Dynamics of non-conservative voters

Abstract

We study a family of opinion formation models in one dimension where the propensity for a voter to align with its local environment depends non-linearly on the fraction of disagreeing neighbors. Depending on this non-linearity in the voting rule, the population may exhibit a bias toward zero magnetization or toward consensus, and the average magnetization is generally not conserved. We use a decoupling approximation to truncate the equation hierarchy for multi-point spin correlations and thereby derive the probability to reach a final state of ↑ consensus as a function of the initial magnetization. The case when voters are influenced by more distant voters is also considered by investigating the Sznajd model.

Nonlinearq-voter model with inflexible zealots

“…(3) has two stable absorbing fixed points, x = 0 (all Bsupporters) and x = 1 (all A-supporters) corresponding to consensus with either A or B party, separated by an unstable fixed point x = 1/2 (mixture of A-and Bvoters) [14]. It is worth noting that the dynamics of the qVM without zealots ceases when a consensus is reached and this happens in a finite time when the population size is finite [14][15][16][17][18]. However, in the presence of zealots supporting both parties, the population composition endlessly fluctuates [9,10], see, e.g., Fig.…”

“…When q = 2, the qVM is closely related to the Sznajd model [15][16][17] * Electronic address: M. Mobilia@leeds.ac.uk and to that of Ref. [18]. The properties of the qVM have received much attention and there is a debate on the expression of the exit probability in one dimension [18][19][20].…”

Nonconsensus opinion model on directed networks

“…Over the past decade, numerous opinion models have combined complex network theory and statistical physics. Examples include the Sznajd model [17], the voter model [18][19][20], the majority rule model [21,22], the social impact model [23,24], and the bounded confidence model [25,26]. All of these models ultimately produce a consensus state in which all agents share the same opinion.…”

Dynamical model for competing opinions

“…A great deal of effort has been devoted to developing models for describing the properties of systems made up of agents with competing opinions [1,[4][5][6][7][14][15][16][17][18][19][20]. This is of great relevance as human conflicts very often arise from the simultaneous existence of incompatible opinions in populations.…”

“…Different from many other models, such as those developed in Refs. [4,[16][17][18][19][20], for instance, the interaction between two agents is strictly local, in the sense that it relies only on the interacting agents' properties, i.e., on their individual opinions and convictions. Therefore, during the interaction between a pair of agents, the fact that one of them may eventually be surrounded by a competing opinion or supported by its companions has no influence on the outcome of the interaction.…”