Phase transitions in a two-parameter model of opinion dynamics with random kinetic exchanges

Abstract

Recently, a model of opinion formation with kinetic exchanges has been proposed in which a spontaneous symmetry breaking transition was reported [M. Lallouache et al, Phys. Rev. E, 82 056112 (2010)]. We generalise the model to incorporate two parameters, λ, to represent conviction and µ, to represent the influencing ability of individuals. A phase boundary given by λ = 1 − µ/2 is obtained separating the symmetric and symmetry broken phases: the effect of the influencing term enhances the possibility of reaching a consensus in the society. The time scale diverges near the phase boundary in a power law manner. The order parameter and the condensate also show power law growth close to the phase boundary albeit with different exponents. The exponents in general change along the phase boundary indicating a non-universality. The relaxation times, however, become constant with increasing system size near the phase boundary indicating the absence of any diverging length scale. Consistently, the fluctuations remain finite but show strong dependence on the trajectory along which it is estimated. Opinion can be assumed to be a discrete or continuous variable and it dynamically evolves according to the interactions between the individuals. The change in the opinion of an individual may be effected by binary interactions or may be dictated by a set of other individuals. The evolution usually leads to a steady state characterised either by a homogeneous state where people have similar opinion or a heterogeneous behaviour where people have widely different opinions. The interactions of the individuals in opinion dynamics models can be studied in terms of appropriate tunable parameters and it is of interest to observe whether such parameters can drive a phase transition in the system [6][7][8][9][10].While several different schemes have been proposed for possible evolution of opinions, a number of models have adopted the idea of kinetic exchanges in opinion formation [10][11][12][13][14]. In one such recently introduced model [10], the opinions of individuals, continuously varying from -1 to +1, were assumed to change after pairwise interactions. A parameter representing "conviction" dictated the way opinions were exchanged. Beyond a threshold value of this parameter, the opinions of the individuals were seen to reach a consensus while below this, all individuals remained in a "neutral" state with their opinions attaining a zero value. Hence the model shows spontaneous symmetry breaking. Such symmetry breaking transitions have also been observed earlier [8,9], in binary opinion models in which the ordered phase is one in which a consensus is reached. This is a symmetry broken phase while in the disordered phase, the opinions average out to zero. In [10], the so called disordered phase is very special in the sense the opinion of each individual is identically zero making the average equal to zero trivially. Obviously there is no degeneracy in this case and neither any fluctuation. Here, at the transition point, evidence of the ...

Kinetic Exchange Models in Economics and Sociology

“…In the generalized LCCC model [60], another parameter µ is introduced which is called the 'influence'parameter. It is a measure of the influencing power or the ability of an individual to impose its opinion on some other individual.…”

Noise and disorder: Phase transitions and universality in a model of opinion formation

“…Our model is based on kinetic exchange opinion models (KEOM's) 11,12,13,19,20 . A population of N agents is defined on a fully-connected graph, i.e., each agent can interact with all others, which characterizes a mean-field-like scheme.…”

“…Among typical problems of interest in social models, we highlight the dynamics of opinion formation 4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21 . Recently, the impact of nonconformity in opinion dynamics has been atracted attention of physicists, with many works published 4,5,6,7,8,9 .…”

Diffusion Controlled Model of Opinion Dynamics

“…15 The discretised version of the LCCC model has also been solved exactly 16 which also shows an activeabsorbing phase transition as was seen in the continuous version and the idea of bounded con¯dence has also been implemented. 17 The percolation transition has also been studied on this model in two dimension.…”