网络模仿在纠正性事实场存在下仍维持错误信息

中文摘要 AI 辅助

社会影响可以保留个体本会自行纠正的错误。我们通过将观点表示为语义空间中的方向来研究这种可能性。该表述连接了个人偏好、社会一致性和外部影响的既有模型。一个共同的事实信号将每个观点拉向参考方向，个体保持对其初始偏好的依恋，而相连的个体相互模仿。当事实信号超过偏好强度时，每个孤立个体都会纠正，除了完全相反的初始观点外。我们证明，每个有限无向网络随后都有一个唯一的最小总能量状态，在该状态下所有观点都偏向事实方向。该状态是事实对齐、个人偏好和与邻居一致性之间的最佳整体折衷。然而，在具有平面观点的环上，足够强的模仿可以将相同个体困在保留错误信息的另一个稳定状态中。我们证明了从指定初始观点收敛到该状态。我们还推导了一个网络谱条件，该条件排除竞争性稳定状态，并展示了额外的语义方向如何破坏所构造的平面模式。数值图谱揭示了持续错误、历史依赖性和共存结果，而跨网络比较显示差异无法通过单一谱尺度消除。这些结果区分了个体可纠正性与集体纠正，并识别了吸引力社会影响如何阻碍后者。

英文摘要

Social influence can preserve errors that individuals would correct on their own. We study this possibility by representing opinions as directions in a semantic space. The formulation connects established models of personal preference, social agreement, and external influence. A common factual signal pulls every opinion toward a reference direction, individuals remain attached to their initial preferences, and connected individuals imitate one another. When the factual signal exceeds the preference strength, each isolated individual corrects, apart from an exactly opposite initial opinion. We prove that every finite undirected network then has a unique state of minimum total energy in which all opinions favor the factual direction. This state is the best overall compromise between factual alignment, personal preferences, and agreement with neighbors. Yet on a ring with planar opinions, sufficiently strong imitation can trap the same individuals in a different stable state that retains misinformation. We prove convergence to that state from the specified initial opinions. We also derive a network spectral condition that excludes competing stable states, and show how an additional semantic direction can destabilize the constructed planar pattern. Numerical maps reveal persistent error, history dependence, and coexisting outcomes, while comparisons across networks show differences that a single spectral scale does not remove. These results distinguish individual correctability from collective correction and identify how attractive social influence can obstruct the latter.

发表机构

• Hong Kong Shue Yan University（香港树仁大学）

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