论文标题
选民和多数动态具有偏见和顽固的代理商
Voter and Majority Dynamics with Biased and Stubborn Agents
论文作者
论文摘要
我们在相互作用的代理的完全连接的网络中研究二进制意见动力学。假定代理商根据以下规则之一进行交互：（1）选民规则：更新代理人只是复制另一个随机抽样代理的意见； （2）多数规则：更新代理样品采样多个代理，并在选定的组中采用多数意见。我们专注于代理商偏向于称为{\ em首选意见}的一种情况。使用适当构建的分支过程，我们表明，在这两个规则下，平均达成共识的平均时间为$θ（\ log n）$，其中$ n $是网络中代理的数量。此外，在多数规则模型下，我们表明，即使最初是少数派的意见，也可以在优先意见上达成共识。当存在固定意见的顽固的代理人时，我们还会研究多数规则模型。我们发现，使用平均现场技术，网络中网络中意见的固定分布。
We study binary opinion dynamics in a fully connected network of interacting agents. The agents are assumed to interact according to one of the following rules: (1) Voter rule: An updating agent simply copies the opinion of another randomly sampled agent; (2) Majority rule: An updating agent samples multiple agents and adopts the majority opinion in the selected group. We focus on the scenario where the agents are biased towards one of the opinions called the {\em preferred opinion}. Using suitably constructed branching processes, we show that under both rules the mean time to reach consensus is $Θ(\log N)$, where $N$ is the number of agents in the network. Furthermore, under the majority rule model, we show that consensus can be achieved on the preferred opinion with high probability even if it is initially the opinion of the minority. We also study the majority rule model when stubborn agents with fixed opinions are present. We find that the stationary distribution of opinions in the network in the large system limit using mean field techniques.
