Voter

The Voter model is one of the simplest models of opinion dynamics, originally introduced to analyse competition of species [1] and soon after applied to model elections [2].

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 [3].

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:

  • percentage_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.

Methods

The following class methods are made available to configure, describe and execute the simulation:

Configure

class ndlib.models.opinions.VoterModel.VoterModel(graph)
VoterModel.__init__(graph)

Model Constructor

Parameters:graph – A networkx graph object
VoterModel.set_initial_status(self, configuration)

Set the initial model configuration

Parameters:configuration – a `ndlib.models.ModelConfig.Configuration` object
VoterModel.reset(self)

Reset the simulation setting the actual status to the initial configuration.

Describe

VoterModel.get_info(self)

Describes the current model parameters (nodes, edges, status)

Returns:a dictionary containing for each parameter class the values specified during model configuration
VoterModel.get_status_map(self)

Specify the statuses allowed by the model and their numeric code

Returns:a dictionary (status->code)

Execute Simulation

VoterModel.iteration(self)

Execute a single model iteration

Returns:Iteration_id, Incremental node status (dictionary node->status)
VoterModel.iteration_bunch(self, bunch_size)

Execute a bunch of model iterations

Parameters:
  • bunch_size – the number of iterations to execute
  • node_status – if the incremental node status has to be returned.
Returns:

a list containing for each iteration a dictionary {“iteration”: iteration_id, “status”: dictionary_node_to_status}

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.

import networkx as nx
import ndlib.models.ModelConfig as mc
import ndlib.models.opinions.VoterModel as vt

# Network topology
g = nx.erdos_renyi_graph(1000, 0.1)

# Model selection
model = vt.VoterModel(g)
config = mc.Configuration()
config.add_model_parameter('percentage_infected', 0.1)

model.set_initial_status(config)

# Simulation execution
iterations = model.iteration_bunch(200)
[1]
  1. Clifford and A. Sudbury, “A model for spatial conflict,” Biometrika, vol. 60, no. 3, pp. 581–588, 1973.
[2]
  1. 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.
[3]P.L.Krapivsky,S.Redner,andE.Ben-Naim,Akineticviewofstatistical physics. Cambridge University Press, 2010.