Dynamics of non-conservative voters

I will discuss two models of opinion dynamics. The first one is a non-conservative voter model in 1D where the propensity of 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. The second model which is a non-consensus voter model is more realistic in the sense that it allows for stable coexistence of two opinions by forming clusters of voters holding the same opinion. The model displays a phase transition behavior characterized by a large spanning cluster of voters holding the same opinion appearing when the concentration of voters holding the same opinion (even minority) is above a certain threshold. Simulation studies suggest that the model belong to the same universality class as invasion percolation.

References:

Dynamics of non-conservative voters , R. Lambiotte and S. Redner, EPL, 82 (2008) 18007

Dynamic opinion model and invasion percolation, J. Shao, S. Havlin and H. E. Stanley PRL, 103, 018701 (2009)