The recent availability of huge high resolution datasets on human activities has revealed the heavy-tailed nature of the interevent time distributions. In social simulations of interacting agents the standard approach has been to use Poisson processes to update the state of the agents, which gives rise to very homogeneous activity patterns with a well defined characteristic interevent time. As a paradigmatic opinion model we investigate the voter model and review the standard update rules and propose two new update rules which are able to account for heterogeneous activity patterns. For the new update rules each node gets updated with a probability that depends on the time since the last event of the node, where an event can be an update attempt (exogenous update) or a change of state (endogenous update). We find that both update rules can give rise to power law interevent time distributions, although the endogenous one more robustly. Apart from that for the exogenous update rule and the standard update rules the voter model does not reach consensus in the infinite size limit, while for the endogenous update there exist a coarsening process that drives the system toward consensus configurations.
Reducibility of higher-order to pairwise interactions: Social impact models on hypergraphs
Institute for Cross-disciplinary Physics and Complex Systems IFISC (CSIC-UIB)（跨学科物理与复杂系统研究所 IFISC (CSIC-UIB)）；Instituto de Cálculo, FCEN, Universidad de Buenos Aires and CONICET（布宜诺斯艾利斯大学物理与数学学院计算研究所及阿根廷国家科学研究委员会）
Latane social impact theory predicts recruitment and supportive interactions being responsible for opinion formation. So far only recruitment interactions were considered in the voter models. Here we consider a noisy voter model with supportive interactions, which make voters less likely to change their opinions. This is similar to the voter models with freezing, but instead of interacting with their past selves voters get the support from their peers. We examine two different ways in which the support could be implemented: support deterring imitation as well as independence, support deterring…
The adaptive voter model allows for studying the interplay between homophily, the tendency of like-minded individuals to attract each other, and social influence, the tendency for connected individuals to influence each other. However, it relies on graphs, and thus, it only considers pairwise interactions. We develop a minimal extension of the adaptive voter model to hypergraphs to study the interactions of groups of arbitrary sizes using a threshold parameter. We study $S$-uniform hypergraphs as initial configurations. With numerical simulations, we find new phenomena not found in the counter…
We study the homogeneous symmetrical threshold model with independence (noise) by pair approximation and Monte Carlo simulations on Watts-Strogatz graphs. The model is a modified version of the famous Granovetter's threshold model: with probability $p$ a voter acts independently, i.e. takes randomly one of two states +/-; with complementary probability $1-p$, a voter takes a given state, if sufficiently large fraction (above a given threshold r) of individuals in its neighborhood is in this state. We show that the character of the phase transition, induced by the noise parameter p, depends on …
We introduce a socially motivated extension of the voter model in which individual voters are also influenced by two opposing, fixed-opinion news sources. These sources forestall consensus and instead drive the population to a politically polarized state, with roughly half the population in each opinion state. Two types social networks for the voters are studied: (a) the complete graph of $N$ voters and, more realistically, (b) the two-clique graph with $N$ voters in each clique. For the complete graph, many dynamical properties are soluble within an annealed-link approximation, in which a lin…
Majority-vote model is a much-studied model for social opinion dynamics of two competing opinions. With the recent appreciation that our social network comprises a variety of different layers forming a multiplex network, a natural question arises on how such multiplex interactions affect the social opinion dynamics and consensus formation. Here, the majority-vote model will be studied on multiplex networks to understand the effect of multiplexity on opinion dynamics. We will discuss how global consensus is reached by different types of voters: AND- and OR-rule voters on multiplex-network and v…
Many theoretical studies of the voter model (or variations thereupon) involve order parameters that are population-averaged. While enlightening, such quantities may obscure important statistical features that are only apparent on the level of the individual. In this work, we ask which factors contribute to a single voter maintaining a long-term statistical bias for one opinion over the other in the face of social influence. To this end, a modified version of the network voter model is proposed, which also incorporates quenched disorder in the interaction strengths between individuals and the p…
The voter model is a simple agent-based model to mimic opinion dynamics in social networks: a randomly chosen agent adopts the opinion of a randomly chosen neighbour. This process is repeated until a consensus emerges. Although the basic voter model is theoretically intriguing, it misses an important feature of real opinion dynamics: it does not distinguish between an agent's publicly expressed opinion and her inner conviction. A person may not feel comfortable declaring her conviction if her social circle appears to hold an opposing view. Here we introduce the Concealed Voter Model where we a…
We study the contrarian voter model for opinion formation in a society under the influence of an external oscillating propaganda and stochastic noise. Each agent of the population can hold one of two possible opinions on a given issue --against or in favor, and interacts with its neighbors following either an imitation dynamics (voter behavior) or an anti-alignment dynamics (contrarian behavior): each agent adopts the opinion of a random neighbor with a time-dependent probability $p(t)$, or takes the opposite opinion with probability $1-p(t)$. The imitation probability $p(t)$ is controlled by …
The flourishing of fake news is favored by recommendation algorithms of online social networks which, based on previous users activity, provide content adapted to their preferences and so create filter bubbles. We introduce an analytically tractable voter model with personalized information, in which an external field tends to align the agent opinion with the one she held more frequently in the past. Our model shows a surprisingly rich dynamics despite its simplicity. An analytical mean-field approach, confirmed by numerical simulations, allows us to build a phase diagram and to predict if and…
Over the past two decades, school shootings within the United States have repeatedly devastated communities and shaken public opinion. Many of these attacks appear to be `lone wolf' ones driven by specific individual motivations, and the identification of precursor signals and hence actionable policy measures would thus seem highly unlikely. Here, we take a system-wide view and investigate the timing of school attacks and the dynamical feedback with social media. We identify a trend divergence in which college attacks have continued to accelerate over the last 25 years while those carried out …
We investigate a nonlinear version of coevolving voter models, in which node states and network structure update as a coupled stochastic dynamical process. Most prior work on coevolving voter models has focused on linear update rules with fixed and homogeneous rewiring and adopting probabilities. By contrast, in our nonlinear version, the probability that a node rewires or adopts is a function of how well it "fits in" within its neighborhood. To explore this idea, we incorporate a parameter $σ$ that represents the fraction of neighbors of an updating node that share its opinion state. In an up…
