Dynamics of confident voting

Abstract

We introduce the confident voter model, in which each voter can be in one of two opinions and can additionally have two levels of commitment to an opinion -confident and unsure. Upon interacting with an agent of a different opinion, a confident voter becomes less committed, or unsure, but does not change opinion. However, an unsure agent changes opinion by interacting with an agent of a different opinion. In the meanfield limit, a population of size N is quickly driven to a mixed state and remains close to this state before consensus is eventually achieved in a time of the order of ln N . In two dimensions, the distribution of consensus times is characterized by two distinct times -one that scales linearly with N and another that appears to scale as N 3/2 . The longer time arises from configurations that fall into long-lived states that consist of two (or more) single-opinion stripes before consensus is reached. These stripe states arise from an effective surface tension between domains of different opinions.

The influence of persuasion in opinion formation and polarization

“…The two extremists consensus x ±M = 1 are absorbing states of the system, thus they are the only possible final states in the long run. The length of the plateau increases with the system size as ln N (not shown), a typical time scale that appears in models with intermediate states [10,14]. We shall see that this particular scaling is also a consequence of the discrete nature of the system when a small initial asymmetry is introduced [14].…”

Reality-inspired voter models: A mini-review

“…Such threshold behavior also arises in the q-voter model [40] and in contagion models [41]. We investigate the role of a threshold through the confident voter model (CVM) [42], in which each voter has two opinion states and two levels of commitment to an opinion-confident and unsure. Upon interacting with an agent of a different opinion, a confident voter becomes unsure but keeps its opinion, while an unsure agent changes opinion.…”

“…Marginal: Extremal: Solving these equations [42] gives the following basic results: For a symmetric population with equal densities of ↑ and ↓ voters, the final densities are P c = M c = 0 and P u = M u = 1 for the marginal model and…”

Role of social environment and social clustering in spread of opinions in coevolving networks

“…[6][7][8][9][10][11][12][13][14][15] In such studies, individuals in the society are represented by nodes with edges indicating relationships between them, and then techniques from social network analysis and from statistical and nonlinear science are employed to analyze plausible models of the dynamics of spread of social contagions on a network. 1,[16][17][18][19][20][21][22][23][24][25][26] We propose a variation of the simplest coevolving network voter model of opinion formation, studied by Holme and Newman. 1 In the model of Holme and Newman, an edge between individuals with different opinions is either rewired to connect two nodes having the same opinion or the opinion of an individual is changed to agree with the opinion of one of its neighbors.…”

“…A minimal mathematical model that has been used to model the social phenomena of collective opinion formation is the coevolving voter model. 1,[16][17][18][19][20][21][22][23][24][25][26] We introduce two additional attributes to the multi-opinion coevolving voter model, in order to describe processes and networks that are closer to real-world situations within a still relatively simple model. Our model includes a "social environment," modeling the inherent heterogeneity and asymmetry in relationships within a social group.…”