***** Voter ***** The Voter model is one of the simplest models of opinion dynamics, originally introduced to analyse competition of species [#]_ and soon after applied to model elections [#]_. The model assumes the opinion of an individual to be a discrete variable ±1. The state of the population varies based on a very simple update rule: at each iteration, a random individual is selected, who then copies the opinion of one random neighbour. Starting from any initial configuration, on a complete network the entire population converges to consensus on one of the two options. The probability that consensus is reached on opinion +1 is equal to the initial fraction of individuals holding that opinion [#]_. -------- Statuses -------- During the simulation a node can experience the following statuses: =========== ==== Name Code =========== ==== Susceptible 0 Infected 1 =========== ==== ---------- Parameters ---------- The initial infection status can be defined via: - **fraction_infected**: Model Parameter, float in [0, 1] - **Infected**: Status Parameter, set of nodes The initial blocked nodes can be defined via: - **percentage_blocked**: Model Parameter, float in [0, 1] - **Blocked**: Status Parameter, set of nodes In both cases, the two options are mutually exclusive and the latter takes precedence over the former. ------- Example ------- In the code below is shown an example of instantiation and execution of a Voter model simulation on a random graph: we set the initial infected node set to the 10% of the overall population. .. code-block:: python import networkx as nx import ndlib.models.ModelConfig as mc import ndlib.models.opinions as op # Network topology g = nx.erdos_renyi_graph(1000, 0.1) # Model selection model = op.VoterModel(g) config = mc.Configuration() config.add_model_parameter('fraction_infected', 0.1) model.set_initial_status(config) # Simulation execution iterations = model.iteration_bunch(200) .. [#] P. Clifford and A. Sudbury, “A model for spatial conflict,” Biometrika, vol. 60, no. 3, pp. 581–588, 1973. .. [#] R. Holley and T. Liggett, “Ergodic theorems for weakly interacting infinite systems and the voter model,” Ann. Probab., vol. 3, no. 4, pp. 643–663, Aug 1975. .. [#] P.L.Krapivsky,S.Redner,andE.Ben-Naim,Akineticviewofstatistical physics. Cambridge University Press, 2010.