论文标题
共识的漫长途径:在二元选择投票模型中的两个阶段变形
Long route to consensus: Two stage coarsening in a binary choice voting model
论文作者
论文摘要
共识的形成,是二进制/否类型的投票,是一个明确的过程。但是,即使在有明确的激励措施的情况下,涉及的动态也可能非常复杂。具体而言,大量相似的个人的形成可能会产生“支撑泡”或自发极化的条件,这实际上是无法实现的(例如,英国退出欧盟的问题)。较早的尝试通过简单的$ z_2 $ - 对称模型来捕获社会共识形成的动态,希望从统计意义上捕获大量个人的平均行为的基本动力。但是,在没有外部噪声的情况下,它们倾向于以碎片和极化状态(即两个或多个具有冷冻动力学的类似构想的组组,都具有碎片和极化状态的冷冻状态。在这里,我们在考虑$ l \ times l $方格的动力学交流意见模型(KEM)中显示,尽管可以避免这种冷冻状态,但表现出了指数缓慢的共识方法。具体而言,该系统可以在比例为$ l^2 $的时间内达成共识,或者长期存在的亚稳态状态(称为域壁状态),对于共识的形成需要时间缩放为$ l^{3.6} $。后一种行为可与以前研究过的一些类似选民的模型相媲美。时间尺度上的晚期异常反映在模型的持久性概率中。最后,平均意见的零交叉间隔,即,平均意见不变符号的时间间隔显示出遵循无标度分布的时间间隔,这与在过去40年中有关英国脱欧和相关问题的观点调查中所见。还通过计算退出概率来解决少数群体扩散问题。
Formation of consensus, in binary yes/no type of voting, is a well defined process. However, even in presence of clear incentives, the dynamics involved can be incredibly complex. Specifically, formations of large groups of similarly opinionated individuals could create a condition of `support-bubbles' or spontaneous polarization that renders consensus virtually unattainable (e.g., the question of the UK exiting the EU). There have been earlier attempts in capturing the dynamics of consensus formation in societies through simple $Z_2$-symmetric models hoping to capture the essential dynamics of average behaviorof a large number of individuals in a statistical sense. However, in absence of external noise, they tend to reach a frozen state with fragmented and polarized states i.e., two or more groups of similarly opinionated groups with frozen dynamics. Here we show in a kinetic exchange opinion model (KEM) considered on $L \times L$ square lattices, that while such frozen states could be avoided, an exponentially slow approach to consensus is manifested. Specifically, the system could either reach consensus in a time that scales as $L^2$ or a long lived metastable state (termed a domain-wall state) for which formation of consensus takes a time scaling as $L^{3.6}$. The latter behavior is comparable to some voter-like models with intermediate states studied previously. The late-time anomaly in the time scale is reflected in the persistence probability of the model. Finally, the interval of zero-crossing of the average opinion i.e., the time interval over which the average opinion does not change sign is shown to follow a scale free distribution, which is compared with that seen in the opinion surveys regarding Brexit and associated issues in the last 40 years. The issue of minority spreading is also addressed by calculating the exit probability.