Abstract
In this work, Krasnoshchekov’s model, which describes the behavior of people in a community under social and informational influences, is generalized to include the case of a system with a sophisticated structure of social interaction. In particular, the situation when an isolated group of people is formed who are not familiar with the rest of the community, which corresponds to a decomposable matrix of social interactions, is studied. The conditions for the solution of the system of equations describing the behavior of such a community to exist and be unique are considered. The problem of finding the relation between Krasnoshchekov’s and De Groot’s models is solved. The way this matrix of social interactions and the social independence of individuals affect the structure of the solution of this system, which describes in particularl how beliefs spread among people, is studied.
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References
G. V. Grachev and I. K. Melnik, Manipulation Person: Organization, Methods and Technologies of Information-Psychological Influence (IF RAN, Moscow, 1999), Vol. 63 [in Russian].
J. C. Turner, Social Influence (Cole Publ., Thomson Brooks, 1991).
D. A. Gubanov, D. A. Novikov, and A. G. Chkhartishvili, Social Networks: Models of Informational Influence, Control and Confrontation (Fizmatlit, Moscow, 2010) [in Russian].
D. A. Gubanov, D. A. Novikov, and A. G. Chkhartishvili, “Models of influence in social networks (review),” Upravl. Bol’sh. Sist., No. 27, 205–281 (2009).
D. A. Gubanov, D. A. Novikov, and A. G. Chkhartishvili, “Informational influence and information control models in social networks,” Autom. Remote Control. 72, 1557–1567 (2011).
A. M. Raigorodskii, Internet Models (Intellekt, Dolgoprudnyi, 2013) [in Russian].
E. Bonson, S. Royo, and M. Ratkai, “Citizens’ engagement on local governments' Facebook sites. An empirical analysis: the impact of different media and content types in Western Europe,” Government Inform. Quart. 32, 52–62 (2015).
K. Peters, Y. Chen, A. M. Kaplan, B. Ognibeni, and K. Pauwels, “Social media metrics–a framework and guidelines for managing social media,” J. Interact. Market. 27, 281–298 (2013).
R. M. Bond et al., “A 61-million-person experiment in social influence and political mobilization,” Nature (London, U.K.) 489, 295–298 (2012).
S. Boulianne, “Social media use and participation: a meta-analysis of current research,” Inform., Commun. Soc. 18, 524–538 (2015).
S. Stieglitz and L. Dang-Xuan, “Social media and political communication: a social media analytics framework,” Social Network Anal. Mining 3, 1277–1291 (2013).
P. Sobkowicz, M. Kaschesky, and G. Bouchard, “Opinion mining in social media: Modeling, simulating, and forecasting political opinions in the web,” Government Inform. Quart. 29, 470–479 (2012).
M. H. de Groot, “Reaching a consensus,” J. Am. Statist. Assoc. 69, 118–121 (1974).
N. E. Friedkin and E. C. Johnsen, “Social influence networks and opinion change,” Adv. Group Processes 16, 1–29 (1999).
P. S. Krasnoshchekov, “The simplest mathematical model of behaviour. Psychology of conformism,” Mat. Model. 10, 76–92 (1998).
S. E. Asch, “Studies of independence and conformity: I. A minority of one against a unanimous majority,” Psychol. Monographs: Gen. Appl. 70, 1 (1956).
D. Kempe, J. Kleinberg, and E. Tardos, “Maximizing the spread of influence through a social network,” in Proceedings of the 9th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining ACM, 2003, pp. 137–146.
D. J. Watts and P. S. Dodds, “Influentials, networks, and public opinion formation,” J. Consumer Res. 34, 441–458 (2007).
F. R. Gantmacher, Matrix Theory (Chelsea, New York, 1959), Vol. 21.
S. A. Ashmanov, Introduction to Mathematical Economics (Nauka, Moscow, 1984) [in Russian].
F. Harary et al., Graph Theory (Addison-Wesley, Reading, MA, 1969).
A. A. Belolipetskii and I. V. Kozitsin, “Dynamic variant of mathematical model of collective behavior,” J. Comput. Syst. Sci. Int. 56, 385–396 (2017).
C. Castellano, S. Fortunato, and V. Loreto, “Statistical physics of social dynamics,” Rev. Mod. Phys. 81, 591 (2009).
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Original Russian Text © I.V. Kozitsin, 2017, published in Matematicheskoe Modelirovanie, 2017, Vol. 29, No. 12, pp. 3–15.
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Kozitsin, I.V. Generalization of Krasnoshchekov’s Model for the Case of a Decomposable Matrix of Social Interactions. Math Models Comput Simul 10, 398–406 (2018). https://doi.org/10.1134/S2070048218040075
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DOI: https://doi.org/10.1134/S2070048218040075