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Binary Opinion Dynamics with Biased Agents and Agents with Different Degrees of Stubbornness

机译：带有偏见代理人和具有不同固执程度的代理人的二元意见动力学

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In this paper, we investigate the impact of random interactions between agents in a social network on the diffusion of opinions in the network. Opinion of each agent is assumed to be a binary variable and each agent is assumed to be able to interact with any other agent in the network. This models scenarios where every agent in the network has to choose from two available options and the size of the neighborhood of each agent is an increasing function of the total number agents in the network. It is assumed that each agent updates its opinion at random instants upon interacting with other randomly sampled agents. We consider two simple rules of interaction: (1) the voter rule in which the updating agent simply copies the opinion of another randomly sampled agent, (2) the majority rule, in which the updating agent samples multiple agents and adopts the majority opinion among the sampled agents and the agent itself. Under each rule, we consider two different scenarios which have not been considered in the literature thus far: (1) where the agents are 'biased' towards one of the opinions, (2) where different agents have different degrees of stubbornness. We show that the presence of biased agents reduces the consensus time for the voter rule exponentially as compared to the case where the agents are unbiased. For the majority rule model with biased agents, we show that the network reaches consensus on a particular opinion with high probability only when the initial fraction of agents having that opinion is above a certain threshold. For the majority rule model with stubborn agents, we observe metastability where the network switches back and forth between stable states spending long intervals in each state.
机译：在本文中，我们研究了社交网络中代理之间的随机交互对网络中观点传播的影响。假定每个代理的观点是二进制变量，并且假定每个代理能够与网络中的任何其他代理进行交互。此模型为以下场景建模：网络中的每个代理都必须从两个可用选项中进行选择，并且每个代理的邻域大小是网络中代理总数的递增函数。假定每个代理在与其他随机采样的代理进行交互时会在随机瞬间更新其观点。我们考虑了两个简单的交互规则：（1）投票者规则，其中更新代理简单地复制另一个随机采样的代理的意见，（2）多数规则，其中更新代理对多个代理进行抽样并在其中采用多数意见采样的代理和代理本身。根据每条规则，我们考虑迄今为止文献中尚未考虑的两种不同情况：（1）行为人被“偏向”其中一种观点;（2）不同行为人的固执程度不同。我们显示，与代理人无偏见的情况相比，有偏见的代理人的存在以指数方式减少了选民规则的共识时间。对于具有偏向主体的多数规则模型，我们表明只有当具有该主体的主体的初始分数高于某个阈值时，网络才有可能以较高的概率达成共识。对于具有顽固代理的多数规则模型，我们观察到亚稳态，其中网络在每个状态花费较长时间的稳定状态之间来回切换。

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