带偏见的加权中位数观点动力学收敛性分析
Convergence Analysis of Weighted-Median Opinion Dynamics with Prejudice
AI总结：
针对FJ模型加权平均机制易被单个偏见主导的局限，本文研究带偏见的加权中位数观点动力学，给出全偏见情形的收敛性与收敛速度及部分偏见情形的渐近共识充要条件。
摘要：
Friedkin-Johnsen（FJ）模型将偏见引入观点演化，并已在许多实际场景中得到成功验证；然而，由于其加权平均机制，在连通的影响网络下，仅一个带偏见的智能体就总能引导所有无偏见智能体同步到其偏见，这可能不符合某些社会现实。为从根本上解决加权平均机制的局限，近期有人提出了一种加权中位数观点动力学；但由于其非线性特性，对其进行理论分析具有挑战性。本文研究带偏见的加权中位数观点动力学，得到了所有智能体均带偏见时的收敛性和收敛速度，以及部分智能体带偏见时渐近共识的充要条件。这些结果首次分析了采用加权中位数机制的离散时间同步观点动力学，并解决了FJ模型中少数具有相同偏见的智能体加入无偏见群体时连通性导致共识的现象。
英文摘要：
The Friedkin-Johnsen (FJ) model introduces prejudice into the opinion evolution and has been successfully validated in many practical scenarios; however, due to its weighted average mechanism, only one prejudiced agent can always guide all unprejudiced agents synchronizing to its prejudice under the connected influence network, which may not be in line with some social realities. To fundamentally address the limitation of the weighted average mechanism, a weighted-median opinion dynamics has been recently proposed; however, its theoretical analysis is challenging due to its nonlinear nature. This paper studies the weighted-median opinion dynamics with prejudice, and obtains the convergence and convergence rate when all agents have prejudice, and a necessary and sufficient condition for asymptotic consensus when a portion of agents have prejudice. These results are the first time to analyze the discrete-time and synchronous opinion dynamics with the weighted median mechanism, and address the phenomenon of the FJ model that connectivity leads to consensus when a few agents with the same prejudice join in an unprejudiced group.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
