International Journal of Modern Physics C

25-10 (2014) 1450050

Dynamics of opinion formation

with strengthen selection probability

Haifeng Zhang，Zhen Jin，Bing-Hong Wang

The local majority rule is extensively accepted as a paradigmatic model to reflect the formation of opinion. In this paper, we study a model of opinion formation where opinion update rule is not based on the majority rule or linear selection probability but on a strengthen selection probability controlled by an adjustable parameter β. In particular, our proposed probability function can proximately fit the two extreme cases–linear probability function and majority rule or in between the two cases under different values of β. By studying such model on different kinds of networks, including different regular networks and complex networks, we find that there exists an optimal value of β giving the most efficient convergence to consensus regardless of the topology of networks. This work reveals that, compared with the majority rule and linear  selection probability,  the strengthen selection probability might be a more proper model in understanding the formation of opinions in society.

Keywords: Opinion formation; strengthen selection probability; majority rule.

强化选择概率的舆情形成动力学

张海峰，靳祯， 汪秉宏

大多数原则的舆论传播模型是最为经典的舆论传播模型之一，此策略假设一旦邻居中采取观点“+”(“-”)的比例大于总邻居数的一半，则个体必然采取“+”（“-”）的观点，不再考虑“+”和“-”的具体数量差。现实中，个体采取某种观点的概率往往与两种观点的相对差有关，而且具有一定的随机因素，基于以上原因我们提出一种具有强化效应的概率函数刻画舆论传播中个体的更新观点的策略，此概率函数一方面与“+”和“-”的数量差有关，而且与一个强化因子β有关。更为重要的是，此概率函数在β不同的时候可以导出经典的大多数原则模型和线性函数模型，因此具有更一般性。通过研究发现，与经典的大多数一样原则相比，该模型可以更快的导致系统趋向统一态，同时存在一个最优的β导致系统最快的趋向统一态，而且本机制对于不同的网络结构都具有普适性。

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IJMPC25-10(2014)1450050 ZhangHF JinZ WangBH.pdf