With the availability of cell phones, internet, social media etc. the interconnectedness of people within most societies has increased drastically over the past three decades. Across the same timespan, we are observing the phenomenon of increasing levels of fragmentation in society into relatively small and isolated groups that have been termed filter bubbles, or echo chambers. These pose a number of threats to open societies, in particular, a radicalisation in political, social or cultural issues, and a limited access to facts. In this paper we show that these two phenomena might be tightly related. We study a simple stochastic co-evolutionary model of a society of interacting people. People are not only able to update their opinions within their social context, but can also update their social links from collaborative to hostile, and vice versa. The latter is implemented such that social balance is realised. We find that there exists a critical level of interconnectedness, above which society fragments into small sub-communities that are positively linked within and hostile towards other groups. We argue that the existence of a critical communication density is a universal phenomenon in all societies that exhibit social balance. The necessity arises from the underlying mathematical structure of a phase transition phenomenon that is known from the theory of a kind of disordered magnets called spin glasses. We discuss the consequences of this phase transition for social fragmentation in society.
Fragmentation, echo chambers, and their amelioration in social networks have been a growing concern in the academic and non-academic world. This paper shows how, under the assumption of homophily, echo chambers and fragmentation are system-immanent phenomena of highly flexible social networks, even under ideal conditions for heterogeneity. We achieve this by finding an analytical, network-based solution to the Schelling model and by proving that weak ties do not hinder the process. Furthermore, we derive that no level of positive algorithmic bias in the form of rewiring is capable of preventin…
Relating the microscopic rules in coalescence-fragmentation models to the macroscopic cluster size distributions which emerge
聚结-碎裂问题是物理学、生物学和最近的社会科学领域的一个热点问题。它们通常从速率方程的角度进行研究，这些模型的核心是用于合并和碎裂的规则。在这里，我们将讨论如何在这些微观规则的变化影响宏观集群大小分布出现的解决方案的速率方程。更一般地说，我们的工作阐明了至关重要的作用，破碎规则可以在这样的动态分组模型。我们专注于两个著名的模型，其碎片化规则位于相反的极端设置的模型在更广泛的背景下的二元聚结-碎片化模型。此外，我们提供了一系列的推广和新的分析结果的一个著名的模型的社会群体形成[V。M。Eguiluz和M. G. Zimmermann，Phys. Rev. Lett. 85，5659（2000）]。我们开发了解析摄动处理的原始模型，并扩展到增长和下降的人口的治疗的数学。
Balance theory explains the forces behind the structure of social systems, which are commonly modeled as static undirected signed networks. We expand this modeling approach to incorporate directionality of edges, and consider three levels of analysis: triads, subgroups, and the whole network. For triad-level balance, we operationalize a new measure by utilizing semicycles that satisfy the condition of transitivity. For subgroup-level balance, we propose measures of cohesiveness (intra-group solidarity) and divisiveness (inter-group antagonism) to capture balance within and among subgroups of t…
Recent attempts to understand the origin of social fragmentation are based on spin models which include terms accounting for two social phenomena: homophily -- the tendency for people with similar opinions to establish positive relations -- and social balance -- the tendency for people to establish balanced triadic relations. Spins represent attribute vectors that encode multiple (binary) opinions of individuals and social interactions between individuals can be positive or negative. Recent work suggests that large systems of N >> 1 individuals never reach a balanced state (where unbalanced tr…
In a recent work [R. Shojaei et al, Physical Review E 100, 022303 (2019)] the Authors calculate numerically the critical temperature $T_c$ of the balanced-imbalanced phase transition in a fully connected graph. According to their findings, $T_c$ decreases with the number of nodes $N$. Here we calculate the same critical temperature using the heat-bath algorithm. We show that $T_c$ increases with $N$ as $N^γ$, with $γ$ close to 0.5 or 1.0. This value depends on the initial fraction of positive bonds.
Reducing Frustration in Spin Systems: Social Balance as an XOR-SAT problem
Antal \emph{et al.} [ T. Antal，P. L. Krapivsky和S. Redner，Phys. Rev. E { \bf 72}，036121（2005）。].我们将它们的三元动力学推广到任意整数$k$的$k$ -圈动力学.我们推导出的相结构，确定固定的解决方案，并计算所需的时间达到冻结状态。作为$k$的函数的相结构的主要差异与$k$是偶数还是奇数有关。作为第二个推广，我们将Antal \emph{et al.}所考虑的全对全耦合稀释为连接概率为$w<1$的随机网络。...
The arise of disagreement is an emergent phenomenon that can be observed within a growing social group and, beyond a certain threshold, can lead to group fragmentation. To better understand how disagreement emerges, we introduce an analytically tractable model of group formation where individuals have multidimensional binary opinions and the group grows through a noisy homophily principle, i.e., like-minded individuals attract each other with exceptions occurring with some small probability. Assuming that the level of disagreement is correlated with the number of different opinions coexisting …
Recently, we introduced [Physical Review E 100, 022303 (2019)] a stochastic social balance model with Glauber dynamics which takes into account the role of randomness in the individual's behavior. One important finding of our study was a phase transition from a balance state to an imbalance state as the randomness crosses a critical value, which was shown to vanish in the thermodynamic limit. In a recent similar study [K. Malarz and K. Kułakowskiy, (2020), arXiv:2009.10136], it was shown that the critical randomness tends to infinity as the system size diverges. This led the authors to questio…
Within the context of social balance theory, much attention has been paid to the attainment and stability of unipolar or bipolar societies. However, multipolar societies are commonplace in the real world, despite the fact that the mechanism of their emergence is much less explored. Here, we investigate the evolution of a society of interacting agents with friendly (positive) and enmity (negative) relations into a final stable multipolar state. Triads are assigned energy according to the degree of tension they impose on the network. Agents update their connections in order to decrease the total…
On the dynamics of Social Balance on general networks (with an application to XOR-SAT)
我们研究离散动力系统的非确定性和概率版本（由于T。Antal，P. L. Krapivsky和S. Redner）的社会平衡理论的启发。我们研究了几类图的收敛时间的动态。我们的贡献包括：1.我们指出了三重动力学和广义的零化走超图之间的连接。特别是，这种连接使我们能够完全表征图中的递归状态，其中每条边最多属于两个三角形。2.我们还解决了超图不包含由一个或两个顶点组成的边的情况。3.我们证明了在所谓的“三元圈”图上，收敛时间是线性的。4.我们得到了2-正则三元单形G的收敛时间的三次上界。这个界可以进一步改进到一个依赖于G的Cheeger常数的量。特别是这提供了一些严格的对应以前的实验观察。我们还指出了一个应用程序的随机游走算法的分析在某些情况下的3-异或-SAT问题。
University of Sydney（悉尼大学）；Goethe University Frankfurt（法兰克福歌德大学）；IT:U Interdisciplinary Transformation University（IT：U跨学科转型大学）；Central European University（中欧大学）；Complexity Science Hub（复杂性科学中心）
