A rumor spreading model based on information entropy

Rumor spreading can have a significant impact on people’s lives, distorting scientific facts and influencing political opinions. With technologies that have democratized the production and reproduction of information, the rate at which misinformation can spread has increased significantly, leading many to describe contemporary times as a ‘post-truth era’. Research into rumor spreading has primarily been based on either model of social and biological contagion, or upon models of opinion dynamics. Here we present a comprehensive model that is based on information entropy, which allows for the incorporation of considerations like the role of memory, conformity effects, differences in the subjective propensity to produce distortions, and variations in the degree of trust that people place in each other. Variations in the degree of trust are controlled by a confidence factor β, while the propensity to produce distortions is controlled by a conservation factor K. Simulations were performed using a Barabási–Albert (BA) scale-free network seeded with a single piece of information. The influence of β and K upon the temporal evolution of the system was subsequently analyzed regarding average information entropy, opinion fragmentation, and the range of rumor spread. These results can aid in decision-making to limit the spread of rumors.

[1]  Peter Sheridan Dodds,et al.  Universal behavior in a generalized model of contagion. , 2004, Physical review letters.

[2]  Long Wang,et al.  Coevolutionary dynamics of opinions and networks: from diversity to uniformity. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[3]  Katarzyna Sznajd-Weron,et al.  Opinion evolution in closed community , 2000, cond-mat/0101130.

[4]  Yamir Moreno,et al.  Dynamics of rumor spreading in complex networks. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[5]  Serge Galam,et al.  Modelling rumors: the no plane Pentagon French hoax case , 2002, cond-mat/0211571.

[6]  Duncan J. Watts,et al.  Collective dynamics of ‘small-world’ networks , 1998, Nature.

[7]  R. Selten.  Reexamination of the perfectness concept for equilibrium points in extensive games , 1975, Classics in Game Theory.

[8]  Vito Latora,et al.  OPINION FORMATION MODELS BASED ON GAME THEORY , 2006 .

[9]  Jingjing Cheng,et al.  SIHR rumor spreading model in social networks , 2012 .

[10]  Albert-László Barabási,et al.  Internet: Diameter of the World-Wide Web , 1999, Nature.

[11]  Werner J. Severin,et al.  Communication Theories: Origins, Methods and Uses in the Mass Media , 1991 .

[12]  Damián H. Zanette,et al.  Opinion spreading and agent segregation on evolving networks , 2006 .

[13]  Dietrich Stauffer,et al.  GENERALIZATION TO SQUARE LATTICE OF SZNAJD SOCIOPHYSICS MODEL , 2000 .

[14]  Jeffrey C. Carver,et al.  Building reputation in StackOverflow: An empirical investigation , 2013, 2013 10th Working Conference on Mining Software Repositories (MSR).

[15]  D. Stauffer,et al.  Election results and the Sznajd model on Barabasi network , 2001, cond-mat/0111147.

[16]  Duanbing Chen,et al.  The small world yields the most effective information spreading , 2011, ArXiv.

[17]  S. Redner,et al.  Voter model on heterogeneous graphs. , 2004, Physical review letters.

[18]  D. Stau,et al.  Election results and the Sznajd model on Barabasi network , 2002 .

[19]  Martin T. Dove.  Structure and Dynamics , 2003 .

[20]  M. Kosfeld.  Rumours and Markets , 2005 .

[21]  Ahmed S. Elgazzar,et al.  APPLICATION OF THE SZNAJD SOCIOPHYSICS MODEL TO SMALL-WORLD NETWORKS , 2001 .

[22]  B. Guerin,et al.  Analyzing Rumors, Gossip, and Urban Legends Through Their Conversational Properties , 2006 .

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

[24]  A. Coughlan,et al.  An Empirical Investigation * , 2002 .

[25]  Robbert van Renesse,et al.  The power of epidemics: robust communication for large-scale distributed systems , 2003, CCRV.

[26]  André C R Martins,et al.  Mobility and social network effects on extremist opinions. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[27]  Yamir Moreno,et al.  Theory of Rumour Spreading in Complex Social Networks , 2007, ArXiv.

[28]  Scott Shenker,et al.  Epidemic algorithms for replicated database maintenance , 1988, OPSR.

[29]  Andre C. R. Martins,et al.  CONTINUOUS OPINIONS AND DISCRETE ACTIONS IN OPINION DYNAMICS PROBLEMS , 2007, 0711.1199.

[30]  Shilpa Chakravartula,et al.  Complex Networks: Structure and Dynamics , 2014 .

[31]  P. Van Mieghem,et al.  Epidemics in networks with nodal self-infection and the epidemic threshold. , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[32]  Matthew Richardson,et al.  Mining knowledge-sharing sites for viral marketing , 2002, KDD.

[33]  S Redner,et al.  Majority rule dynamics in finite dimensions. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[34]  Wanlin Xie,et al.  A rumor spreading model with variable forgetting rate , 2013 .

[35]  Herbert W. Hethcote,et al.  The Mathematics of Infectious Diseases , 2000, SIAM Rev..

[36]  Allan J. Kimmel.  Rumors and Rumor Control : A Manager's Guide to Understanding and Combatting Rumors , 2004 .