Compartmental voter model

Kononovičius, Aleksejus

doi:10.1088/1742-5468/ab409b

Cited by 16 publications

(15 citation statements)

References 56 publications

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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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Section: Introductionmentioning

confidence: 99%

Zealots in the mean-field noisy voter model

2018

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“…This has lead us to explore and model statistical properties of spatially heterogeneous electoral data [ 43 ]. As we have noticed segregation effects in the electoral data, we have continued our investigation by considering the migratory nature of census and electoral data [ 44 ]. Similar approaches were taken by others as well.…”

Section: Agent-based Model Of the Long-range Memory In The Financial Marketsmentioning

confidence: 99%

“…With time, we have developed more complicated ABMs to account for the separation of time scales and order flow [ 41 , 42 ]. We have even branched out into sociophysics [ 43 , 44 , 45 , 46 ] as we have understood that the herding ABM we used to model the financial market is essentially equivalent to the well-known voter model [ 47 , 48 , 49 ].…”

Section: Introductionmentioning

confidence: 99%

Understanding the Nature of the Long-Range Memory Phenomenon in Socioeconomic Systems

Kazakevičius

Kononovičius

Kaulakys

et al. 2021

Entropy

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In the face of the upcoming 30th anniversary of econophysics, we review our contributions and other related works on the modeling of the long-range memory phenomenon in physical, economic, and other social complex systems. Our group has shown that the long-range memory phenomenon can be reproduced using various Markov processes, such as point processes, stochastic differential equations, and agent-based models—reproduced well enough to match other statistical properties of the financial markets, such as return and trading activity distributions and first-passage time distributions. Research has lead us to question whether the observed long-range memory is a result of the actual long-range memory process or just a consequence of the non-linearity of Markov processes. As our most recent result, we discuss the long-range memory of the order flow data in the financial markets and other social systems from the perspective of the fractional Lèvy stable motion. We test widely used long-range memory estimators on discrete fractional Lèvy stable motion represented by the auto-regressive fractionally integrated moving average (ARFIMA) sample series. Our newly obtained results seem to indicate that new estimators of self-similarity and long-range memory for analyzing systems with non-Gaussian distributions have to be developed.

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“…The derivation of this simple, explicit, form for the attractor is probably not completely satisfactory. Nevertheless, it is possible to improve this approximate equation by imposing that the first two coefficients of the expansion of F (x) around the fixed point x = 1/2, F (x) = ε 1 (x − x) + ε 3 (x − x) 3 , coincide with the first two coefficients of the exact expansion of the attractor around the same point, as computed in Appendix A. It turns out that this can be achieved by including a constant C of order 1 in the definition of F (x) in Eq.…”

Section: Justification Of the Validity Of The Adiabatic Eliminationmentioning

confidence: 99%

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

Peralta¹,

Khalil²,

Toral³

2020

J. Stat. Mech.

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We study memory dependent binary-state dynamics, focusing on the noisy-voter model. This is a non-Markovian process if we consider the set of binary states of the population as the description variables, or Markovian if we incorporate "age", related to the time one has spent holding the same state, as a part of the description. We show that, in some cases, the model can be reduced to an effective Markovian process, where the age distribution of the population rapidly equilibrates to a quasi-steady state, while the global state of the system is out of equilibrium. This effective Markovian process shares the same phenomenology of the non-linear noisyvoter model and we establish a clear parallelism between these two extensions of the noisy-voter model.

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Compartmental voter model

Cited by 16 publications

References 56 publications

Zealots in the mean-field noisy voter model

Zealots in the mean-field noisy voter model

Understanding the Nature of the Long-Range Memory Phenomenon in Socioeconomic Systems

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

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