Analysis of the high-dimensional naming game with committed minorities

Pickering, W. M.; Szymański, Bolesław K.; Lim, Chjan C.

doi:10.1103/physreve.93.052311

Cited by 22 publications

(28 citation statements)

References 37 publications

(61 reference statements)

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“…At the early time t = 1, {x} looks nearly uniform in all cases, but then evolves towards a distribution that depends on ∆. In the noiseless case ∆ = 0 (left column) the system reaches a final delta distribution corresponding to a configuration where all particles are in the same states cannot longer evolve, and corresponds to one of the S = 100 possible absorbing states of the MSVM [10,11]. Instead, for ∆ = 1 (center column) the distribution {x} becomes narrower with time and seems to adopt a bell shape for long times, while for ∆ = 5 (right column) {x} looks quite uniform for any time.…”

Section: Simulation Resultsmentioning

confidence: 99%

“…More recently, this type of social imitation rule was introduced to study the flocking dynamics of a large group of animals [9], for instance birds, where each bird aligns its flying direction with that of a nearby random bird. In the case of all-to-all interactions, this flocking voter model is equivalent to the well known multi-state voter model (MSVM) [10,11] for opinion dynamics, where the moving direction of a bird is associated to its opinion or decision. The MSVM considers a population composed by a fixed number of agents (voters) subject to pairwise interactions, where each voter can hold one of S possible states that represent different opinions or positions on a given issue.…”

Section: Introductionmentioning

confidence: 99%

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Multistate voter model with imperfect copying

2019

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The voter model with multiple states has found applications in areas as diverse as population genetics, opinion formation, species competition and language dynamics, among others. In a single step of the dynamics, an individual chosen at random copies the state of a random neighbor in the population. In this basic formulation it is assumed that the copying is perfect, and thus an exact copy of an individual is generated at each time step. Here we introduce and study a variant of the multi-state voter model in mean-field that incorporates a degree of imperfection or error in the copying process, which leaves the states of the two interacting individuals similar but not exactly equal. This dynamics can also be interpreted as a perfect copying with the addition of noise; a minimalistic model for flocking. We found that the ordering properties of this multi-state noisy voter model, measured by a parameter ψ in [0, 1], depend on the amplitude η of the copying error or noise and the population size N . In the case of perfect copying η = 0 the system reaches an absorbing configuration with complete order (ψ = 1) for all values of N . However, for any degree of imperfection η > 0, we show that the average value of ψ at the stationary state decreases with N as ψ ≃ 6/(π 2 η 2 N ) for η ≪ 1 and η 2 N 1, and thus the system becomes totally disordered in the thermodynamic limit N → ∞. We also show that ψ ≃ 1 − 1.64 η 2 N in the vanishing small error limit η → 0, which implies that complete order is never achieved for η > 0. These results are supported by Monte Carlo simulations of the model, which allow to study other scenarios as well.

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Section: Simulation Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Multistate voter model with imperfect copying

2019

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“…Those realizations were not considered in the calculation of τ . In the static case scenario v = 0 (circles) τ decreases with ρ and approaches the MF value (τ MF ≃ 2N = 1200) for large N [8,9] (horizontal dashed line). As discussed in section 3, the MF limiting case is obtained when L ≤ √ 2 and thus each particle falls in the interaction range of any other particle.…”

Section: Consensus Timesmentioning

confidence: 99%

Flocking dynamics with voter-like interactions

Baglietto¹,

Vázquez²

2018

J. Stat. Mech.

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We study the collective motion of a large set of self-propelled particles subject to voter-like interactions. Each particle moves on a two-dimensional space at a constant speed in a direction that is randomly assigned initially. Then, at every step of the dynamics, each particle adopts the direction of motion of a randomly chosen neighboring particle. We investigate the time evolution of the global alignment of particles measured by the order parameter ϕ, until complete order ϕ = 1.0 is reached (polar consensus). We find that ϕ increases as t 1/2 for short times and approaches exponentially fast to 1.0 for long times. Also, the mean time to consensus τ varies nonmonotonically with the density of particles ρ, reaching a minimum at some intermediate density ρ min . At ρ min , the mean consensus time scales with the system size N as τ min ∼ N 0.765 , and thus the consensus is faster than in the case of all-to-all interactions (large ρ) where τ = 2N . We show that the fast consensus, also observed at intermediate and high densities, is a consequence of the segregation of the system into clusters of equally-oriented particles which breaks the balance of transitions between directional states in well mixed systems.

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“…My alarming got quite a large media impact echoing to the overall feeling that democratic countries were being swept within a wave of rising populism. These works subscribe along the current active study of opinion dynamics and voting [9][10][11][12][13][14][15][16][17][18][19][20][21] within the field of sociophysics [22,23].…”

Section: Introductionmentioning

confidence: 99%

Unavowed Abstention Can Overturn Poll Predictions

Galam

2018

Front. Phys.

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I revisit the 2017 French Presidential election which opposed the far right National Front candidate Marine Le Pen against the center candidate Emmanuel Macron. While voting intentions for Le Pen stuck below 50% and polls kept predicting her failure, I warned on the emergence of a novel phenomenon I defined as unavowed abstention, which could suddenly reverse the ranking at Le Pen benefit on the voting day. My warning got a massive media coverage. She eventually lost the runoff at a score worse than predicted by the polls. Using a quantitative mathematical framing, which reveals the existence of tipping points in respective turnouts, I show that the predicted phenomenon of unavowed abstention did happen. But instead of shattering the expected outcome, against all odds it occurred at Le Pen expense, therefore without impact on the final outcome. The results shed a new light on other national cases such as Obama and Trump victories in the US.

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Analysis of the high-dimensional naming game with committed minorities

Cited by 22 publications

References 37 publications

Multistate voter model with imperfect copying

Multistate voter model with imperfect copying

Flocking dynamics with voter-like interactions

Unavowed Abstention Can Overturn Poll Predictions

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