October  2016, 1(4): 279-298. doi: 10.3934/bdia.2016011

Analyzing opinion dynamics in online social networks

Cheriton School of Computer Science, University of Waterloo, Waterloo, Ontario, Canada

* Corresponding author: Alan Tsang

Revised  January 2017 Published  April 2017

In this paper, we examine the challenge of performing analyses of opinion dynamics in online social networks. We present a model for studying the influence exerted by peers within the network, emphasizing the role that skepticism can play with respect to establishing consensus of opinion. From here, we focus on some key extensions to the model, with respect to the nature of peers (their familiarity relationships, their empathy) and the presence of peers with particular profiles, as well as with specific clustering of peer relationships. Specifically, we show that the influence of trusted confidants on individuals behaves in a predictable fashion; moreover, we show that the underlying model is robust to individual variations in empathy within the population. These empirical results provide important insights to those seeking to examine and analyze patterns of influence within social networks.

Citation: Robin Cohen, Alan Tsang, Krishna Vaidyanathan, Haotian Zhang. Analyzing opinion dynamics in online social networks. Big Data & Information Analytics, 2016, 1 (4) : 279-298. doi: 10.3934/bdia.2016011
References:
[1]

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Y. -S. Cho, G. V. Steeg and A. Galstyan, Co-evolution of selection and influence in social networks, arXiv: 1106. 2788. Google Scholar

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A. DasS. Gollapudi and K. Munagala, Modeling opinion dynamics in social networks, in Proceedings of the 7th ACM international conference on Web search and data mining, ACM,, (2014), 403-412.  doi: 10.1145/2556195.2559896.  Google Scholar

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M.H. DeGroot, Reaching a consensus, Journal of the American Statistical Association, 69 (1974), 118-121.  doi: 10.1080/01621459.1974.10480137.  Google Scholar

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H. FangJ. Zhang and N.M. Thalmann, A trust model stemmed from the diffusion theory for opinion evaluation, in Proceedings of the 2013 international conference on Autonomous agents and multi-agent systems, International Foundation for Autonomous Agents and Multiagent Systems, (2013), 805-812.   Google Scholar

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R. Hegselmann and U. Krause etal. , Opinion dynamics and bounded confidence models, analysis, and simulation, Journal of Artificial Societies and Social Simulation, 5. Google Scholar

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H.U. KataokaN. KoideK. OchiM. Hojat and J.S. Gonnella, Measurement of empathy among japanese medical students: Psychometrics and score differences by gender and level of medical education, Academic Medicine, 84 (2009), 1192-1197.  doi: 10.1097/ACM.0b013e3181b180d4.  Google Scholar

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M. McPhersonL. Smith-Lovin and J.M. Cook, Birds of a feather: Homophily in social networks, Annual Review of Sociology, 27 (2001), 415-444.  doi: 10.1146/annurev.soc.27.1.415.  Google Scholar

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L. Muchnik, S. Pei, L. C. Parra, S. D. Reis, J. S. AndradeJr, S. Havlin and H. A. Makse, Origins of power-law degree distribution in the heterogeneity of human activity in social networks, Scientific reports, 3. Google Scholar

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H. ParunakT.C. BeldingR. Hilscher and S. Brueckner, Modeling and managing collective cognitive convergence, in Proceedings of the 7th international joint conference on Autonomous agents and multiagent systems, International Foundation for Autonomous Agents and Multiagent Systems, 3 (2008), 1505-1508.   Google Scholar

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O. PryymakA. Rogers and N.R. Jennings, Efficient opinion sharing in large decentralised teams, in Proceedings of the 11th International Conference on Autonomous Agents and Multiagent Systems-Volume 1, International Foundation for Autonomous Agents and Multiagent Systems, (2012), 543-550.   Google Scholar

[14]

M.-S. RohB.-J. HahmD.H. Lee and D.H. Suh, Evaluation of empathy among korean medical students: A cross-sectional study using the korean version of the jefferson scale of physician empathy, Teaching and Learning in Medicine, 22 (2010), 167-171.   Google Scholar

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R. Srinivasan, Lecture notes for topics in complex networks, 2013, URL https://www.ma.utexas.edu/users/rav/ComplexNetworks/ComplexNetworks.Lecture12.Notes.pdf. Google Scholar

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S. SwarupA. Apolloni and Z. Fagyal, A model of norm emergence and innovation in language change, in The 10th International Conference on Autonomous Agents and Multiagent Systems-Volume 2, International Foundation for Autonomous Agents and Multiagent Systems, (2011), 693-700.   Google Scholar

[17]

A. Tsang and K. Larson, Opinion dynamics of skeptical agents, in Proceedings of the 2014 international conference on Autonomous agents and multi-agent systems, International Foundation for Autonomous Agents and Multiagent Systems, (2014), 277-284.   Google Scholar

[18]

L.H. WongP. Pattison and G. Robins, A spatial model for social networks, Physica A: Statistical Mechanics and its Applications, 360 (2006), 99-120.   Google Scholar

show all references

References:
[1]

H. Bless, K. Fiedler and F. Strack, Social Cognition: How Individuals Construct Social Reality, Psychology Press, 2004. Google Scholar

[2]

Y. -S. Cho, G. V. Steeg and A. Galstyan, Co-evolution of selection and influence in social networks, arXiv: 1106. 2788. Google Scholar

[3]

A. DasS. Gollapudi and K. Munagala, Modeling opinion dynamics in social networks, in Proceedings of the 7th ACM international conference on Web search and data mining, ACM,, (2014), 403-412.  doi: 10.1145/2556195.2559896.  Google Scholar

[4]

G. Deffuant, Comparing extremism propagation patterns in continuous opinion models, Journal of Artificial Societies and Social Simulation, 9. Google Scholar

[5]

M.H. DeGroot, Reaching a consensus, Journal of the American Statistical Association, 69 (1974), 118-121.  doi: 10.1080/01621459.1974.10480137.  Google Scholar

[6]

H. FangJ. Zhang and N.M. Thalmann, A trust model stemmed from the diffusion theory for opinion evaluation, in Proceedings of the 2013 international conference on Autonomous agents and multi-agent systems, International Foundation for Autonomous Agents and Multiagent Systems, (2013), 805-812.   Google Scholar

[7]

R. Hegselmann and U. Krause etal. , Opinion dynamics and bounded confidence models, analysis, and simulation, Journal of Artificial Societies and Social Simulation, 5. Google Scholar

[8]

H.U. KataokaN. KoideK. OchiM. Hojat and J.S. Gonnella, Measurement of empathy among japanese medical students: Psychometrics and score differences by gender and level of medical education, Academic Medicine, 84 (2009), 1192-1197.  doi: 10.1097/ACM.0b013e3181b180d4.  Google Scholar

[9]

Z. Kunda, The case for motivated reasoning, Psychological Bulletin, 108 (1990), 480-498.  doi: 10.1037/0033-2909.108.3.480.  Google Scholar

[10]

M. McPhersonL. Smith-Lovin and J.M. Cook, Birds of a feather: Homophily in social networks, Annual Review of Sociology, 27 (2001), 415-444.  doi: 10.1146/annurev.soc.27.1.415.  Google Scholar

[11]

L. Muchnik, S. Pei, L. C. Parra, S. D. Reis, J. S. AndradeJr, S. Havlin and H. A. Makse, Origins of power-law degree distribution in the heterogeneity of human activity in social networks, Scientific reports, 3. Google Scholar

[12]

H. ParunakT.C. BeldingR. Hilscher and S. Brueckner, Modeling and managing collective cognitive convergence, in Proceedings of the 7th international joint conference on Autonomous agents and multiagent systems, International Foundation for Autonomous Agents and Multiagent Systems, 3 (2008), 1505-1508.   Google Scholar

[13]

O. PryymakA. Rogers and N.R. Jennings, Efficient opinion sharing in large decentralised teams, in Proceedings of the 11th International Conference on Autonomous Agents and Multiagent Systems-Volume 1, International Foundation for Autonomous Agents and Multiagent Systems, (2012), 543-550.   Google Scholar

[14]

M.-S. RohB.-J. HahmD.H. Lee and D.H. Suh, Evaluation of empathy among korean medical students: A cross-sectional study using the korean version of the jefferson scale of physician empathy, Teaching and Learning in Medicine, 22 (2010), 167-171.   Google Scholar

[15]

R. Srinivasan, Lecture notes for topics in complex networks, 2013, URL https://www.ma.utexas.edu/users/rav/ComplexNetworks/ComplexNetworks.Lecture12.Notes.pdf. Google Scholar

[16]

S. SwarupA. Apolloni and Z. Fagyal, A model of norm emergence and innovation in language change, in The 10th International Conference on Autonomous Agents and Multiagent Systems-Volume 2, International Foundation for Autonomous Agents and Multiagent Systems, (2011), 693-700.   Google Scholar

[17]

A. Tsang and K. Larson, Opinion dynamics of skeptical agents, in Proceedings of the 2014 international conference on Autonomous agents and multi-agent systems, International Foundation for Autonomous Agents and Multiagent Systems, (2014), 277-284.   Google Scholar

[18]

L.H. WongP. Pattison and G. Robins, A spatial model for social networks, Physica A: Statistical Mechanics and its Applications, 360 (2006), 99-120.   Google Scholar

Figure 1.  In this caveman graph, the nodes of cliques which are connected to other cliques correspond to users who are part of different communities
Figure 2.  40 nodes Erdös Rényi random graph with homophily. The color of node stands for initial opinion, with progression from white (0) to orange (1)
Figure 3.  Evolution of opinions in moderates, on a modified ERgraph with homophily, with partially polarized initial opinions
Figure 4.  The gap between average opinion difference between agents and confidants with average difference between agents and acquaintances
Figure 5.  The average polarization of moderates when exposed to 10% 1-extremists and 10% 0-extremists without curmudgeons. The graph on the left is an Erdos Reyni graph without homophily (95% C.Ⅰ. within ±0:08) while the graph on the right is an Erdos Reyni graph with homophily (95% C.Ⅰ. within ±0:07). Both were averaged by 75 trials
Figure 6.  The average polarization of moderates when exposed to 10% 1-extremists and 10% 0-extremists without curmudgeons. The graph is a Barabasi-Albert graph (95% C.Ⅰ. within ±0:08), averaged by 25 trials
Figure 7.  The average final opinion of moderates when exposed to 10% 1-extremists without curmudgeons. The graph on the left is a graph on the Erdos Reyni graph without homophily (95% C.Ⅰ. within ±0:11) while the right is an Erdos Reyni graph with homophily (95% C.Ⅰ. within ±0:11). Both were averaged by 25 trials
Figure 8.  The average final opinion of moderates when exposed to 10% 1-extremists without curmudgeons. The graph is a BarabasiAlbert graph (95% C.Ⅰ. within ±0:10), averaged by 25 trials
Figure 9.  The average polarization of moderates when exposed to 10% 1-extremists and 10% 0-extremists with 10% curmudgeons. The graph on the left is an Erdos-Reyni graph without homophily (95% C.Ⅰ. within ±0:08) while the right is with homophily (95% C.Ⅰ. within ±0:08). Both were averaged by 25 trials
Figure 10.  The average polarization of moderates when exposed to 10% 1-extremists and 10% 0-extremists with 20% curmudgeons. The graph on the left is an Erdos-Reyni graph without homophily (95% C.Ⅰ. within ±0:08) while the right is with homophily (95% C.Ⅰ. within ±0:08). Both were averaged by 25 trials
Figure 11.  The average final opinion of moderates when exposed to 10% 1-extremists with 10% curmudgeons. The graph on the left is an Erdos-Reyni graph without homophily (95% C.Ⅰ. within ±0:10) while the right is with homophily (95% C.Ⅰ. within ±0:11). Both were averaged by 25 trials
Figure 12.  The average final opinion of moderates when exposed to 10% 1-extremists with 20% curmudgeons. The graph on the left is an Erdos-Reyni graph without homophily (95% C.Ⅰ. within ±0:10) while the right is with homophily (95% C.Ⅰ. within ±0:11). Both were averaged by 25 trials
Figure 13.  The average polarization of moderates when exposed to 10% 1-extremists and 10% 0-extremists for Barabasi-Albert graphs. The graph on the left has 10% curmudgeons (95% C.Ⅰ. within ±0:08) while the right has 20% curmudgeons (95% C.Ⅰ. within ±0:08). Both were averaged by 25 trials
Figure 14.  The average final opinion of moderates when exposed to 10% 1-extremists for Barabasi-Albert graphs. The graph on the left has 10% curmudgeons (95% C.Ⅰ. within ±0:11) while the right has 20% curmudgeons (95% C.Ⅰ. within ±0:12). Both were averaged by 25 trials
Figure 15.  The average polarization of moderates when exposed to 10% 1-extremists and 10% 0-extremists for Barabasi-Albert graph without its empathy being varied and without curmudgeons. It has a 95% C.Ⅰ. within ±0:08, averaged by 25 trials
Figure 16.  The average polarization of moderates when exposed to 10% 1-extremists and 10% 0-extremists for an Erdos-Reyni graph without its empathy being varied and without curmudgeons. It has a 95% C.Ⅰ. within ±0:09
Figure 17.  The average polarization of moderates when exposed to 10% 1-extremists and 10% 0-extremists for an Erdos-Reyni graph without its empathy being varied and without curmudgeons. It has a 95% C.Ⅰ. within ±0:09
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