Majority versus minority dynamics: Phase transition in an interacting two-state spin system

Mobilia, Mauro; Redner, S.

doi:10.1103/physreve.68.046106

Cited by 117 publications

(104 citation statements)

References 33 publications

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“…In one dimension, however, the mean-field assumption is not justified. To determine the behavior of the system when γ = 2, we therefore use the approach developed in [5] (see also [8]) to truncate the hierarchy of equations for multi-spin correlation functions. Consider the rate equation for the nearest-neighbor correlation function σ j σ j+1 :…”

Section: Fig 1: Update Illustrationmentioning

confidence: 99%

Dynamics of non-conservative voters

Lambiotte¹,

Redner²

2008

Europhys. Lett.

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106

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We study a family of opinion formation models in one dimension where the propensity for a voter to align with its local environment depends non-linearly on the fraction of disagreeing neighbors. Depending on this non-linearity in the voting rule, the population may exhibit a bias toward zero magnetization or toward consensus, and the average magnetization is generally not conserved. We use a decoupling approximation to truncate the equation hierarchy for multi-point spin correlations and thereby derive the probability to reach a final state of ↑ consensus as a function of the initial magnetization. The case when voters are influenced by more distant voters is also considered by investigating the Sznajd model.

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Section: Fig 1: Update Illustrationmentioning

confidence: 99%

Dynamics of non-conservative voters

Lambiotte¹,

Redner²

2008

Europhys. Lett.

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106

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“…While networks have been widely used by physicists to study e.g. porous media [1] or a system of interacting spins [2,3,4], they can also be used to study social systems. Social networks have helped to further understand the structure and evolution of social systems, where people and their acquaintances are represented by the nodes and links of the network respectively.…”

Section: Introduction and Modelmentioning

confidence: 99%

Spreading gossip in social networks

et al. 2007

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We study a simple model of information propagation in social networks, where two quantities are introduced: the spread factor, which measures the average maximal fraction of neighbors of a given node that interchange information among each other, and the spreading time needed for the information to reach such fraction of nodes. When the information refers to a particular node at which both quantities are measured, the model can be taken as a model for gossip propagation. In this context, we apply the model to real empirical networks of social acquaintances and compare the underlying spreading dynamics with different types of scale-free and small-world networks. We find that the number of friendship connections strongly influences the probability of being gossiped. Finally, we discuss how the spread factor is able to be applied to other situations.

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“…The model is simple and can be analyzed by the mean-field approach [6]. Other discrete opinion models also have been presented in terms of realistic systems, such as the majority model [7,8], and the Sznajd model [9,10]. In the continuous group, the bounded confidence is introduced to make agents trust only those neighbors who hold similar beliefs [11,12].…”

Section: Introductionmentioning

confidence: 99%

“…Moreover, agents form their personal confidence gradually during the interaction, and therefore, initial conviction of each agent 0 C does not have any distinct impact on the average magnetization. Figure 4 (from top to bottom) are [10,61] , [5,47] and [2,35] respectively, while those in the right plot are [2,24] , [2,18] and [2,8] respectively. As in many opinion models, agents holding the same opinion gather together to form a cluster, and agents inside the cluster are not easy to persuade.…”

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confidence: 99%

Competition of Dynamic Self-Confidence and Inhomogeneous Individual Influence in Voter Models

Xiong

Liu

Zhu

2013

Entropy

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Abstract:In social systems, agents often have different ability to persuade neighbors to adopt their opinions. In this paper, we aim to investigate how the location and heterogeneity of influencers in social networks can improve convergence. We propose a voter model with dynamic self-conviction and heterogeneous individual influence which is related to the underlying network topology. An agent may keep its current opinion according to personal conviction, or otherwise, it may preferentially choose the opinion of the neighbor that has a great influence. Individual conviction evolves during the dynamic process, and can be strengthened by social recognition. Simulations indicate our model has three nontrivial results. First, the conservation of average magnetization in the voter model is broken under the effect of individual conviction and influence, and the system evolves to an ordered state in which one opinion is dominant, but total consensus is prevented by extremists. Furthermore, individual influence has a subtle action on opinion evolution. The heterogeneity of individual influence accelerates the relaxation process, but, with the action of dynamic conviction, more heterogeneous influence does not mean the average magnetization will be more ordered. In addition, when competing with agents' conviction, more heterogeneous individual influence plays a more significant role in agents' decisions. These results are helpful for understanding some aspects of collective phenomena that occur on online social media. OPEN ACCESSEntropy 2013, 15 5293

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Majority versus minority dynamics: Phase transition in an interacting two-state spin system

Cited by 117 publications

References 33 publications

Dynamics of non-conservative voters

Dynamics of non-conservative voters

Spreading gossip in social networks

Competition of Dynamic Self-Confidence and Inhomogeneous Individual Influence in Voter Models

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