Abstract
We analyze a nonlinear q-voter model with stochastic noise, interpreted in the social context as independence, on a duplex network. The size of the lobby q (i.e., the pressure group) is a crucial parameter that changes the behavior of the system. The q-voter model has been applied on multiplex networks, and it has been shown that the character of the phase transition depends on the number of levels in the multiplex network as well as on the value of q. The primary aim of this study is to examine phase transition character in the case when on each level of the network the lobby size is different, resulting in two parameters and . In a system of a duplex clique (i.e., two fully overlapped complete graphs) we find evidence of successive phase transitions when a continuous phase transition is followed by a discontinuous one or two consecutive discontinuous phase transitions appear, depending on the parameter. When analyzing this system, we even encounter mixed-order (or hybrid) phase transition. The observation of successive phase transitions is a new quantity in binary state opinion formation models and we show that our analytical considerations are fully supported by Monte-Carlo simulations.
Highlights
It is pretty obvious that modeling opinion dynamics [1,2,3,4,5,6] is a tricky task that can be seen as maneuvering between two distinct extremes
The major drawback of such a setting of the q-voter model on multiplex networks that we want to tackle in this paper lays in its symmetry, i.e., the lobby acting on an individual on each level has the same size q. Such an assumption does not seem to be justified as it is rather clear that we pay more attention to some groups while almost neglecting others—if a person is less devoted to on-line groups than to real-life friends, even a smaller set chosen from the latter will affect him/her stronger than larger group recruiting from the first ones. To overcome these issues we introduce in this study an asymmetric q-voter model with independence on a duplex clique where lobby sizes on different levels are described by parameters q1 and q2
At the beginning of the paper we tried to draw a suggestive picture of two possible roads to modeling of opinion dynamics, distinguishing between binary state models and an agent-based approach
Summary
It is pretty obvious that modeling opinion dynamics [1,2,3,4,5,6] is a tricky task that can be seen as maneuvering between two distinct extremes. That are often subject to exact analytical treatment, their assumptions and formulation can be seen as oversimplified, especially from the social science point of view. As underlined before [12], the so-called q-voter model with independence, understood as stochastic noise (later on in this paper referred as q-voter model for brevity), is of particular interest in the group of binary opinion models. The idea that q-lobby (a group of q nodes chosen form of all the neighbors of an agent) acting on an individual needs to be unanimous in order to change agent’s opinion has solid grounds in social sciences.
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