We describe a model for polarization in multi-agent systems based on Esteban and Ray's standard family of polarization measures from economics. Agents evolve by updating their beliefs (opinions) based on an underlying influence graph, as in the standard DeGroot model for social learning, but under a confirmation bias; i.e., a discounting of opinions of agents with dissimilar views. We show that even under this bias polarization eventually vanishes (converges to zero) if the influence graph is strongly-connected. If the influence graph is a regular symmetric circulation, we determine the unique belief value to which all agents converge. Our more insightful result establishes that, under some natural assumptions, if polarization does not eventually vanish then either there is a disconnected subgroup of agents, or some agent influences others more than she is influenced. We also prove that polarization does not necessarily vanish in weakly-connected graphs under confirmation bias. Furthermore, we show how our model relates to the classic DeGroot model for social learning. We illustrate our model with several simulations of a running example about polarization over vaccines and of other case studies. The theoretical results and simulations will provide insight into the phenomenon of polarization.

翻译：我们基于Esteban和Ray提出的经济学标准极化度量族，描述了一种多智能体系统中的极化模型。智能体通过底层影响图更新其信念（观点）进行演化，这与标准DeGroot社会学习模型一致，但引入了确认偏见机制——即对持有不同观点的智能体意见进行折损处理。研究表明，即使存在这种偏见，当影响图为强连通图时，极化现象最终会消失（收敛至零）。针对正则对称环流图，我们确定了所有智能体收敛的唯一信念值。更具洞察力的结果表明，在若干自然假设下，若极化未能最终消失，则必然存在某个非连通子群，或存在某个智能体对他人的影响力大于被影响力。此外，我们证明了在弱连通图中，确认偏见下的极化未必会消失。同时揭示了该模型与经典DeGroot社会学习模型的内在关联。通过关于疫苗极化的运行实例及其他案例的多次仿真实验，我们对模型进行了验证。理论结果与仿真将为极化现象研究提供深刻洞见。