Voter model with non-Poissonian interevent intervals

Takaguchi, Taro; Masuda, Naoki

doi:10.1103/physreve.84.036115

Cited by 43 publications

(52 citation statements)

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“…Some models display a disorderorder transition [7][8][9][10][11][12], from a regime in which opinions are arbitrarily diverse to one in which most individuals hold the same opinion. Other models focus the emergence of a global consensus [13][14][15][16][17][18], in which all agents finally share the same opinion.In this Letter, we propose an opinion model based on the evolutionary game. Evolutionary game theory as a powerful mathematical framework, has been widely used to understand cooperative behavior [19,20], traffic flow [21,22], epidemic spreading [23,24] and so on.…”

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confidence: 99%

A consensus opinion model based on the evolutionary game

Yang

2016

EPL

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Abstract. -We propose a consensus opinion model based on the evolutionary game. In our model, both of the two connected agents receive a benefit if they have the same opinion, otherwise they both pay a cost. Agents update their opinions by comparing payo?s with neighbors. The opinion of an agent with higher payoff is more likely to be imitated. We apply this model in scalefree networks with tunable degree distribution. Interestingly, we find that there exists an optimal ratio of cost to benefit, leading to the shortest consensus time. Qualitative analysis is obtained by examining the evolution of the opinion clusters. Moreover, we find that the consensus time decreases as the average degree of the network increases, but increases with the noise introduced to permit irrational choices. The dependence of the consensus time on the network size is found to be a power-law form. For small or larger ratio of cost to benefit, the consensus time decreases as the degree exponent increases. However, for moderate ratio of cost to benefit, the consensus time increases with the degree exponent. Our results may provide new insights into opinion dynamics driven by the evolutionary game theory.Introduction. -The dynamics of opinion sharing and competing and the emergence of consensus have become an active topic of recent research in statistical and nonlinear physics [1]. One of the most successful methodologies used in opinion dynamics is agent-based modeling. The idea is to construct the computational devices (known as agents with some properties) and then simulate them in parallel to model the real phenomena. In physics this technique can be traced back to Monte Carlo simulations. A number of agent-based models have been proposed, which include the voter model [2], the majority rule-model [3,4], the bounded-confidence model [5] and the social impact model [6]. Some models display a disorderorder transition [7][8][9][10][11][12], from a regime in which opinions are arbitrarily diverse to one in which most individuals hold the same opinion. Other models focus the emergence of a global consensus [13][14][15][16][17][18], in which all agents finally share the same opinion.In this Letter, we propose an opinion model based on the evolutionary game. Evolutionary game theory as a powerful mathematical framework, has been widely used to understand cooperative behavior [19,20], traffic flow [21,22], epidemic spreading [23,24] and so on. However, to the best of our knowledge, the impact of evolutionary games on the

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confidence: 99%

A consensus opinion model based on the evolutionary game

Yang

2016

EPL

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“…[24,25,26]. Stark et al [24] introduced an update rule similar to our endogenous update and focused on consensus times.…”

Section: Discussionmentioning

confidence: 99%

“…We will see that the answer to this question depends crucially on the timing of interactions. Related work on the voter model, discussed later, include the papers by Stark et al [24], Baxter [25] and Takaguchi and Masuda [26]. In Sect.…”

Section: Introductionmentioning

confidence: 99%

Timing Interactions in Social Simulations: The Voter Model

Fernández-Gracia

Eguı́luz

Miguel

2013

Understanding Complex Systems

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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.

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“…Recently, the non-Markovian generalizations of the VM have been considered by introducing the latency period, the inertia effect, or non-Poissonian interevent interval distributions [23][24][25][26]. Non-Markovian dynamics of Ising-like systems with time-delayed interactions has also been studied in Refs.…”

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Time-Delay Induced Dimensional Crossover in the Voter Model

Kim

Noh

2017

Phys. Rev. Lett.

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We investigate the ordering dynamics of the voter model with time-delayed interactions. The dynamical process in the d-dimensional lattice is shown to be equivalent to the first passage problem of a random walker in the (d + 1)-dimensional strip of a finite width determined by the delay time. The equivalence reveals that the time delay leads to the dimensional crossover from the (d + 1)-dimensional scaling behavior at a short time to the d-dimensional scaling behavior at a long time. The scaling property in both regimes and the crossover time scale are obtained analytically, which are confirmed with the numerical simulation results.PACS numbers: 02.70.Rr Interactions among spatially distributed elements are subjected to a time delay. Any physical interaction propagates at a finite speed. Complex interactions among biological oscillators are mediated by biochemical materials moving at a finite speed [1]. Such a limited signal propagation speed causes a time delay. When a delay time is comparable to or larger than characteristic time scales, the time delay brings about rich phenomena. It leads to multistable synchronized states for phase oscillators [1][2][3][4][5][6][7], amplitude death for coupled limitcycle oscillators [8,9], stabilization of periodic orbits in chaotic systems [10], a resonant behavior in stochastic systems [11][12][13], dynamic instability in feedback control systems [14], a pattern formation in evolutionary game dynamics [15,16], and so on.In this Letter, we investigate the effects of time delay on the ordering dynamics in the context of the voter model (VM). The VM is a prototypical model for opinion dynamics [17][18][19][20][21][22]. In the VM, a voter takes one of the two opinions represented by an Ising spin variable. Each voter selects randomly one of its nearest neighbors and updates its spin state by copying that of the selected neighbor. Note that the interaction in the VM is instantaneous. In a realistic situation, however, an information propagates at a finite speed so that a voter can have an access to the past states of others. Thus, it is natural to consider the time-delayed interaction in the opinion dynamics, which has never been studied before. We introduce a time-delayed voter model (DVM) by incorporating the time delay into the VM and investigate the dynamic scaling behavior. We find that the time delay leads to the dimensional crossover: the DVM in d dimension displays the (d + 1)-dimensional scaling behavior at a short time and then d-dimensional scaling behavior at a long time.The time delay makes the dynamics of the DVM nonMarkovian. Recently, the non-Markovian generalizations of the VM have been considered by introducing the latency period, the inertia effect, or non-Poissonian interevent interval distributions [23][24][25][26]. Non-Markovian dynamics of Ising-like systems with time-delayed interactions has also been studied in Refs. [27][28][29]. Our study reveals a new aspect of time-delayed interactions.The DVM in the d-dimensional hypercube Z d is defined as fol...

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Voter model with non-Poissonian interevent intervals

Cited by 43 publications

References 37 publications

A consensus opinion model based on the evolutionary game

A consensus opinion model based on the evolutionary game

Timing Interactions in Social Simulations: The Voter Model

Time-Delay Induced Dimensional Crossover in the Voter Model

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