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：我们描述了一个基于Esteban和Ray经济学中标准极化度量族的多智能体系统极化模型。智能体通过更新其信念（观点）进行演化，该更新基于底层的社交影响图（如标准DeGroot社会学习模型），但受制于确认偏见，即对观点相异者的意见进行折扣。我们证明：若影响图是强连通的，即使存在这种偏见，极化现象最终也会消失（收敛至零）。若影响图是正则对称循环图，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：在自然假设下，若极化未最终消失，则要么存在不相连的智能体子群，要么某些智能体对他人的影响超过其受他人影响的程度。我们还证明在弱连通图中，确认偏见下的极化未必消失。此外，我们展示了本模型与经典DeGroot社会学习模型的关联。通过疫苗极化案例及其他案例的多组仿真实验，我们验证了该模型。理论结果与仿真将为极化现象提供深刻见解。