Department of Physics, PUC-Rio, Rua Marquês de São Vicente, 225, 22451-900, Rio de Janeiro, Brazil.
National Institute of Science and Technology for Complex Systems, Brazil.
Phys Rev E. 2018 May;97(5-1):052106. doi: 10.1103/PhysRevE.97.052106.
We introduce the threshold q-voter opinion dynamics where an agent, facing a binary choice, can change its mind when at least q_{0} among q neighbors share the opposite opinion. Otherwise, the agent can still change its mind with a certain probability ɛ. This threshold dynamics contemplates the possibility of persuasion by an influence group even when there is not full agreement among its members. In fact, individuals can follow their peers not only when there is unanimity (q_{0}=q) in the lobby group, as assumed in the q-voter model, but also, depending on the circumstances, when there is simple majority (q_{0}>q/2), Byzantine consensus (q_{0}>2q/3), or any minimal number q_{0} among q. This realistic threshold gives place to emerging collective states and phase transitions which are not observed in the standard q voter. The threshold q_{0}, together with the stochasticity introduced by ɛ, yields a phenomenology that mimics as particular cases the q voter with stochastic drivings such as nonconformity and independence. In particular, nonconsensus majority states are possible, as well as mixed phases. Continuous and discontinuous phase transitions can occur, but also transitions from fluctuating phases into absorbing states.
我们介绍了阈值 q-投票者意见动态，其中一个面对二元选择的主体，当至少 q0 个邻居持相反意见时，它可以改变主意。否则，该主体仍可以以一定的概率ɛ改变主意。这种阈值动态考虑了即使在其成员之间没有完全一致的情况下，游说团体也可以进行说服的可能性。实际上，个人不仅可以在游说团体中存在一致意见（q0=q）的情况下跟随他们的同龄人，就像 q-投票者模型所假设的那样，而且还可以根据情况，在存在简单多数（q0>q/2）、拜占庭共识（q0>2q/3）或 q 中任意最小数量 q0 时跟随他们的同龄人。这种现实的阈值产生了新兴的集体状态和相变，这在标准的 q 投票者中是观察不到的。阈值 q0 与ɛ引入的随机性一起产生了一种现象学，它可以作为具有随机驱动的 q 投票者的特例，例如不服从和独立性。特别是，可以存在非共识多数状态以及混合相。可能发生连续和不连续的相变，但也可能从波动相转变为吸收状态。
