]

J. Lorenz, Continuous opinion dynamics under bounded confidence: A survey,, International Journal of Modern Physics C, 18 (2007), 1819.  doi: 10.1142/S0129183107011789.  Google Scholar

[16]

N. Oreskes and E. M. Conway, Merchants of Doubt - How a Handful of Scientists Obscured the Truth on Issues from Tobacco Smoke to Global Warming,, Bloomsbury Press, (2010).   Google Scholar

[17]

G. G. Polhill, L. R. Izquierdo and N. M. Gotts, The ghost in the model (and other effects of floating point arithmetic),, Journal of Artificial Societies and Social Simulation, 8 (2005).   Google Scholar

[18]

S. Wongkaew, M. Caponigro and A. Borzí, On the control through leadership of the Hegselmann-Krause opinion formation model,, Mathematical Models and Methods in Applied Sciences, 25 (2015), 565.  doi: 10.1142/S0218202515400060.  Google Scholar

[19]

H. Xia, H. Wang and Z. Xuan, Opinion dynamics: A multidisciplinary review and perspective on future research,, International Journal of Knowledge and Systems Science, 2 (2011), 72.  doi: 10.4018/978-1-4666-3998-0.ch021.  Google Scholar

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