Takaguchi Taro, 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. 2011 Sep;84(3 Pt 2):036115. doi: 10.1103/PhysRevE.84.036115. Epub 2011 Sep 26.
Recent analysis of social communications among humans has revealed that the interval between interactions for a pair of individuals and for an individual often follows a long-tail distribution. We investigate the effect of such a non-Poissonian nature of human behavior on dynamics of opinion formation. We use a variant of the voter model and numerically compare the time to consensus of all the voters with different distributions of interevent intervals and different networks. Compared with the exponential distribution of interevent intervals (i.e., the standard voter model), the power-law distribution of interevent intervals slows down consensus on the ring. This is because of the memory effect; in the power-law case, the expected time until the next update event on a link is large if the link has not had an update event for a long time. On the complete graph, the consensus time in the power-law case is close to that in the exponential case. Regular graphs bridge these two results such that the slowing down of the consensus in the power-law case as compared to the exponential case is less pronounced as the degree increases.
近期对人类社会交流的分析表明，一对个体之间以及单个个体的互动间隔往往遵循长尾分布。我们研究人类行为的这种非泊松性质对意见形成动态的影响。我们使用选民模型的一个变体，并通过数值方法比较具有不同事件间隔分布和不同网络的所有选民达成共识的时间。与事件间隔的指数分布（即标准选民模型）相比，事件间隔的幂律分布会减缓环上的共识达成。这是由于记忆效应；在幂律情况下，如果一条链路很长时间没有更新事件，那么直到该链路上下一次更新事件的预期时间会很长。在完全图上，幂律情况下的共识时间与指数情况下的接近。正则图连接了这两个结果，使得与指数情况相比，幂律情况下共识的减缓随着度数增加而不那么明显。
