Analysis and Application of Bounded Confidence Opinion Dynamics With Universal Gravitation-like
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摘要: 在社会网络中, Hegselmann-Krause模型描述了置信阈值内不同邻居对个体的观点影响权重都相同且邻居对个体的吸引力与它们的观点差值成正比, 这是不切实际的. 为了克服经典Hegselmann-Krause模型的不足, 提出具有类万有引力的有界置信观点动力学模型, 描述个体观点的更新依赖于观点之间的差值和邻居的权威性, 且不同邻居对个体的观点影响权重不同. 根据置信矩阵的性质证明观点的收敛性, 并分析具有衰减置信阈值的观点动力学行为, 给出观点收敛速率的显式解. 最后, 利用提出的观点动力学模型, 研究社会心理学中的“权威效应”和“非零和效应”. 仿真结果表明, 邻居的权威性有利于观点达成一致.Abstract: In the social networks, the Hegselmann-Krause model describes that the different neighbors within the confidence threshold have the same influence weight on the individual＇s opinion, and the attractiveness of neighbors to the individual is proportional to the opinion distance, which is unrealistic. In order to overcome the shortcoming of the classical Hegselmann-Krause model, we propose a bounded confidence opinion dynamics model with universal gravitation-like in this paper, which captures the update of the individual opinion depending on both the opinion distance and the authority of neighbors, and it is shown that different neighbors have different influence weights on individual opinions. The convergence of opinions is proved in terms of the property of confidence matrix, and moreover, the dynamic behavior of the opinion with decaying confidence threshold is analyzed and the explicit solution of the opinion convergence rate is given. Finally, by employing our proposed opinion dynamics model, we study the authority effect and the non-zero-sum effect in social psychology. Simulation analyses reveal that the authority of the neighbor is beneficial to opinion achieving consensus.
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Key words:
- Opinion dynamics /
- universal gravitation-like /
- bounded confidence /
- social networks /
- convergence
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图 1 $d_{ij}(k)$关于$\vert N_j\vert$和$x_j(k)-x_i(k)$的函数图
Fig. 1 The trajectories of $d_{ij}(k)$ with respect to $\vert N_j\vert$ and $x_j(k)-x_i(k)$
图 2 个体$j$对个体$i$观点的影响
Fig. 2 The influence of individual $j$ on the opinion of individual $i$
图 3 网络拓扑结构 (个体4为权威个体)
Fig. 3 Network structure (individual 4 is the authoritative individual)
图 4 权威效应 (个体4为权威个体)
Fig. 4 Authority effect (individual 4 is the authoritative individual)
图 5 网络拓扑结构 (个体5为权威个体)
Fig. 5 Network structure (individual 5 is the authoritative individual)
图 6 权威效应 (个体5为权威个体)
Fig. 6 Authority effect (individual 5 is the authoritative individual)
图 8 初值为均匀分布时的观点演化
Fig. 8 Opinion evolution when the initial value is uniformly distributed
图 9 初值为正态分布时的观点演化
Fig. 9 Opinion evolution when the initial value is normally distributed
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