Uncertain Opinion Evolution with Bounded Confidence Effects in Social Networks

Abstract

When people express their opinions for an issue, they can express both exact opinions and uncertain opinions, such as numerical interval opinions. Moreover, social network is a crucial medium of opinion interaction and evolution. In this paper, uncertain opinion evolution with bounded confidence effects in social networks is investigated by theoretical demonstration and numerical examples analyses, and experiments simulations analyses. Theoretical results show when all the agents are with uncertainty tolerances, then the ratios of agents expressing uncertain opinions are impossible to decrease, even increase, as time increases; while when all the agents are without uncertainty tolerances, then the ratios of agents expressing uncertain opinions are impossible to increase, even decrease, as time increases. Moreover, the average widths of uncertain opinions are always smaller than the maximum opinion width of all the initial opinions among agents. Experiments simulations results show different ratios of agents with uncertainty tolerances and different ratios of agents expressing uncertain opinions have strong impact on the ratios of the agents expressing the uncertain opinions in the stable state, and the average widths of uncertain opinions in the stable state.

Keywords

Opinion evolution / uncertainty / bounded confidence / social network

References

[1] Afshar M, Asadpour M. Opinion formation by informed agents. Journal of Artificial Societies and Social Simulation, 2010, 13(4): 1-5.

[2] Barabasi AL, Albert R. Emergence of scaling in random networks. Science, 1999, 286(5439): 509-512.

[3] Barrio RA, Govezensky T, Dunbar R, Lniguez G, Kaski K. Dynamics of deceptive interactions in social networks. Journal of the Royal Society Interface, 2015, 12(112): 463-474.

[4] Bashar MA, Hipel KW, Kilgour DM, Obeidi A. Interval fuzzy preferences in the graph model for conflict resolution. Fuzzy Optimization and Decision Making, 2018, 17: 287-315.

[5] Bashar MA, Obeidi A, Kilgour DM, Hipel KW. Modeling fuzzy and interval fuzzy preferences within a graph model framework. IEEE Transactions on Fuzzy Systems, 2016, 24(4): 765-778.

[6] Basu R, Sly A. Evolving voter model on dense random graphs. The Annals of Applied Probability, 2017, 27(2): 1235-1288.

[7] Ben-Naim E, Frachebourg L, Krapivsky PL. Coarsening and persistence in the voter model. Physical Review E, 1996, 53(4): 3078-3087.

[8] Berger RL. A necessary and sufficient condition for reaching a consensus using DeGroot’s method. Journal of the American Statistical Association, 1981, 76(374): 415-418.

[9] Bernardes AT, Stauffer D, Kertesz J. Election results and the Sznajd model on Barabasi network. The European Physical Journal B, 2002, 25(1): 123-127.

[10] Bimpikis K, Ozdaglar A, Yildiz E. Competitive targeted advertising over networks. Operations Research, 2016, 64(3): 705-720.

[11] Black R. Continuous opinion dynamics under bounded confidence: A survey. International Journal of Modern Physics C, 2007, 18(12): 1819-1838.

[12] Boccaletti S, Latora V, Moreno Y, Chavez M, Hwang DU. Complex networks: Structure and dynamics. Physics Reports, 2006, 424(4): 175-308.

[13] Bravomarquez F, Gayoavello D, Mendoza M, Poblete B. Opinion dynamics of elections in Twitter. IEEE Computer Society, 2012 32-39.

[14] Carro A, Toral R, San Miguel M. The noisy voter model on complex networks. Scientific Reports, 2016, 6(24775): 1-13.

[15] Chen S, Glass DH, McCartney M. Characteristics of successful opinion leaders in a bounded confidence model. Physica A: Statistical Mechanics and Its Applications, 2016, 449: 426-436.

[16] Chen X, Zhang HJ, Dong YC. The fusion process with heterogeneous preference structures in group decision making: A survey. Information Fusion, 2015, 24: 72-83.

[17] Crokidakis N, Blanco VH, Anteneodo C. Impact of contrarians and intransigents in a kinetic model of opinion dynamics. Physical Review E, 2014, 89(1): 013310.

[18] Deffuant G, Neau D, Amblard F. Mixing beliefs among interacting agents. Advances in Complex Systems, 2000, 3: 87-98.

[19] DeGroot MH. Reaching a consensus. Journal of the American Statistical Association, 1974, 69(345): 118-121.

[20] Dittmer JC. Consensus formation under bounded confidence. Nonlinear Analysis: Theory, Methods & Applications, 2001, 47(7): 4615-4621.

[21] Dong YC, Ding ZG, Martínez L, Herrera F. Managing consensus based on leadership in opinion dynamics. Information Sciences, 2017, 397–398: 187-205.

[22] Dong YC, Zha QB, Zhang HJ, Kou G, Fujita H, Chiclana F, Herrere-Viedma E. Consensus reaching in social network group decision making: Research paradigms and challenges. Knowledge-Based Systems, 2018, 162: 3-13.

[23] Dong YC, Zhan M, Kou G, Ding ZG, Liang HM. A survey on the fusion process in opinion dynamics. Information Fusion, 2018, 43: 57-65.

[24] Dong YC, Zhang GQ, Hong WC, Yu S. Linguistic computational model based on 2-tuples and intervals. IEEE Transactions on Fuzzy Systems, 2013, 21: 1006-1018.

[25] Dong YC, Zhao SH, Zhang HJ, Chiclana F, Herrera-Viedma E. A self-management mechanism for non-cooperative behaviors in large-scale group consensus reaching processes. IEEE Transactions on Fuzzy Systems, 2018, 26: 3276-3288.

[26] Fortunato S. Damage spreading and opinion dynamics on scale-free networks. Physica A: Statistical Mechanics and Its Applications, 2005, 348: 683-690.

[27] French JRP. A formal theory of social power. Psychological Review, 1956, 63(3): 181-194.

[28] Friedkin NE, Johnsen EC. Social influence and opinions. Journal of Mathematical Sociology, 1990, 15: 193-205.

[29] Friedkin NE, Proskurnikov AV, Tempo R, Parsegov SE. Network science on belief system dynamics under logic constraints. Science, 2016, 354(6310): 321-326.

[30] Friedkin NE, Bullo F. Howtruth wins in opinion dynamics along issue sequences. Proceedings of the National Academy of Sciences, 2017, 114(43): 11380-11385.

[31] Gong ZW, Xu XX, Zhang HH, Ozturk UA, Herrera-Viedma E, Xu C. The consensus models with interval preference opinions and their economic interpretation. Omega, 2015, 55: 81-90.

[32] Hegselmann R, Krause U. Opinion dynamics and bounded confidence models, analysis, and simulation. Journal of Artificial Societies and Social Simulation, 2002, 5(3): 1-33.

[33] Holley RA, Liggett TM. Ergodic theorems forweakly interacting infinite systems and the voter model. The Annals of Probability, 1975, 3(4): 643-663.

[34] Iñiguez G, Kertész J, Kaski K, Barrio R. Opinion and community formation in coevolving networks. Physical Review E, 2009, 80: 066119.

[35] Li CC, Dong YC, Herrera F. A consensus model for large-scale linguistic group decision making with a feedback recommendation based on clustered personalized individual semantics and opposing consensus groups. Ieee Transactions On Fuzzy Systems, 2019, 27(2): 221-233.

[36] Li Q, Liu Y, Tian R, Ma N. Opinion dynamics on triad scale free network. LectureNotes inComputer Science, 2012, 7669: 445-450.

[37] Journal of Artificial Societies and Social Simulation, 2016, 19(4):

[38] Liu YT, Dong YC, Liang HM, Chiclana F, Herrera-Viedma E. Multiple attribute strategicweight manipulation with minimum cost in a group decision making context with interval attributeweights information. IEEE Transactions on Systems, Man and Cybernetics: Systems, 2018

[39] Lorenz J. Heterogeneous bounds of confidence: Meet, discuss and find consensus. Complexity, 2010, 15(4): 43-52.

[40] Martins ACR. Continuous opinions and discrete actions in opinion dynamics problems. International Journal of Modern Physics C, 2008, 19(04): 617-624.

[41] Newman MEJ, Watts DJ. Renormalization group analysis of the small-world network model. Physics Letters A, 1999, 263(4): 341-346.

[42] Peng J, Mirtabatabaei A, Friedkin NE, Bullo F. Opinion dynamics and the evolution of social power in influence networks. Siam Review, 2015, 57(3): 367-397.

[43] Perez IJ, Cabrerizo FJ, Alonso S, Dong YC, Chiclana F, Herrera-Viedma E. On dynamic consensus processes in group decision making problems. Information Sciences, 2018, 459: 20-35.

[44] Pineda M, Toral R, Hernández-García E. The noisy Hegselmann-Krause model for opinion dynamics. The European Physical Journal B: Condensed Matter and Complex Systems, 2013, 86(12): 1-10.

[45] Presutti E, Spohn H. Hydrodynamics of the voter model. The Annals of Probability, 1983, 11(4): 867-875.

[46] Quattrociocchi W, Caldarelli G, Scala A. Opinion dynamics on interacting networks: Media competition and social influence. Scientific Reports, 2014, 4(21): 4938

[47] Sîrbu A, Loreto V, Servedio VDP, Tria F. Opinion dynamics: Models, extensions and external effects. Participatory Sensing, Opinions and Collective Awareness, 2016 363-401.

[48] Song X, Zhang S, Qian L. Opinion dynamics in networked command and control organizations. Physica A: Statistical Mechanics and Its Applications, 2013, 392(20): 5206-5217.

[49] Sood V, Redner S. Voter model on heterogeneous graphs. Physical Review Letters, 2005, 94(17): 178-701.

[50] Stamoulas ST, Rathinam M. Convergence, stability, and robustness of multidimensional opinion dynamics in continuous time. SIAM Journal on Control and Optimization, 2018, 56(3): 1938-1967.

[51] Su W, Chen G, Hong Y. Noise leads to quasiconsensus of Hegselmann-Krause opinion dynamics. Automatica, 2016, 85: 448-454.

[52] Sznajd-Weron K, Weron R. How effective is advertising in duopoly markets?. Physica A: Statistical Mechanics and Its Applications, 2003, 324(1): 437-444.

[53] Tan X, Gong ZW, Chiclana F, Zhang N. Consensus modeling with cost chance constraint under uncertainty opinions. Applied Soft Computing, 2018, 67: 721-727.

[54] Urena R, Kou G, Dong YC, Chiclana F, Herrera-Viedma E. A review on trust propagation and opinion dynamics in social networks and group decision making frameworks. Information Sciences, 2019, 478: 461-475.

[55] Varma VS, Mor IC, Lasaulce S, Martin S. Opinion dynamics aware marketing strategies in duopolies. IEEE Conference on Decision and Control, 2017

[56] Walker SB, Hipel KW, Inohara T. Dominating attitudes in the graph model for conflict resolution. Journal Of Systems Science And Systems Engineering, 2012, 21(3): 316-336.

[57] Wang LH, Gong ZW, Zhang N. Consensus modeling on interval-valued fuzzy preference relations with normal distribution. International Journal of Computational Intelligence Systems, 2018, 11: 706-715.

[58] Wang LX, Mendel JM. Fuzzy opinion networks: A mathematical framework for the evolution of opinions and their uncertainties across social networks. IEEE Transactions on Fuzzy Systems, 2016, 24(4): 880-905.

[59] Weisbuch G, Deffuant G, Amblard F, Nadal J. Meet, discuss and segregate. Complexity, 2002, 7(3): 55-63.

[60] Yildiz E, Ozdaglar A, Acemoglu D, Saberi A, Scaglione A. Binary opinion dynamics with stubborn agents. ACM Transactions on Economics and Computation, 2013, 1(4): 1-30.

[61] Zhan M, Ding ZG, Dong YC. Some results on consensus in uncertain opinion dynamics at a social network. Proceedings of the 18th International Conference on Group Decision and Negotiation, 2018 503-506.

[62] Zhang HJ, Dong YC, Herrera-Viedma E. Consensus building for the heterogeneous large-scale GDM with the individual concerns and satisfactions. IEEE Transactions on Fuzzy Systems, 2018, 26: 884-898.

[63] Zollman KJS. Social network structure and the achievement of consensus. Politics, Philosophy & Economics, 2012, 11(1): 26-44.