Agent-based Modeling And Analysis Of Opinion Dynamics With Heterogenous Interaction

Almost all of individuals’ decisions and social behaviors are shaped by their own opinion. Research on the dynamics of opinion formation is thus of great theoretical value and practical significance. Opinion dynamics aims at devising the elementary rules that determine individual’s opinion transition to analyze opinion evolution and collective behavior of population. It is becoming one of hot interdisciplinary topics recently and has attracted lots of researchers’ attentions from different fields, such as sociophisics, economics, mathematics, computer science, information and system control science. Although up to now various mathematical models have been presented to investigate opinion dynamics, most of these models only coordinate few factors that affect individual’s opinion. Opinion formation is a very complex process, and there are still lots of challenges.Generally speaking, individual’s opinion evolves as the result of endogenous factors, social network structure and the information received from his interactive individuals and other such information sources as media news. In this thesis, by incorporating some social psychological findings on human behavior from empirical studies, novel agent-based models are proposed to investigate the dynamics of opinion formation from three aspects including opinion consensus, opinion bi-polarization and opinion fluctuation. The main work and results of this thesis are presented as follows:Firstly, by considering the fact that in the real world there are some people who are too conservative to change their opinion easily while some other people who are ready to accept the new things, it is assumed that individuals fall into three types:open-minded agent, moderate-minded agent and close-minded agent. A slightly modified Hegselmann-Krause(HK) model is proposed based on non-Bayesian rule. The individual’s opinion is assumed to be continuous in the interval [0, 1], the bounded confidences of the individuals of each type are assumed to be uniformly distributed in three different intervals respectively. Numerical simulations are presented. It is also interesting to find that open-minded agents cannot contribute to forging opinion consensus, and will even make the final opinion of the population more diversified;open-minded agents cannot always speed up convergence rate, and only when the proportion of open-minded agents is large enough can it reduces convergence time steps of the population; for the fixed proportion of close-minded agents, the relative size of the largest opinion cluster varies along concave-parabola-like curve as the proportion of open-minded agents increases and there is a tipping point when the number of the moderate-minded agents is almost equal to that of the open-minded agents.Secondly, a novel agent-based model incorporating the influence of biased assimilation and homophily is proposed to investigate opinion bi-polarization. Based on persuasive argument theory, individual’s opinion is represented by a sequence of arguments and individuals exchange their opinion through a randomly selected argument rather than the exact value of their opinion. The behavior of biased assimilation is characterized by a modified Urn process. Theoretical analysis shows that the proposed model results in either bi-polarization or complete consensus. Numerical simulations on different network structures are presented. It is found that homophily and biased assimilation can not only contribute to bi-polarization and enhance the degree of bipolarization, but also accelerate convergence; in the complete network homophily plays a necessary role on opinion bi-polarization, and if the strength of homophily is zero,it it hardly to achieve bi-polarization, while in the WS small-world network and karate network, even without homophily the population can easily result in bi-polarization. In the S-W small-world network, larger average degree ?K? and reconnecting probability p can prevent the population from forming opinion bi-polarization, but they can speed up convergence rate.Thirdly, by considering the influence of stubborn agent, an extended state-dependent model is proposed to investigate opinion consensus and opinion fluctuation, where individuals are classified into regular agent and stubborn agent. Stubborn agent will never change his opinion, while regular agent updates his opinion to the average of his own opinion and the interactive agent, who is selected from his neighbors with the probability depending on the similarity of their own opinion and popularity of that agent.Convergence analysis of the proposed model is presented based on random matrix theory, so are the results of numerical simulations on various connected social networks.It shows that if all of the stubborn agents have the same initial opinion, the final opinion of the population will reach consensus at the stubborn agents’ opinion; in ER random network the convergence time will decrease and then keep stable as the edge connecting probability increases, and in WS small world network as the edge reconnecting probability and the average degree increases, the convergence time will also decreases sharply at the beginning and then keep almost unchanged. It is also found that if the stubborn agents have different initial opinion, the regular agent’s opinion may result in long-run disagreement and persistent fluctuation on the condition that there exists at least one path for the regular agent to reach stubborn agents with different opinion, and the upper bound of the fluctuation of the regular agent is the largest opinion of the reachable stubborn agents while the lower bound is the smallest opinion of the reachable stubborn agents.