Multistate voter model with imperfect copying

FEDERICO VAZQUEZ; E. S. LOSCAR; G. BAGLIETTO

Physical Review E

American Physical Society

Lugar: New York; Año: 2019 vol. 100

2470-0045

The voter model with multiple states has found applications in areas as diverse as population genetics, opinion formation, species competition, and language dynamics, among others. In a single step of the dynamics, an individual chosen at random copies the state of a random neighbor in the population. In this basic formulation, it is assumed that the copying is perfect, and thus an exact copy of an individual is generated at each time step. Here, we introduce and study a variant of the multistate voter model in mean field that incorporates a degree of imperfection or error in the copying process, which leaves the states of the two interacting individuals similar but not exactly equal. This dynamics can also be interpreted as a perfect copying with the addition of noise: a minimalistic model for flocking. We found that the ordering properties of this multistate noisy voter model, measured by a parameter psi in [0,1], depend on the amplitude eta of the copying error or noise and the population size N. In the case of perfect copying eta=0, the system reaches an absorbing configuration with complete order (psi=1) for all values of N. However, for any degree of imperfection eta>0, we show that the average value of psi at the stationary state decreases with N as =6/(pi^2eta^2N) for etainf. We also show that =1-pi^2eta^2N/6 in the vanishing small error limit eta->0, which implies that complete order is never achieved for eta>0. These results are supported by Monte Carlo simulations of the model, which allow to study other scenarios as well.