Committed activists and the reshaping of status-quo social consensus

Mathematical modeling of disinformation and effectiveness of mitigation policies

Disinformation is spread to manipulate public opinion for malicious purposes. Mathematical modeling was used to examine and optimize several strategies for combating disinformation-content moderation, education, and counter-campaigns. We implemented these strategies in a modified binary agreement model and investigated their impacts on properties of the tipping point. Social interactions were described by weighted, directed, and heterogeneous networks. Real social network data was examined as well. We find that content moderation achieved by removing randomly selected agents who spread disinformation is comparable to that achieved by removing highly influential agents; removing disinformation anywhere in a network could be an effective way to counter disinformation. An education strategy that increases public skepticism was more effective than one that targets already biased agents. Successful counter-campaign strategies required a substantial population of agents to influence other agents to oppose disinformation. These results can be used to inform choices of effective strategies for combating disinformation.

Multistability, intermittency, and hybrid transitions in social contagion models on hypergraphs

Although ubiquitous, interactions in groups of individuals are not yet thoroughly studied. Frequently, single groups are modeled as critical-mass dynamics, which is a widespread concept used not only by academics but also by politicians and the media. However, less explored questions are how a collection of groups will behave and how their intersection might change the dynamics. Here, we formulate this process as binary-state dynamics on hypergraphs. We showed that our model has a rich behavior beyond discontinuous transitions. Notably, we have multistability and intermittency. We demonstrated that this phenomenology could be associated with community structures, where we might have multistability or intermittency by controlling the number or size of bridges between communities. Furthermore, we provided evidence that the observed transitions are hybrid. Our findings open new paths for research, ranging from physics, on the formal calculation of quantities of interest, to social sciences, where new experiments can be designed.

Robot swarm democracy: the importance of informed individuals against zealots

In this paper we study a generalized case of best-of-n model, which considers three kind of agents: zealots, individuals who remain stubborn and do not change their opinion; informed agents, individuals that can change their opinion, are able to assess the quality of the different options; and uninformed agents, individuals that can change their opinion but are not able to assess the quality of the different opinions. We study the consensus in different regimes: we vary the quality of the options, the percentage of zealots and the percentage of informed versus uninformed agents. We also consider two decision mechanisms: the voter and majority rule. We study this problem using numerical simulations and mathematical models, and we validate our findings on physical kilobot experiments. We find that (1) if the number of zealots for the lowest quality option is not too high, the decision-making process is driven toward the highest quality option; (2) this effect can be improved increasing the number of informed agents that can counteract the effect of adverse zealots; (3) when the two options have very similar qualities, in order to keep high consensus to the best quality it is necessary to have higher proportions of informed agents.

Interplay between [Formula: see text]-core and community structure in complex networks

The organisation of a network in a maximal set of nodes having at least k neighbours within the set, known as [Formula: see text]-core decomposition, has been used for studying various phenomena. It has been shown that nodes in the innermost [Formula: see text]-shells play a crucial role in contagion processes, emergence of consensus, and resilience of the system. It is known that the [Formula: see text]-core decomposition of many empirical networks cannot be explained by the degree of each node alone, or equivalently, random graph models that preserve the degree of each node (i.e., configuration model). Here we study the [Formula: see text]-core decomposition of some empirical networks as well as that of some randomised counterparts, and examine the extent to which the [Formula: see text]-shell structure of the networks can be accounted for by the community structure. We find that preserving the community structure in the randomisation process is crucial for generating networks whose [Formula: see text]-core decomposition is close to the empirical one. We also highlight the existence, in some networks, of a concentration of the nodes in the innermost [Formula: see text]-shells into a small number of communities.

Modelling Population Dynamics of Social Protests in Time and Space: The Reaction-Diffusion Approach

Understanding of the dynamics of riots, protests, and social unrest more generally is important in order to ensure a stable, sustainable development of various social groups, as well as the society as a whole. Mathematical models of social dynamics have been increasingly recognized as a powerful research tool to facilitate the progress in this field. However, the question as to what should be an adequate mathematical framework to describe the corresponding social processes is largely open. In particular, a great majority of the previous studies dealt with non-spatial or spatially implicit systems, but the literature dealing with spatial systems remains meagre. Meanwhile, in many cases, the dynamics of social protests has a clear spatial aspect. In this paper, we attempt to close this gap partially by considering a spatial extension of a few recently developed models of social protests. We show that even a straightforward spatial extension immediately bring new dynamical behaviours, in particular predicting a new scenario of the protests’ termination.

Spreading of computer viruses on time-varying networks

Social networks are the prime channel for the spreading of computer viruses. Yet the study of their propagation neglects the temporal nature of social interactions and the heterogeneity of users' susceptibility. Here, we introduce a theoretical framework that captures both properties. We study two realistic types of viruses propagating on temporal networks featuring Q categories of susceptibility and derive analytically the invasion threshold. We found that the temporal coupling of categories might increase the fragility of the system to cyber threats. Our results show that networks' dynamics and their interplay with users' features are crucial for the spreading of computer viruses.

Epidemic spreading on time-varying multiplex networks

Social interactions are stratified in multiple contexts and are subject to complex temporal dynamics. The systematic study of these two features of social systems has started only very recently, mainly thanks to the development of multiplex and time-varying networks. However, these two advancements have progressed almost in parallel with very little overlap. Thus, the interplay between multiplexity and the temporal nature of connectivity patterns is poorly understood. Here, we aim to tackle this limitation by introducing a time-varying model of multiplex networks. We are interested in characterizing how these two properties affect contagion processes. To this end, we study susceptible-infected-susceptible epidemic models unfolding at comparable timescale with respect to the evolution of the multiplex network. We study both analytically and numerically the epidemic threshold as a function of the multiplexity and the features of each layer. We found that higher values of multiplexity significantly reduce the epidemic threshold especially when the temporal activation patterns of nodes present on multiple layers are positively correlated. Furthermore, when the average connectivity across layers is very different, the contagion dynamics is driven by the features of the more densely connected layer. Here, the epidemic threshold is equivalent to that of a single layered graph and the impact of the disease, in the layer driving the contagion, is independent of the multiplexity. However, this is not the case in the other layers where the spreading dynamics is sharply influenced by it. The results presented provide another step towards the characterization of the properties of real networks and their effects on contagion phenomena.

The dynamics of norm change in the cultural evolution of language

What happens when a new social convention replaces an old one? While the possible forces favoring norm change-such as institutions or committed activists-have been identified for a long time, little is known about how a population adopts a new convention, due to the difficulties of finding representative data. Here, we address this issue by looking at changes that occurred to 2,541 orthographic and lexical norms in English and Spanish through the analysis of a large corpora of books published between the years 1800 and 2008. We detect three markedly distinct patterns in the data, depending on whether the behavioral change results from the action of a formal institution, an informal authority, or a spontaneous process of unregulated evolution. We propose a simple evolutionary model able to capture all of the observed behaviors, and we show that it reproduces quantitatively the empirical data. This work identifies general mechanisms of norm change, and we anticipate that it will be of interest to researchers investigating the cultural evolution of language and, more broadly, human collective behavior.

The emergence of consensus: a primer

The origin of population-scale coordination has puzzled philosophers and scientists for centuries. Recently, game theory, evolutionary approaches and complex systems science have provided quantitative insights on the mechanisms of social consensus. However, the literature is vast and widely scattered across fields, making it hard for the single researcher to navigate it. This short review aims to provide a compact overview of the main dimensions over which the debate has unfolded and to discuss some representative examples. It focuses on those situations in which consensus emerges 'spontaneously' in the absence of centralized institutions and covers topics that include the macroscopic consequences of the different microscopic rules of behavioural contagion, the role of social networks and the mechanisms that prevent the formation of a consensus or alter it after it has emerged. Special attention is devoted to the recent wave of experiments on the emergence of consensus in social systems.

Domain learning naming game for color categorization

Naming game simulates the evolution of vocabulary in a population of agents. Through pairwise interactions in the games, agents acquire a set of vocabulary in their memory for object naming. The existing model confines to a one-to-one mapping between a name and an object. Focus is usually put onto name consensus in the population rather than knowledge learning in agents, and hence simple learning model is usually adopted. However, the cognition system of human being is much more complex and knowledge is usually presented in a complicated form. Therefore, in this work, we extend the agent learning model and design a new game to incorporate domain learning, which is essential for more complicated form of knowledge. In particular, we demonstrate the evolution of color categorization and naming in a population of agents. We incorporate the human perceptive model into the agents and introduce two new concepts, namely subjective perception and subliminal stimulation, in domain learning. Simulation results show that, even without any supervision or pre-requisition, a consensus of a color naming system can be reached in a population solely via the interactions. Our work confirms the importance of society interactions in color categorization, which is a long debate topic in human cognition. Moreover, our work also demonstrates the possibility of cognitive system development in autonomous intelligent agents.

Effects of communication burstiness on consensus formation and tipping points in social dynamics

Current models for opinion dynamics typically utilize a Poisson process for speaker selection, making the waiting time between events exponentially distributed. Human interaction tends to be bursty though, having higher probabilities of either extremely short waiting times or long periods of silence. To quantify the burstiness effects on the dynamics of social models, we place in competition two groups exhibiting different speakers' waiting-time distributions. These competitions are implemented in the binary naming game and show that the relevant aspect of the waiting-time distribution is the density of the head rather than that of the tail. We show that even with identical mean waiting times, a group with a higher density of short waiting times is favored in competition over the other group. This effect remains in the presence of nodes holding a single opinion that never changes, as the fraction of such committed individuals necessary for achieving consensus decreases dramatically when they have a higher head density than the holders of the competing opinion. Finally, to quantify differences in burstiness, we introduce the expected number of small-time activations and use it to characterize the early-time regime of the system.

The impact of variable commitment in the Naming Game on consensus formation

The Naming Game has proven to be an important model of opinion dynamics in complex networks. It is significantly enriched by the introduction of nodes committed to a single opinion. The resulting model is still simple but captures core concepts of opinion dynamics in networks. This model limitation is rigid commitment which never changes. Here we study the effect that making commitment variable has on the dynamics of the system. Committed nodes are assigned a commitment strength, w, defining their willingness to lose (in waning), gain (for increasing) or both (in variable) commitment to an opinion. Such model has committed nodes that can stick to a single opinion for some time without losing their flexibility to change it in the long run. The traditional Naming Game corresponds to setting w at infinity. A change in commitment strength impacts the critical fraction of population necessary for a minority consensus. Increasing w lowers critical fraction for waning commitment but increases this fraction for increasing commitment. Further, we show that if different nodes have different values of w, higher standard deviation of w increases the critical fraction for waning commitment and decrease this fraction for increasing commitment.

Collective Dynamics of Belief Evolution under Cognitive Coherence and Social Conformity

Human history has been marked by social instability and conflict, often driven by the irreconcilability of opposing sets of beliefs, ideologies, and religious dogmas. The dynamics of belief systems has been studied mainly from two distinct perspectives, namely how cognitive biases lead to individual belief rigidity and how social influence leads to social conformity. Here we propose a unifying framework that connects cognitive and social forces together in order to study the dynamics of societal belief evolution. Each individual is endowed with a network of interacting beliefs that evolves through interaction with other individuals in a social network. The adoption of beliefs is affected by both internal coherence and social conformity. Our framework may offer explanations for how social transitions can arise in otherwise homogeneous populations, how small numbers of zealots with highly coherent beliefs can overturn societal consensus, and how belief rigidity protects fringe groups and cults against invasion from mainstream beliefs, allowing them to persist and even thrive in larger societies. Our results suggest that strong consensus may be insufficient to guarantee social stability, that the cognitive coherence of belief-systems is vital in determining their ability to spread, and that coherent belief-systems may pose a serious problem for resolving social polarization, due to their ability to prevent consensus even under high levels of social exposure. We argue that the inclusion of cognitive factors into a social model could provide a more complete picture of collective human dynamics.

Analysis of the high-dimensional naming game with committed minorities

The naming game has become an archetype for linguistic evolution and mathematical social behavioral analysis. In the model presented here, there are N individuals and K words. Our contribution is developing a robust method that handles the case when K=O(N). The initial condition plays a crucial role in the ordering of the system. We find that the system with high Shannon entropy has a higher consensus time and a lower critical fraction of zealots compared to low-entropy states. We also show that the critical number of committed agents decreases with the number of opinions and grows with the community size for each word. These results complement earlier conclusions that diversity of opinion is essential for evolution; without it, the system stagnates in the status quo [S. A. Marvel et al., Phys. Rev. Lett. 109, 118702 (2012)PRLTAO0031-900710.1103/PhysRevLett.109.118702]. In contrast, our results suggest that committed minorities can more easily conquer highly diverse systems, showing them to be inherently unstable.