Biased-voter model: How persuasive a small group can be?

Czaplicka, Agnieszka; Charalambous, Christos; Toral, Raúl; Miguel, M. San

doi:10.1016/j.chaos.2022.112363

Cited by 6 publications

(10 citation statements)

References 48 publications

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“…Using these transition probabilities, the evolution of the variable σ can be treated as a random walk. This random walk system coincides with the system of a biased voter model [18] (see appendix for the equivalence). In the same manner as [18], thus, we obtain the exit probability P +1 (σ) that a network with n nodes reaches consensus to state +1 (targeted state) and the time τ n (σ) to reach consensus in the continuous approximation with second order as…”

Section: Homogeneous Networkmentioning

confidence: 67%

“…Next, we consider heterogeneous networks in which the degree fluctuation cannot be ignored. In the mean-field approximation (see appendix) and the pair approximation (see [18]), P +1 and τ n are given as the same forms of equations ( 11) and ( 13) with an effective size µ 2 1 µ2 n are given as…”

Section: Homogeneous Networkmentioning

confidence: 99%

“…In this study, we treat the voter model with adversarial attacks in the mean-field theory, showing that the model is mathematically identical to the biased voter model [18]. In the same manner as [18], we obtain the exit probability of reaching the target state and the mean time to reach a consensus. The exit probability asymptotically reaches unity with an increase in the system size n given ϵ > 0.…”

Section: Introductionmentioning

confidence: 96%

“…In theoretical studies, the effect of zealot presence on the voter model has been investigated [12][13][14][15][16][17]. Recently, a variant of the voter model called the biased voter model has been proposed [18]. This model considers that un and (1 − u)n agents are biased and unbiased, respectively.…”

Section: Introductionmentioning

confidence: 99%

“…For unbiased agents, v = 0; that is, they copy the state of a random neighbor with a probability of 1/2. Czaplicka et al [18] has solved the biased voter model for networks in the mean-field and pair approximations and has shown that τ n scales as τ n ∼ (ln uvn)/uv. The probability of reaching the preferred state at the final state becomes unity for a sufficiently large n. The presence of biased agents drastically changes the behavior of voter dynamics.…”

Section: Introductionmentioning

confidence: 99%

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Crossover phenomenon in adversarial attacks on voter model

Mizutaka

2023

J. Phys. Complex.

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A recent study (Chiyomaru and Takemoto 2022 Phys. Rev. E 106 014301) considered adversarial attacks conducted to distort voter model dynamics in networks. This method intervenes in the interaction patterns of individuals and induces them to be in a target opinion state through a small perturbation ε. In this study, we investigate adversarial attacks on voter dynamics in random networks of finite size n. The exit probability P +1 to reach the target absorbing state and the mean time τ n to reach consensus are analyzed in the mean-field approximation. Given ε > 0, the exit probability P +1 converges asymptotically to unity as n increases. The mean time τ n to reach consensus scales as ( ln ϵ n ) / ϵ for homogeneous networks with a large finite n. By contrast, it scales as ( ln ( ϵ μ 1 2 n / μ 2 ) ) / ϵ for heterogeneous networks with a large finite n, where µ 1 and µ 2 represent the first and second moments of the degree distribution, respectively. Moreover, we observe the crossover phenomenon of τ n from a linear scale to a logarithmic scale and find n c o ∼ ϵ − 1 / α above which the state of all nodes becomes the target state in logarithmic time. Here, α = 1 for homogeneous networks and α = ( γ − 1 ) / 2 for scale-free networks with a degree exponent 2 < γ < 3 .

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Section: Homogeneous Networkmentioning

confidence: 67%

Section: Homogeneous Networkmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 96%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Crossover phenomenon in adversarial attacks on voter model

Mizutaka

2023

J. Phys. Complex.

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Time scales in the dynamics of political opinions and the voter model

Meyer,

Metzler

2024

New J. Phys.

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Opinions in human societies are measured by political polls on time scales ofmonths to years. Such opinion polls do not resolve the effects of individualinteractions but constitute a stochastic process. Voter models with zealots(individuals who do not change their opinions) can describe the mean-fielddynamics in systems where no consensus is reached. We show that for largepopulations, the voter model with zealots is equivalent to the noisy votermodel and it has a single characteristic time scale associated with thenumber of zealots in the population. We discuss which parameters areobservable in real data by analysing time series of approval ratings ofseveral political leaders that match the statistical behaviour of the votermodel using the technique of the time-averaged mean squared displacement.The characteristic time scale of political opinions in societies is around 12months, so it cannot be resolved by analysing election data, for which theresolution is several years. The effective population size in all fitteddata sets is much smaller than the real population size, which indicatespositive correlations of successive voter model steps. We also discussthe heterogeneity of voters as a cause of subdiffusion on long time scales,i.e., slow changes in the society.

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