Masuda Naoki
Department of Mathematical Informatics, The University of Tokyo, 7-3-1 Hongo, Bunkyo, Tokyo 113-8656, Japan.
Phys Rev E Stat Nonlin Soft Matter Phys. 2013 Nov;88(5):052803. doi: 10.1103/PhysRevE.88.052803. Epub 2013 Nov 4.
In the voter and many other opinion formation models, agents are assumed to behave as congregators (also called the conformists); they are attracted to the opinions of others. In this study I investigate linear extensions of the voter model with contrarian agents. An agent is either congregator or contrarian and assumes a binary opinion. I investigate three models that differ in the behavior of the contrarian toward other agents. In model 1, contrarians mimic the opinions of other contrarians and oppose (i.e., try to select the opinion opposite to) those of congregators. In model 2, contrarians mimic the opinions of congregators and oppose those of other contrarians. In model 3, contrarians oppose anybody. In all models, congregators are assumed to like anybody. I show that even a small number of contrarians prohibits the consensus in the entire population to be reached in all three models. I also obtain the equilibrium distributions using the van Kampen small-fluctuation approximation and the Fokker-Planck equation for the case of many contrarians and a single contrarian, respectively. I show that the fluctuation around the symmetric coexistence equilibrium is much larger in model 2 than in models 1 and 3 when contrarians are rare.
在选民模型及许多其他意见形成模型中，主体被假定表现为聚集者（也称为顺从者）；他们会被他人的意见所吸引。在本研究中，我研究了带有逆势主体的选民模型的线性扩展。一个主体要么是聚集者要么是逆势者，并持有二元意见。我研究了三种模型，它们在逆势者对其他主体的行为方面存在差异。在模型1中，逆势者模仿其他逆势者的意见，并反对（即试图选择与之相反的意见）聚集者的意见。在模型2中，逆势者模仿聚集者的意见，并反对其他逆势者的意见。在模型3中，逆势者反对任何人。在所有模型中，假定聚集者喜欢任何人。我表明，即使是少量的逆势者也会阻碍在所有这三种模型中达成全体人口的共识。我还分别针对许多逆势者和单个逆势者的情况，使用范坎彭小波动近似和福克 - 普朗克方程得到了平衡分布。我表明，当逆势者很少时，模型2中围绕对称共存平衡的波动比模型1和模型3中的要大得多。
