Three-State Opinion Q-Voter Model with Bounded Confidence

Consensus, Polarization and Hysteresis in the Three-State Noisy q-Voter Model with Bounded Confidence

“…In the framework of discrete models, this rule typically involves prohibiting interactions between agents whose opinions differ by more than one [ 8 , 9 , 10 , 14 , 36 ]. This means, for example, that leftists and rightists do not interact [ 10 ].…”

“…This means, for example, that leftists and rightists do not interact [ 10 ]. Recently, the BC rule has also been extended to other types of social response, such as independence, which means that no change in the state of an agent can be greater than one during a single update [ 36 ]. We will not use this extended definition of BC here for reasons that will be discussed in the last section of this paper.…”

“…The logic behind qVM is the following: even if an agent has many friends, at a given moment, it interacts only with a few of them. We show that a variety of collective social phenomena can be observed depending on the size of the influence group q , which could not be observed within the three-state qVM without BC [ 24 ] or within the three-state qVM with an extended definition of BC [ 36 ].…”

“…On the other hand, for larger groups of influence and low independence, consensus on extreme opinion can be achieved. In contrast, in [ 24 , 36 ], polarization cannot be observed for any value of the model parameters. In this work, we use the term consensus as defined by Webster’s or Oxford dictionary, which define it as a general agreement and distinguish it from unanimity.…”

“…Summarizing, the purpose of this work is twofold: Socially motivated: to determine the role of the size of the influence group on the emerging social behavior (consensus, polarization, hysteresis, etc.). Theoretically motivated: to evaluate the impact of a small change introduced to the model at the microscopic level on its performance at the macroscopic level, since the results for this model without BC [ 24 ] and with an extended definition of BC [ 36 ] are already known. …”