Ising percolation in a three-state majority vote model

Balankin, Alexander S.; Martínez-Cruz, M.A.; Martínez, Felipe Gayosso; Mena, B.; Tobon, Atalo; Patiño-Ortiz, Julián; Patiño-Ortiz, Miguel; Samayoa, Didier

doi:10.1016/j.physleta.2016.12.001

Cited by 14 publications

(14 citation statements)

References 38 publications

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“…Each individual i (i = 1, 2, ..., N) carries one of three possible opinions, represented by o i = +1, −1 or 0. This scenario mimics any polarized public debate, for example an electoral process with two different candidates A and B, where each agent (or elector) votes for the candidate A (opinion +1), for the candidate B (opinion −1) or remains undecided/neutral (opinion 0) [9,21,22]. In addition to a kinetic exchange rule of interaction, we consider a fraction a of contrarians in the population, similarly to the approach of Galam in the majority-rule model [7].…”

Section: Model I: Pairwise Interactions and Contrariansmentioning

confidence: 99%

The influence of contrarians in the dynamics of opinion formation

Gambaro

Crokidakis

2017

Physica A: Statistical Mechanics and its Applications

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In this work we consider the presence of contrarian agents in discrete 3-state kinetic exchange opinion models. The contrarians are individuals that adopt the choice opposite to the prevailing choice of their contacts, whatever this choice is. We consider binary as well as three-agent interactions, with stochastic parameters, in a fully-connected population. Our numerical results suggest that the presence of contrarians destroys the absorbing state of the original model, changing the transition to the para-ferromagnetic type. In this case, the consequence for the society is that the three opinions coexist in the population, in both phases (ordered and disordered). Furthermore, the order-disorder transition is suppressed for a sufficient large fraction of contrarians. In some cases the transition is discontinuous, and it changes to continuous before it is suppressed. Some of our results are complemented by analytical calculations based on the master equation.

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Section: Model I: Pairwise Interactions and Contrariansmentioning

confidence: 99%

The influence of contrarians in the dynamics of opinion formation

Gambaro

Crokidakis

2017

Physica A: Statistical Mechanics and its Applications

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“…Modifications of the above-mentioned probabilistic rule have also been considered, consisting in, e.g., inclusion of agents with independence [15], heterogeneous agents [16], agents with more than two opinions [17], agents with inertia, which leads to the occurrence of a discontinuous FM transition [18], and anticonformist agents, which leads to antiferromagnetic (AFM) or spin-glass-like (SG) rather than FM transition [19,20]. The latter modification amounts to associating AFM-like interactions (not necessarily symmetric) with edges attached to the nodes with anticonformist agents.…”

Section: Introductionmentioning

confidence: 99%

Ferromagnetic and spin-glass-like transition in the majority vote model on complete and random graphs

Krawiecki

2020

Eur. Phys. J. B

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Ferromagnetic and spin-glass-like transitions in nonequilibrium spin models in contact with two thermal baths with different temperatures are investigated. The models comprise the Sherrington-Kirkpatrick model and the dilute spin glass model which are the Ising models on complete and random graphs, respectively, with edges corresponding, with certain probability, to positive and negative exchange integrals. The spin flip rates are combinations of two Glauber rates at the two temperatures, and by varying the coefficients of this combination probabilities of contact of the model with each thermal bath and thus the level of thermal noise in the model are changed. Particular attention is devoted to the majority vote model in which one of the two above-mentioned temperatures is zero and the other one tends to infinity. Only in rare cases such nonequilibrium models can be mapped onto equilibrium ones at certain effective temperature. Nevertheless, Monte Carlo simulations show that transitions from the paramagnetic to the ferromagnetic and spin-glass-like phases occur in all cases under study as the level of thermal noise is varied, and the phase diagrams resemble qualitatively those for the corresponding equilibrium models obtained with varying temperature. Theoretical investigation of the model on complete and random graphs is performed using the TAP equations as well as mean-field and pair approximations, respectively. In all cases theoretical calculations yield reasonably correct predictions concerning location of the phase border between the paramagnetic and ferromagnetic phases. In the case of the spin-glass-like transition only qualitative agreement between theoretical and numerical results is achieved using the TAP equations, and the mean-field and pair approximations are not suitable for the study of this transition. The obtained results can be interesting for modeling opinion formation by means of the majority-vote and related models and suggest that in the presence of negative interactions between agents, apart from the ferromagnetic phase corresponding to consensus formation, spin-glass-like phase can occur in the society characterized by local rather than long-range ordering. Graphical abstract

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“…To some extent, the absence of majority in groups abstracts situations of stress or frustration. Specially, 2-state MR models with updates on discussion groups of even cardinality necessarily face ties, and this feature has relevant implications into the system, by instance, in producing stable states (Balankin et al, 2017). In this work, the effects of coalition ties produced through particular rules to untie them were quantitatively analyzed.…”

Section: Discussionmentioning

confidence: 99%

Majority rule dynamics between a double coalition and a third opinion: coalition profit models and majority coalition ties

Martínez

Balankin

2020

Adaptive Behavior

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This article explores the opinion dynamics of a double coalition opinion against a third opinion under majority rule updates on odd fixed size connected groups. For this purpose, coalition benefit criteria and three opinion formation models which extend the 2-state majority rule model on lattices are introduced. The proposed models focus on the coalition profit of its constituent coalition opinions and cover the possible final scenarios from coalition alliance perspective: either minor opinion or major opinion is favored, or dynamics do not favor to any coalition opinion. Opinion exchanges take place on a torus embedded lattice network of a 3-state system having in consideration tie configurations and two rules to break them: either by random choice or leaving ties unaltered. Models were analyzed in the statistical mechanics spirit through Monte Carlo simulations without node replacement. Estimations for coalition benefits, the growth of coalition ties, and consensus probabilities are reported. The loss of coalition strengths due to coalition ties and its indecision is indicated. In particular, the logistic decay of consensus probability is due to the logistic adaptive growth of coalition ties. Scaling behaviors for consensus time and coalition ties in terms of network size are suggested. The results of numerical simulations are discussed in the context of social influence and social dynamics.

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Ising percolation in a three-state majority vote model

Cited by 14 publications

References 38 publications

The influence of contrarians in the dynamics of opinion formation

The influence of contrarians in the dynamics of opinion formation

Ferromagnetic and spin-glass-like transition in the majority vote model on complete and random graphs

Majority rule dynamics between a double coalition and a third opinion: coalition profit models and majority coalition ties

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