Open Access Open Access  Restricted Access Subscription Access

A Dynamical Model of Growth of Membership to an Opinion


Affiliations
1 Institute of Frontier Science and Applications, Bengaluru 560 037, India
2 CSIR National Institute of Science, Technology and Development Studies, Dr K.S. Krishnan Marg, New Delhi 110 012, India
 

Many social processes, from elections to terrorism, depend on growth of memberships to opinions. In a generic sense, an opinion is a proposition that for an individual has financial, cultural and emotional impli-cations. The individual responses in turn create a ‘social response’ which influences the individual response resulting in a dynamical system with two-way feed-backs. We consider a set of deterministic dynamical equations that describe individual response to a class of prescribed opinions. The time-dependent opinion dynamics model exhibits nearly complete acceptance to nearly complete rejection with complex evolution, providing the framework for a mechanistic descrip-tion of opinion formation.

Keywords

Dynamic Model, Growth of Membership, Opinion Dynamics, Social Engineering.
User
Notifications
Font Size

  • Jalili, M., Social power and opinion formation in complex networks. Phys. A, 2013, 392(4), 959–966.
  • Hegselmann, R. and Flache, A., Understanding complex social dynamics – a plea for cellular automata based modelling. J. Art. Soci. Soc. Simul., 1998, 1.
  • Li, P. P. and Hui, P. M., Dynamics of opinion formation in hierar-chical social networks: networks structure and initial bias. Eur. Phys. J.B, 2008, 61, 371–376.
  • Toral R. and Tessone, C. J., Finite size effects in the dynamics of opinion formation. Commun. Comput. Phys., 2007, 2, 177–195.
  • Wu, F. and Huberman, B., Social structure and opinion formation. Comput. Econ., 2004, 0407002.
  • Moussaid, M., Kammer, J. E., Analytis, P. P. and Neth, H., Social influence and the collective dynamics of opinion formation. PLoS ONE, 2013, 8(11), e78433.
  • Krause, U., A discrete nonlinear and non-autonomous model of consensus formation. In Communications in Difference Equations (eds Flaydi, S. et al.), Gordon and Breach Publication, Amster-dam, 2000, pp. 227–236.
  • Shang, Y., Consensus formation of two-level opinion dynamics. Acta Math. Sci., 2014, 34(4), 1029–1040.
  • Takao, F., A simple model of consensus formation. Okayama Econ. Rev., 1999, 31, 95–100.
  • Galam, S., The dynamics of minority opinions in democratic debate. Phys. A, 2004, 336, 56–62.
  • Laguna, M. F., Abramson, G. and Zanette, D., Minorities in a model for opinion formation. Complexity, 2004, 9(4), 31–36.
  • Mogilner, A., Edelstein-Keshet, L., Bent, L. and Spiros, A., Mutual interactions, potentials, and individual distance in a social aggre-gation. J. Math. Biol., 2003, 47, 353–389.
  • Mobilia, M. and Redner, S., Majority versus minority dynamics: phase transition in an interacting two-state spin system. Phys. Rev. E, 2003, 68(4), 046106.
  • Boccara, N., Models of opinion formation: influence of opinion leaders. Int. J. Mod. Phys. C, 2008, 19, 93–109.
  • Crespi, B. J., The evolution of social behaviour in micro-organisms. Trends Ecol. Evol., 2001, 16(4), 178–183.
  • Wollman, N. P. et al., The dynamics of animal social networks: analytical, conceptual, and theoretical advances. Behav. Ecol., 2013, 25(2), 242–255.
  • Ghosh, R. and Lerman, K., The impact of network flows on com-munity formation in models of opinion dynamics. J. Math. Soc., 2015, 39(2), 109–124.
  • Hoylst, J. A., Kacperski, K. and Schweitzer, F., Social impact models of opinion dynamics. Ann. Rev. Comput. Phys., 2001, IX, 253–273.
  • Antal, T., Krapivsky, P. L. and Redner, S., Dynamics of social balance on networks. Phys. Rev. E, 2005, 72, 036121.
  • Altafini, C., Dynamics of opinion forming in structurally balanced social networks. PLoS ONE, 2012, 7(6), e38135.
  • Gueron, S., Levin, S. A. and Rubenstein, D. I., The dynamics of herds: from individuals to aggregations. J. Theor. Biol., 1996, 182(1), 85–98.
  • Fieldhouse, E., Shryane, N. and Pickles, A., Strategic voting and constituency context: modelling party preference and vote in multiparty elections. Polit. Geogr., 2007, 26(2), 159–178.
  • Jiao, Y., Syau, Y. R. and Lee, E. S., Fuzzy adaptive network in presidential elections. Math. Comput. Model., 2006, 43, 244–253.
  • Berger, R. L., A necessary and sufficient condition for reaching a consensus using DeGischolar_main’s method. J. Am. Stat. Assoc., 1981, 76(374), 415–418.
  • Kosse, K., Group size and societal complexity: thresholds in the long-term memory. J. Anthropol. Archaeol., 1990, 9, 275–303.
  • Farine, D. R. et al., The role of social and ecological processes in structuring animal populations: a case study from automated track-ing of wild birds. R. Soc. Open Sci., 2015, 2, 150057.
  • Belenky, A. S. and King, D. C., A mathematical model for esti-mating the potential margin of state undecided voters for a candi-date in a US Federal election. Math. Comput. Model., 2007, 45, 585–593.
  • Mishra, A. K., A simple mathematical model for the spread of two political parties. Nonlinear Anal. Model. Control, 2012, 17, 343–354.
  • Farley, J. D., Evolutionary dynamics of the insurgency in Iraq: a mathematical model of the battle for hearts and minds. Stud. Confl. Terror., 2007, 30(11), 947–962.
  • Anderton, C. H. and Carter, J. R., On rational choice theory and the study of terrorism. Def. Peace Econ., 2005, 16, 275–282.
  • Facchetti, G., Iacono, G. and Altafini, C., Computing global struc-tural balance in large-scale signed social networks. Proc. Natl. Acad. Sci., 2011, 108(52), 20953–20958.
  • Latane, B. and Nowak, A., Self-organizing social systems, neces-sary and sufficient conditions for the emergence of clustering, consolidation, and continuing diversity. In Progress in Communi-cation Science: Advances in Persuasion (eds Barnet, G. and Bostner, F.), Norwood, NJ, USA, Ablex Publishing Corporation, 1997, pp. 43–74.
  • Iacono, G. and Altafini, C., Monotonicity, frustration, and ordered response: an analysis of the energy landscape of perturbed large-scale biological networks. BMC Syst. Biol., 2010, 4(1), 83.
  • Weisbuch, G., Deffuant, G. and Amblard, F., Persuasion dynamics. Phys. A, 2005, 353, 555–575.
  • Kawachi, K., Deterministic models for rumor transmission. Non-linear Anal. Real World Appl., 2008, 9, 1989–2028.
  • Hegselmann, R. and Krause, U., Opinion dynamics and bounded confidence: models, analysis, and simulation. JASSS, 2002, 5(3), 1–33.
  • Klir, G. J. and Yuan, B., Fuzzy Sets and Fuzzy Logic; Theory and Applications, Prentice Hall PTR, New Jersey, 1995.
  • Cao, S., Dehmer, M. and Shi, Y., Extremality of degree-based graph entropies. Inf. Sci., 2014, 278, 22–33.
  • Chen, Z., Dehmer, M., Emmert-Streib, F. and Shi, Y., Entropy of weighted graphs with Randi’c weights. Entropy, 2015, 17(6), 3710–3723.
  • Chen, Z., Dehmer, M. and Shi, Y., A note on distance-based graph entropies. Entropy, 2014, 16(10), 5416–5427.
  • Chen, Z., Dehmer, M. and Shi, Y., Bounds for degree-based network entropies. Appl. Math. Comput, 2015, 265, 983–993.
  • Saganowski, S. et al., Predicting community evolution in social networks. Entropy, 2015, 17(5), 3053–3096.

Abstract Views: 266

PDF Views: 89




  • A Dynamical Model of Growth of Membership to an Opinion

Abstract Views: 266  |  PDF Views: 89

Authors

Prashant Goswami
Institute of Frontier Science and Applications, Bengaluru 560 037, India
Shivnarayan Nishad
CSIR National Institute of Science, Technology and Development Studies, Dr K.S. Krishnan Marg, New Delhi 110 012, India

Abstract


Many social processes, from elections to terrorism, depend on growth of memberships to opinions. In a generic sense, an opinion is a proposition that for an individual has financial, cultural and emotional impli-cations. The individual responses in turn create a ‘social response’ which influences the individual response resulting in a dynamical system with two-way feed-backs. We consider a set of deterministic dynamical equations that describe individual response to a class of prescribed opinions. The time-dependent opinion dynamics model exhibits nearly complete acceptance to nearly complete rejection with complex evolution, providing the framework for a mechanistic descrip-tion of opinion formation.

Keywords


Dynamic Model, Growth of Membership, Opinion Dynamics, Social Engineering.

References





DOI: https://doi.org/10.18520/cs%2Fv116%2Fi4%2F577-591