# Analytical expression for the exit probability of the q-voter model in one dimension.

@article{Timpanaro2014AnalyticalEF, title={Analytical expression for the exit probability of the q-voter model in one dimension.}, author={Andr{\'e} M. Timpanaro and Serge Galam}, journal={Physical review. E, Statistical, nonlinear, and soft matter physics}, year={2014}, volume={92 1}, pages={ 012807 } }

We present in this paper an approximation that is able to give an analytical expression for the exit probability of the q-voter model in one dimension. This expression gives a better fit for the more recent data about simulations in large networks [A. M. Timpanaro and C. P. C. do Prado, Phys. Rev. E 89, 052808 (2014)] and as such departs from the expression ρ(q)/ρ(q)+(1-ρ)(q) found in papers that investigated small networks only [R. Lambiotte and S. Redner, Europhys. Lett. 82, 18007 (2008); P…

## 19 Citations

### Threshold q-voter model

- EconomicsPhysical review. E
- 2018

The threshold q-voter opinion dynamics where an agent, facing a binary choice, can change its mind when at least q_{0} among q neighbors share the opposite opinion is introduced, which yields a phenomenology that mimics as particular cases the q voter with stochastic drivings such as nonconformity and independence.

### Universal features of exit probability in opinion dynamics models with domain size dependent dynamics

- Mathematics
- 2014

We study the exit probability for several binary opinion dynamics models in one dimension in which the opinion state (represented by ± 1 ?> ) of an agent is determined by dynamical rules dependent on…

### Conformity in numbers—Does criticality in social responses exist?

- Computer SciencePloS one
- 2018

This paper considers the threshold q-voter model when the responses of the Willis-Nail model, a well-established two-dimensional model of social response, are used as a foundation and introduces independently two thresholds: one needed for conformity, as well as a second one for anticonformity.

### q-Neighbor Ising model on random networks

- PhysicsInternational Journal of Modern Physics C
- 2018

A modified kinetic Ising model with Metropolis dynamics, so-called [Formula: see text]-neighbor Ising model, is investigated on random graphs. In this model, each spin interacts only with [Formula:…

### Nonequilibrium dynamics in Ising-like models with biased initial condition.

- PhysicsPhysical review. E
- 2021

The stability analysis of the fixed points in the mean field calculation shows the existence of an exponent that depends on the coordination number z in the Ising model, which is consistent with the conserved magnetization in the system.

### The Hunt Opinion Model—An Agent Based Approach to Recurring Fashion Cycles

- MathematicsPloS one
- 2016

We study a simple agent-based model of the recurring fashion cycles in the society that consists of two interacting communities: “snobs” and “followers” (or “opinion hunters”, hence the name of the…

### 2 5 S ep 2 01 5 Testing the validity of the Kirkwood approximation using an extended Sznajd model

- Physics
- 2018

We revisit the deduction of the exit probability of the one di mensional Sznajd model through the Kirkwood approximation [F. Slaninaet al., Europhys. Lett.82, 18006 (2008)]. This approximation is…

### Impact of memory on opinion dynamics

- EconomicsPhysica A: Statistical Mechanics and its Applications
- 2018

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

- PhysicsThe European Physical Journal B
- 2020

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…

## References

SHOWING 1-6 OF 6 REFERENCES

### Exit probability of the one-dimensional q-voter model: analytical results and simulations for large networks.

- PhysicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2014

The exit probability of the one-dimensional q-voter model is discussed and the result that the exit probability cannot be a step function can be reconciled with the Galam unified frame, which was also a source of controversy.

### Exit probability in a one-dimensional nonlinear q-voter model.

- Mathematics, PhysicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2011

An analytical formula is derived for the exit probability in the one-dimensional nonlinear q-voter model and it is shown that it agrees perfectly with Monte Carlo simulations.

### Nonlinear q-voter model.

- PhysicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2009

A nonlinear variant of the voter model, the q-voter model, in which q neighbors are consulted for a voter to change opinion is introduced, and in mean field the model exhibits a disordered phase for high epsilon and an ordered one for low Epsilon.

### Pitfalls driven by the sole use of local updates in dynamical systems

- Physics
- 2011

The recent claim that the exit probability (EP) of a slightly modified version of the Sznadj model is a continuous function of the initial magnetization is questioned. This result has been obtained…

### Some new results on one-dimensional outflow dynamics

- Physics
- 2008

In this paper we introduce a modified version of the one-dimensional outflow dynamics in the spirit of the Sznajd model, which simplifies the analytical treatment. The equivalence between original…

### Dynamics of nonconservative voters

- Europhysics Letters ,
- 2008