Generalized Independence in the q-Voter Model: How Do Parameters Influence the Phase Transition?

Angelika Abramiuk,Katarzyna Sznajd-Weron

doi:10.3390/e22010120

Angelika Abramiuk, Katarzyna Sznajd-Weron

Open Access

https://doi.org/10.3390/e22010120

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Abstract

We study the q-voter model with flexibility, which allows for describing a broad spectrum of independence from zealots, inflexibility, or stubbornness through noisy voters to self-anticonformity. Analyzing the model within the pair approximation allows us to derive the analytical formula for the critical point, below which an ordered (agreement) phase is stable. We determine the role of flexibility, which can be understood as an amount of variability associated with an independent behavior, as well as the role of the average network degree in shaping the character of the phase transition. We check the existence of the scaling relation, which previously was derived for the Sznajd model. We show that the scaling is universal, in a sense that it does not depend neither on the size of the group of influence nor on the average network degree. Analyzing the model in terms of the rescaled parameter, we determine the critical point, the jump of the order parameter, as well as the width of the hysteresis as a function of the average network degree and the size of the group of influence q.

Highlights

Independence appears in models of opinion dynamics under various forms and names, including noise [1,2,3,4,5,6,7,8], inflexibility [9,10,11], zealots [12,13,14,15], non-social state [16,17], social temperature [18,19] or just independence [10,20,21,22,23,24,25]
The model studied in this paper is a straightforward generalization of the q-voter model with independence, proposed originally in [21] and is directly inspired by the self-influence dimension introduced in a diamond model of social response [26,28,32]
As we have already written in the Introduction, we are interested in the dependencies between the main characteristics of the phase transition that appears in this model, and average network degree hki, as well as the size of the influence group q

Summary

Introduction

Independence appears in models of opinion dynamics under various forms and names, including noise [1,2,3,4,5,6,7,8], inflexibility [9,10,11], zealots [12,13,14,15], non-social state [16,17], social temperature [18,19] or just independence [10,20,21,22,23,24,25]. It seems that asking a target about the preference (A or B) before exposing her or him to the group of influence would be helpful, but it doesn’t solve the problem [26,27] For this reason, many different descriptive models defining basic types of social response have been introduced. Despite the existence of many models, independence is almost always defined in the same way, i.e., as no change in individual’s opinion/behavior Such a definition makes independence easy to recognize within an experiment. This is consistent with the idea of zealots, inflexibility, or stubbornness Such a definition does not allow for taking into account situations in which a change of opinion or behavior is not caused directly by the group of influence but results from the individual’s own thoughts, mood, past experiences, etc. We systematically analyze the dependence between the main characteristics of the phase transition (including the jump of the order parameter and the width of hysteresis) and model’s, as well as graph’s parameters

The q-Voter Model with Generalized Independence

Results

Conclusions