Multimedialne seminarium z ekono- i socjofizyki

The majority vote (MV) model is a stochastic model for the opinion formation devised as a nonequilibrium version of the Ising model. In its most popular version agents update their opinions at discrete time steps following the opinion of the majority of their neighbors with probability 1-q, where positive q smaller than ½ controls the degree of internal noise. The MV model on regular two- and three-dimensional lattices was shown to exhibit a continuous ordering transition with decreasing q, with the critical exponents belonging to the universality class of the corresponding Ising model. It was also studied and successfully described using the mean-field approximation on various complex networks, in particular on scale-free networks which reflect heterogeneity of human social and economic interactions. In this seminar the above-mentioned basic facts about the MV model are recollected, and certain new results are presented. First, the studies of the MV model on complex networks are extended to the case of multiplex networks in which the agents interact via different communications channels corresponding to independently generated, heterogeneous layers of the multiplex network and make decisions based on the opinions of the majorities of their neighbors within all layers. This model exhibits ordering transition which is quantitatively correctly described in the mean-field approximation. Second, the MV model on complex networks is investigated in which part of agents are anticonformists who with probability 1-q assume opinions opposite to the majority of their neighbors. Numerical evidence for the possibility of the occurrence of a spin-glass-like transition in this model is provided. Finally, response of the MV model to external periodic stimulation is investigated numerically and using the mean-field approximation. Stochastic resonance is observed, i.e., maximization of the response of the model at non-zero level of internal noise.