论文标题
具有2个选择规则的有偏见动态的相变
Phase Transitions in Biased Opinion Dynamics with 2-choices Rule
论文作者
论文摘要
我们考虑了一种二进制观点动态模型，其中一种观点本质上比另一个观点“优越”，而社会代理人则表现出对上级替代方案的“偏见”。具体而言，假定代理商将其选择更新为上级替代方案，而概率$α> 0 $，而不论其当前的意见和其他代理商的意见如何。有了$ 1-α$的概率，它在两个随机抽样的邻居及其本身中采用了多数意见。我们对网络收敛到所有代理人采用优越选择的共识状态所需的时间感兴趣。在一个尺寸$ n $的完全连接的网络中，我们表明，无论网络的初始配置如何，当偏见参数$α$的平均时间为$θ（n \ log n）$，即足够高，即，即$α_c$ a $α_c$是$α_c$是thresholdy的heasholdy parametery。 When the bias is low, i.e., when $α\in (0,α_c]$, we show that the same rate of convergence can only be achieved if the initial proportion of agents with the superior opinion is above certain threshold $p_c(α)$. If this is not the case, then we show that the network takes $Ω(\exp(Θ(n)))$ time on average to reach consensus. Through numerical simulations we观察其他类别的类似行为。
We consider a model of binary opinion dynamics where one opinion is inherently 'superior' than the other and social agents exhibit a 'bias' towards the superior alternative. Specifically, it is assumed that an agent updates its choice to the superior alternative with probability $α>0$ irrespective of its current opinion and the opinions of the other agents. With probability $1-α$ it adopts the majority opinion among two randomly sampled neighbours and itself. We are interested in the time it takes for the network to converge to a consensus state where all the agents adopt the superior alternative. In a fully connected network of size $n$, we show that irrespective of the initial configuration of the network, the average time to reach consensus scales as $Θ(n \log n)$ when the bias parameter $α$ is sufficiently high, i.e., $α> α_c$ where $α_c$ is a threshold parameter that is uniquely characterised. When the bias is low, i.e., when $α\in (0,α_c]$, we show that the same rate of convergence can only be achieved if the initial proportion of agents with the superior opinion is above certain threshold $p_c(α)$. If this is not the case, then we show that the network takes $Ω(\exp(Θ(n)))$ time on average to reach consensus. Through numerical simulations we observe similar behaviour for other classes of graphs.
