With the success of general conceptual frameworks of statistical physics,
many scholars have tried to apply these concepts to other interdisciplinary
fields, such as socio-politics, economics, biology, medicine, and many more. In
this work, we study the effect of mass media on opinion evolution based on the
nonlinear q-voter by mean with probability p a voter adopts the mass media
opinion whenever a q-sized agent in the population is in unanimous agreement
(have the same opinion). We perform analytical and numerical calculations for
some quantities of macroscopic parameters of the model such as order parameter
(representing an average of public opinion), consensus (relaxation) time, and
exit probability, and obtain the agreement results. We find the power-law
relations for some quantities of the model. (1) The probability threshold
pt​, i.e a probability that makes the system reaches a homogeneous state,
follows the power-law relation pt​∼qγ with the q-sized agent,
where γ=−1.00±0.01 is the best fitting parameter. The probability
threshold pt​ also eliminates the standard phase transition of the model. (2)
The relaxation or consensus time (which is the time needed by the system to
reach consensus) Ï„ with the population size N is obtained in the form of
τ∼Nδ, where δ depends on the probability p and
q-sized agent. We also approximate the critical point rc​ and the system's
scaling parameters by employing the standard finite-size scaling relation. Our
results suggest a similar scaling behavior to the voting distribution in the
1998 Brazilian election reported by Costa et al.Comment: 14 pages and 12 figure