ABSTRACT In this paper, we extend the voter model (VM) and the threshold voter model (TVM) to include external influences modeled as a jump process. We study the newly-formulated models both analytically and computationally, employing diffusion approximations and mean field approximations. We derive results pertaining to the probability of reaching consensus on a particular opinion and also the expected consensus time. We find that although including an external influence leads to a faster consensus in general, this effect is more pronounced in the VM as compared to the TVM. Our findings suggest the potential importance of external influences in addition to local interactions.

中文翻译：

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选民模型和外部影响

摘要 在本文中，我们扩展了选民模型 (VM) 和阈值选民模型 (TVM) 以包括建模为跳跃过程的外部影响。我们使用扩散近似和平均场近似，从分析和计算上研究新制定的模型。我们得出与就特定意见达成共识的可能性以及预期的共识时间有关的结果。我们发现，虽然包括外部影响通常会导致更快的共识，但与 TVM 相比，这种效果在 VM 中更为明显。我们的研究结果表明，除了局部相互作用之外，外部影响的潜在重要性。