Opinion dynamics and influencing on random geometric graphs

Curvature-driven growth and interfacial noise in the voter model with self-induced zealots

We introduce a variant of the voter model in which agents may have different degrees of confidence in their opinions. Those with low confidence are normal voters whose state can change upon a single contact with a different neighboring opinion. However, confidence increases with opinion reinforcement, and above a certain threshold, these agents become zealots, irreducible agents who do not change their opinion. We show that both strategies, normal voters and zealots, may coexist (in the thermodynamical limit), leading to competition between two different kinetic mechanisms: curvature-driven growth and interfacial noise. The kinetically constrained zealots are formed well inside the clusters, away from the different opinions at the surfaces that help limit their confidence. Normal voters concentrate in a region around the interfaces, and their number, which is related to the distance between the surface and the zealotry bulk, depends on the rate at which the confidence changes. Despite this interface being rough and fragmented, typical of the voter model, the presence of zealots in the bulk of these domains induces a curvature-driven dynamics, similar to the low temperature coarsening behavior of the nonconserved Ising model after a temperature quench.

Percolation on feature-enriched interconnected systems

Percolation is an emblematic model to assess the robustness of interconnected systems when some of their components are corrupted. It is usually investigated in simple scenarios, such as the removal of the system's units in random order, or sequentially ordered by specific topological descriptors. However, in the vast majority of empirical applications, it is required to dismantle the network following more sophisticated protocols, for instance, by combining topological properties and non-topological node metadata. We propose a novel mathematical framework to fill this gap: networks are enriched with features and their nodes are removed according to the importance in the feature space. We consider features of different nature, from ones related to the network construction to ones related to dynamical processes such as epidemic spreading. Our framework not only provides a natural generalization of percolation but, more importantly, offers an accurate way to test the robustness of networks in realistic scenarios.

Consensus dynamics in online collaboration systems

BACKGROUND

In this paper, we study the process of opinion dynamics and consensus building in online collaboration systems, in which users interact with each other following their common interests and their social profiles. Specifically, we are interested in how users similarity and their social status in the community, as well as the interplay of those two factors, influence the process of consensus dynamics.

METHODS

For our study, we simulate the diffusion of opinions in collaboration systems using the well-known Naming Game model, which we extend by incorporating an interaction mechanism based on user similarity and user social status. We conduct our experiments on collaborative datasets extracted from the Web.

RESULTS

Our findings reveal that when users are guided by their similarity to other users, the process of consensus building in online collaboration systems is delayed. A suitable increase of influence of user social status on their actions can in turn facilitate this process.

CONCLUSIONS

In summary, our results suggest that achieving an optimal consensus building process in collaboration systems requires an appropriate balance between those two factors.

Navigability of Random Geometric Graphs in the Universe and Other Spacetimes

Random geometric graphs in hyperbolic spaces explain many common structural and dynamical properties of real networks, yet they fail to predict the correct values of the exponents of power-law degree distributions observed in real networks. In that respect, random geometric graphs in asymptotically de Sitter spacetimes, such as the Lorentzian spacetime of our accelerating universe, are more attractive as their predictions are more consistent with observations in real networks. Yet another important property of hyperbolic graphs is their navigability, and it remains unclear if de Sitter graphs are as navigable as hyperbolic ones. Here we study the navigability of random geometric graphs in three Lorentzian manifolds corresponding to universes filled only with dark energy (de Sitter spacetime), only with matter, and with a mixture of dark energy and matter. We find these graphs are navigable only in the manifolds with dark energy. This result implies that, in terms of navigability, random geometric graphs in asymptotically de Sitter spacetimes are as good as random hyperbolic graphs. It also establishes a connection between the presence of dark energy and navigability of the discretized causal structure of spacetime, which provides a basis for a different approach to the dark energy problem in cosmology.

Analysis and application of opinion model with multiple topic interactions

To reveal heterogeneous behaviors of opinion evolution in different scenarios, we propose an opinion model with topic interactions. Individual opinions and topic features are represented by a multidimensional vector. We measure an agent's action towards a specific topic by the product of opinion and topic feature. When pairs of agents interact for a topic, their actions are introduced to opinion updates with bounded confidence. Simulation results show that a transition from a disordered state to a consensus state occurs at a critical point of the tolerance threshold, which depends on the opinion dimension. The critical point increases as the dimension of opinions increases. Multiple topics promote opinion interactions and lead to the formation of macroscopic opinion clusters. In addition, more topics accelerate the evolutionary process and weaken the effect of network topology. We use two sets of large-scale real data to evaluate the model, and the results prove its effectiveness in characterizing a real evolutionary process. Our model achieves high performance in individual action prediction and even outperforms state-of-the-art methods. Meanwhile, our model has much smaller computational complexity. This paper provides a demonstration for possible practical applications of theoretical opinion dynamics.

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.

Epidemic spreading in random rectangular networks

The use of network theory to model disease propagation on populations introduces important elements of reality to the classical epidemiological models. The use of random geometric graphs (RGGs) is one of such network models that allows for the consideration of spatial properties on disease propagation. In certain real-world scenarios—like in the analysis of a disease propagating through plants—the shape of the plots and fields where the host of the disease is located may play a fundamental role in the propagation dynamics. Here we consider a generalization of the RGG to account for the variation of the shape of the plots or fields where the hosts of a disease are allocated. We consider a disease propagation taking place on the nodes of a random rectangular graph and we consider a lower bound for the epidemic threshold of a susceptible-infected-susceptible model or a susceptible-infected-recovered model on these networks. Using extensive numerical simulations and based on our analytical results we conclude that (ceteris paribus) the elongation of the plot or field in which the nodes are distributed makes the network more resilient to the propagation of a disease due to the fact that the epidemic threshold increases with the elongation of the rectangle. These results agree with accumulated empirical evidence and simulation results about the propagation of diseases on plants in plots or fields of the same area and different shapes.

Modelling Adaptive Learning Behaviours for Consensus Formation in Human Societies

Learning is an important capability of humans and plays a vital role in human society for forming beliefs and opinions. In this paper, we investigate how learning affects the dynamics of opinion formation in social networks. A novel learning model is proposed, in which agents can dynamically adapt their learning behaviours in order to facilitate the formation of consensus among them, and thus establish a consistent social norm in the whole population more efficiently. In the model, agents adapt their opinions through trail-and-error interactions with others. By exploiting historical interaction experience, a guiding opinion, which is considered to be the most successful opinion in the neighbourhood, can be generated based on the principle of evolutionary game theory. Then, depending on the consistency between its own opinion and the guiding opinion, a focal agent can realize whether its opinion complies with the social norm (i.e., the majority opinion that has been adopted) in the population, and adapt its behaviours accordingly. The highlight of the model lies in that it captures the essential features of people’s adaptive learning behaviours during the evolution and formation of opinions. Experimental results show that the proposed model can facilitate the formation of consensus among agents, and some critical factors such as size of opinion space and network topology can have significant influences on opinion dynamics.

Competing effects of social balance and influence

We study a three-state (leftist, rightist, centrist) model that couples the dynamics of social balance with an external deradicalizing field. The mean-field analysis shows that there exists a critical value of the external field p_{c} such that for a weak external field (p<p_{c}), the system exhibits a metastable fixed point and a saddle point in addition to a stable fixed point. However, if the strength of the external field is sufficiently large (p>p_{c}), there is only one (stable) fixed point, which corresponds to an all-centrist consensus state (absorbing state). In the weak-field regime, the convergence time to the absorbing state is evaluated using the quasistationary distribution and is found to be in agreement with the results obtained by numerical simulations.

The influence of social status and network structure on consensus building in collaboration networks

In this paper, we analyze the influence of social status on opinion dynamics and consensus building in collaboration networks. To that end, we simulate the diffusion of opinions in empirical networks and take into account both the network structure and the individual differences of people reflected through their social status. For our simulations, we adapt a well-known Naming Game model and extend it with the Probabilistic Meeting Rule to account for the social status of individuals participating in a meeting. This mechanism is sufficiently flexible and allows us to model various society forms in collaboration networks, as well as the emergence or disappearance of social classes. In particular, we are interested in the way how these society forms facilitate opinion diffusion. Our experimental findings reveal that (i) opinion dynamics in collaboration networks is indeed affected by the individuals’ social status and (ii) this effect is intricate and non-obvious. Our results suggest that in most of the networks the social status favors consensus building. However, relying on it too strongly can also slow down the opinion diffusion, indicating that there is a specific setting for an optimal benefit of social status on the consensus building. On the other hand, in networks where status does not correlate with degree or in networks with a positive degree assortativity consensus is always reached quickly regardless of the status.