Propensity and stickiness in the naming game: tipping fractions of minorities

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.

Temporal network epistemology: On reaching consensus in a real-world setting

This work develops the concept of the temporal network epistemology model enabling the simulation of the learning process in dynamic networks. The results of the research, conducted on the temporal social network generated using the CogSNet model and on the static topologies as a reference, indicate a significant influence of the network temporal dynamics on the outcome and flow of the learning process. It has been shown that not only the dynamics of reaching consensus is different compared to baseline models but also that previously unobserved phenomena appear, such as uninformed agents or different consensus states for disconnected components. It has also been observed that sometimes only the change of the network structure can contribute to reaching consensus. The introduced approach and the experimental results can be used to better understand the way how human communities collectively solve both complex problems at the scientific level and to inquire into the correctness of less complex but common and equally important beliefs' spreading across entire societies.

Consensus and clustering in opinion formation on networks

Ideas that challenge the status quo either evaporate or dominate. The study of opinion dynamics in the socio-physics literature treats space as uniform and considers individuals in an isolated community, using ordinary differential equation (ODE) models. We extend these ODE models to include multiple communities and their interactions. These extended ODE models can be thought of as being ODEs on directed graphs. We study in detail these models to determine conditions under which there will be consensus and pluralism within the system. Most of the consensus/pluralism analysis is done for the case of one and two cities. However, we numerically show for the case of a symmetric cycle graph that an elementary bifurcation analysis provides insight into the phenomena of clustering. Moreover, for the case of a cycle graph with a hub, we discuss how having a sufficient proportion of zealots in the hub leads to the entire network sharing the opinion of the zealots.This article is part of the theme issue 'Stability of nonlinear waves and patterns and related topics'.

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.

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.

An Analysis of the Matching Hypothesis in Networks

The matching hypothesis in social psychology claims that people are more likely to form a committed relationship with someone equally attractive. Previous works on stochastic models of human mate choice process indicate that patterns supporting the matching hypothesis could occur even when similarity is not the primary consideration in seeking partners. Yet, most if not all of these works concentrate on fully-connected systems. Here we extend the analysis to networks. Our results indicate that the correlation of the couple's attractiveness grows monotonically with the increased average degree and decreased degree diversity of the network. This correlation is lower in sparse networks than in fully-connected systems, because in the former less attractive individuals who find partners are likely to be coupled with ones who are more attractive than them. The chance of failing to be matched decreases exponentially with both the attractiveness and the degree. The matching hypothesis may not hold when the degree-attractiveness correlation is present, which can give rise to negative attractiveness correlation. Finally, we find that the ratio between the number of matched couples and the size of the maximum matching varies non-monotonically with the average degree of the network. Our results reveal the role of network topology in the process of human mate choice and bring insights into future investigations of different matching processes in networks.