Homogeneous Symmetrical Threshold Model with Nonconformity: Independence versus Anticonformity

Bartłomiej Nowak,Katarzyna Sznajd-Weron

doi:10.1155/2019/5150825

Abstract

We study two variants of the modified Watts threshold model with a noise (with nonconformity, in the terminology of social psychology) on a complete graph. Within the first version, a noise is introduced via so-called independence, whereas in the second version anticonformity plays the role of a noise, which destroys the order. The modified Watts threshold model, studied here, is homogeneous and possesses an up-down symmetry, which makes it similar to other binary opinion models with a single-flip dynamics, such as the majority-vote and the q-voter models. Because within the majority-vote model with independence only continuous phase transitions are observed, whereas within the q-voter model with independence also discontinuous phase transitions are possible, we ask the question about the factor, which could be responsible for discontinuity of the order parameter. We investigate the model via the mean-field approach, which gives the exact result in the case of a complete graph, as well as via Monte Carlo simulations. Additionally, we provide a heuristic reasoning, which explains observed phenomena. We show that indeed if the threshold r=0.5, which corresponds to the majority-vote model, an order-disorder transition is continuous. Moreover, results obtained for both versions of the model (one with independence and the second one with anticonformity) give the same results, only rescaled by the factor of 2. However, for r>0.5 the jump of the order parameter and the hysteresis is observed for the model with independence, and both versions of the model give qualitatively different results.

Highlights

Models of opinion dynamics are among the most studied models of complex systems [1,2,3,4]
We wanted to understand the nature of the phase transitions observed within models of binary opinions with a single-flip dynamics and up-down symmetry
The modification of the Watts threshold model that we have proposed here may be treated as a destruction of the model from the social point of view

Summary

Introduction

Models of opinion dynamics are among the most studied models of complex systems [1,2,3,4] This is not surprising, because they can be treated as a zero-level approach to various more complex social processes, including polarization of opinion [5,6,7], diffusion of innovation [8,9,10], or political voting [11,12,13]. Interesting is a subset of the binary opinion models, including the voter model [14], the majority-vote model [14,15,16], the Galam model [17], the Sznajd model [18], the Watts threshold model [19], the qvoter model [20], or the threshold q-voter model [21, 22]. The binary decision/opinion framework is attractive from physicist’s point of view and natural in the social sciences [19, 24]

Objectives

Methods

Results

Conclusion