达成共识的漫长道路：二元选择投票模型中的两阶段粗化
Long route to consensus: Two stage coarsening in a binary choice voting model
摘要：
在二进制是/否类型的投票中形成共识是一个明确定义的过程。然而，即使存在明确的激励措施，所涉及的动态也可能非常复杂。具体而言，形成由类似固执己见的个人组成的大群体可能会造成“支持泡沫”或自发极化的条件，使共识几乎无法达成（例如，英国退出欧盟的问题）。早期的尝试是通过简单的$Z_2$对称模型来捕捉社会中共识形成的动态，希望从统计学意义上捕捉大量个体的平均行为的基本动态。然而，在没有外部噪声的情况下，它们倾向于达到具有碎片和极化状态的冻结状态，即，两个或两个以上的团体，具有相似的固执己见的团体，具有冻结的动力。在这里，我们表明，在一个动力学交换意见模型（KEM）考虑$L \times L$正方形格子，虽然可以避免这种冻结状态，一个指数缓慢的共识的方法表现出来。具体地说，系统可以在按$L^2$缩放的时间内达成共识，也可以在形成共识需要按$L^{3.6}$缩放的时间的长寿命亚稳态（称为畴壁态）中达成共识。后一种行为与先前研究的具有中间状态的类似选民的模型相当。时间尺度上的晚时异常反映在模型的持续概率上。最后，平均意见的零交叉区间，即，平均意见不改变符号的时间间隔显示出遵循无标度分布，这与过去40年关于英国脱欧及其相关问题的民意调查中所见的时间间隔进行了比较。少数蔓延的问题也解决了通过计算退出概率。
英文摘要：
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.
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