| In the classical voter model, each voter can be in one of two opinion states and continuously updates its opinion at a rate proportional to the fraction of opposite-opinion neighbors. This update leads to diffusion of opinion correlations and conservation of the mean opinion. When voters live on nodes of a regular lattice of N sites, consensus is reached in a time TN » N2 in spatial dimension d = 1, TN » N lnN for d = 2, and TN » N in d ¸ 3. On complex networks with a power-law degree distribution k−º, the mean opinion is not conserved, a feature that controls the route by which consensus is achieved. On such networks consensus is achieved quickly: TN » O(1) for º < 2, TN » N(2º−4)/(º−1) for 2 < º < 3 and TN » N for º > 3. We then turn to the reinforced voter model, which which a voter needs to receive multiple input to change state before actually doing so. In this case, a two-time scale approach to consensus occurs, with rich temporal and spatial dynamics that remain incompletely understood. 1 |
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