Ordering dynamics of the multi-state voter model

Starnini, Michele; Baronchelli, Andrea; Pastor-Satorras, Romualdo

doi:10.1088/1742-5468/2012/10/p10027

Cited by 41 publications

(50 citation statements)

References 31 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…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%

“…For the noiseless case ∆ = 0 the model is equivalent to the MSVM recently studied in the literature [10,11] where, in the above example, particle i simply jumps to the site occupied by particle j and stays there. In this case, given that the system is only driven by the stochastic nature of the copying process (the so called genetic drift in population genetics), a site that becomes empty remains empty afterwards, as particles can jump to occupied sites only.…”

Section: The Modelmentioning

confidence: 99%

See 1 more Smart Citation

Multistate voter model with imperfect copying

2019

View full text Add to dashboard Cite

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.

show abstract

Section: Simulation Resultsmentioning

confidence: 99%

Section: The Modelmentioning

confidence: 99%

Multistate voter model with imperfect copying

2019

View full text Add to dashboard Cite

show abstract

“…For example, decision making systems (e.g., neural or animal groups) in nature can be offered multiple options. Numerical simulations, and potentially limited analyses, could be conducted for a dynamical model interpolating between the multistate voter model [35] and a generalization of the Potts model [36].…”

Section: -4mentioning

confidence: 99%

Heterogeneous Preference and Local Nonlinearity in Consensus Decision Making

et al. 2016

View full text Add to dashboard Cite

In recent years, a large body of research has focused on unveiling the fundamental physical processes that living systems utilize to perform functions, such as coordinated action and collective decision making. Here, we demonstrate that important features of collective decision making among higher organisms are captured effectively by a novel formulation of well-characterized physical spin systems, where the spin state is equivalent to two opposing preferences, and a bias in the preferred state represents the strength of individual opinions. We reveal that individuals (spins) without a preference (unbiased or uninformed) play a central role in collective decision making, both in maximizing the ability of the system to achieve consensus (via enhancement of the propagation of spin states) and in minimizing the time taken to do so (via a process reminiscent of stochastic resonance). Which state (option) is selected collectively, however, is shown to depend strongly on the nonlinearity of local interactions. Relatively linear social response results in unbiased individuals reinforcing the majority preference, even in the face of a strongly biased numerical minority (thus promoting democratic outcomes). If interactions are highly nonlinear, however, unbiased individuals exert the opposite influence, promoting a strongly biased minority and inhibiting majority preference. These results enhance our understanding of physical computation in biological collectives and suggest new avenues to explore in the collective dynamics of spin systems. DOI: 10.1103/PhysRevLett.116.038701 Collective decision making is ubiquitous across cellular [1,2], animal [3], human [4,5], and engineered systems [6]. Despite varying greatly in terms of the type and composition of components (agents), common dynamical features allow collectives to make rapid, accurate decisions even in complex environments or amidst conflicting needs [7]. The dynamics of populations of neurons, for example, have been precisely related to binary "spins" (spikes) communicating via pairwise interactions [8,9], a characteristic of models employed widely in statistical physics. Neural dynamics also exhibit striking parallels with collective decision making among organisms themselves, such as the process by which honeybee colonies decide among alternative nest sites [10,11]. Thus, by abstracting microscopic details and relating biological computation directly to that among physical particles, we can obtain considerable insight regarding collective behavior and possibly reveal novel aspects of physical systems.Here, we explore the dynamics of populations making collective decisions. Despite being inspired by recent experimental data from animal groups, we deliberately shift the focus from understanding collective decisions in a particular experimental context to a general understanding of the underlying dynamical interplay among population constitution, space, and the character of local interactions.In doing so we demonstrate that many of the complex, and possibly coun...

show abstract

“…, Q}. The ordering dynamics of the model with no zealots has been discussed in [15], while a variant with committed agents on a weighted network has been more recently studied in [16]. Here, we are interested in a simple formulation of the model with N agents on the complete graph, for which we expect the mean field description to work well.…”

Section: Example 2: Multi-state Voter Model With Zealotsmentioning

confidence: 99%

“…If we define the truncated Taylor expansion 15) then q n,Q−1 = F n (1) represents the total number of matrix rows α for which χ αγ really needs to be computed. In Table 1, we report q n,Q−1 for the first few values of n and Q.…”

Section: Permutational Symmetry Of the Coefficients χ αγmentioning

confidence: 99%

Use of dirichlet distributions and orthogonal projection techniques for the fluctuation analysis of steady-state multivariate birth–death systems

Palombi

Toti

2015

Int. J. Mod. Phys. C

View full text Add to dashboard Cite

Approximate weak solutions of the Fokker-Planck equation represent a useful tool to analyze the equilibrium fluctuations of birth-death systems, as they provide a quantitative knowledge lying in between numerical simulations and exact analytic arguments. In the present paper, we adapt the general mathematical formalism known as the Ritz-Galerkin method for partial differential equations to the Fokker-Planck equation with time-independent polynomial drift and diffusion coefficients on the simplex. Then, we show how the method works in two examples, namely the binary and multistate voter models with zealots.

show abstract

Ordering dynamics of the multi-state voter model

Cited by 41 publications

References 31 publications

Multistate voter model with imperfect copying

Multistate voter model with imperfect copying

Heterogeneous Preference and Local Nonlinearity in Consensus Decision Making

Use of dirichlet distributions and orthogonal projection techniques for the fluctuation analysis of steady-state multivariate birth–death systems

Contact Info

Product

Resources

About