Reduction from non-Markovian to Markovian dynamics: the case of aging in the noisy-voter model

Peralta, Antonio F.; Khalil, Nagi; Toral, Raúl

doi:10.1088/1742-5468/ab6847

Cited by 18 publications

(20 citation statements)

References 59 publications

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“…Note that, due to the symmetries of the model, the function υ(x) can be expanded in a Taylor series containing only odd powers of (x − 1/2). Furthermore, the steady-state probability of finding n agents in state ⊕ can be written, in the limit of large N, in a largedeviation form P st (n) ∝ e −NV (n/N ) , with a potential function [28] V…”

Section: Mean-field Solutionmentioning

confidence: 99%

Pair approximation for the noisy thresholdq-voter model

et al. 2020

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In the standard q-voter model, a given agent can change its opinion only if there is a full consensus of the opposite opinion within a group of influence of size q. A more realistic extension is the threshold q voter, where a minimal agreement (at least 0 < q 0 q opposite opinions) is sufficient to flip the central agent's opinion, including also the possibility of independent (nonconformist) choices. Variants of this model including nonconformist behavior have been previously studied in fully connected networks (mean-field limit). Here we investigate its dynamics in random networks. Particularly, while in the mean-field case it is irrelevant whether repetitions in the influence group are allowed, we show that this is not the case in networks, and we study the impact of both cases, with or without repetition. Furthermore, the results of computer simulations are compared with the predictions of the pair approximation derived for uncorrelated networks of arbitrary degree distributions.

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Section: Mean-field Solutionmentioning

confidence: 99%

Pair approximation for the noisy thresholdq-voter model

et al. 2020

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“…Owing to its simplicity and analytical tractability, the NVM has been studied and generalized [15][16][17][18][19][20][21][22][23][24][25][26][27] in various different directions. This includes nonlinearity in the imitation rates [28,29], memory effects [30][31][32][33], the introduction of contrarians [34] or zealots [35], and multi-state noisy voter models [36].…”

Section: Introductionmentioning

confidence: 99%

Zealots in the mean-field noisy voter model

2018

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The influence of zealots on the noisy voter model is studied theoretically and numerically at the mean-field level. The noisy voter model is a modification of the voter model that includes a second mechanism for transitions between states: apart from the original herding processes, voters may change their states because of an intrinsic, noisy in origin source. By increasing the importance of the noise with respect to the herding, the system exhibits a finite-size phase transition from a quasiconsensus state, where most of the voters share the same opinion, to a one with coexistence. Upon introducing some zealots, or voters with fixed opinion, the latter scenario may change significantly. We unveil the new situations by carrying out a systematic numerical and analytical study of a fully connected network for voters, but allowing different voters to be directly influenced by different zealots. We show that this general system is equivalent to a system of voters without zealots, but with heterogeneous values of their parameters characterizing herding and noisy dynamics. We find excellent agreement between our analytical and numerical results. Noise and herding/zealotry acting together in the voter model yields not a trivial mixture of the scenarios with the two mechanisms acting alone: it represents a situation where the global-local (noise-herding) competitions is coupled to a symmetry breaking (zealots). In general, the zealotry enhances the effective noise of the system, which may destroy the original quasi-consensus state, and can introduce a bias towards the opinion of the majority of zealots, hence breaking the symmetry of the system and giving rise to new phases. In the most general case we find two different transitions: a discontinuous transition form an asymmetric bimodal phase to an extreme asymmetric phase and a second continuous transition from the extreme asymmetric phase to an asymmetric unimodal phase.

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“…An alternative implementation of algorithmic bias in binary-state models has been proposed in [24]. In this case, the social platform records information about all the previous opinions of individuals, and then influences them to keep the opinion that has been held for the longest time, similarly to a memory or 'inertia' effect [25][26][27]. All these implementations of algorithmic bias in opinion dynamics modeling suggest that polarization is a consequence of both the social behavior of individuals and the content filtering algorithms constraining their actions.…”

Section: Introductionmentioning

confidence: 99%

Opinion formation on social networks with algorithmic bias: Dynamics and bias imbalance

Peralta¹,

Kertész²,

Iñiguez³

2021

Preprint

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We investigate opinion dynamics and information spreading on networks under the influence of content filtering technologies. The filtering mechanism, present in many online social platforms, reduces individuals' exposure to disagreeing opinions, producing algorithmic bias. We derive evolution equations for global opinion variables in the presence of algorithmic bias, network community structure, noise (independent behavior of individuals), and pairwise or group interactions. We consider the case where the social platform shows a predilection for one opinion over its opposite, unbalancing the dynamics in favor of that opinion. We show that if the imbalance is strong enough, it may determine the final global opinion and the dynamical behavior of the population. We find a complex phase diagram including phases of coexistence, consensus, and polarization of opinions as possible final states of the model, with phase transitions of different order between them. The fixed point structure of the equations determines the dynamics to a large extent. We focus on the time needed for convergence and conclude that this quantity varies within a wide range, showing occasionally signatures of critical slowing down and meta-stability.

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Reduction from non-Markovian to Markovian dynamics: the case of aging in the noisy-voter model

Cited by 18 publications

References 59 publications

Pair approximation for the noisy thresholdq-voter model

Pair approximation for the noisy thresholdq-voter model

Zealots in the mean-field noisy voter model

Opinion formation on social networks with algorithmic bias: Dynamics and bias imbalance

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