In some research involving opinion formation, there are some details that have not been studied deeply, just as the role of a person’s self-confidence in opinion dynamics. This small but important detail needs to be cleared up. Hence, in this paper, we want to discuss the self-confidence in opinion dynamics with regard to some common linear and nonlinear models: DeGroot, Friedkin–Johnsen, Deffuant–Weisbuch and Hegselmann–Krause (HK) model. We unfold that (1) A person’s self-confidence assumption has an important impact on the consensus condition in DeGroot model; (2) The relationship between the self-confidence on the initial opinion and the current opinion follows a Kuznets curve in Friedkin–Johnsen model; (3) A person’s self-confidence has a close relationship with the convergence parameter in Deffuant–Weisbuch model, which has little impact on the number of opinion clusters at the stable stage; and (4) A person’s self-confidence varies with time at first and then stays at a certain level finally in the HK model, while the person’s self-confidence does not change with time in above three models.

中文翻译：

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关于意见动态中的自信的注释

在一些涉及意见形成的研究中，有一些细节没有深入研究，就像一个人的自信心在意见动态中的作用一样。这个小而重要的细节需要澄清。因此，在本文中，我们想讨论一些常见的线性和非线性模型对意见动态的自信：DeGroot、Friedkin-Johnsen、Deffuant-Weisbuch 和 Hegselmann-Krause (HK) 模型。我们揭示了（1）一个人的自信假设对DeGroot模型中的共识条件有重要影响；(2) 对初始观点的自信与当前观点之间的关系遵循 Friedkin-Johnsen 模型中的库兹涅茨曲线；(3) 一个人的自信心与 Deffuant-Weisbuch 模型中的收敛参数有密切关系，对稳定阶段的意见簇数量影响不大；(4)在HK模型中，人的自信心先随时间变化，然后最终保持在一定水平，而在上述三种模型中，人的自信心不随时间变化。