Majority Rule¶

The Majority Rule model is a discrete model of opinion dynamics, proposed to describe public debates [1].

Agents take discrete opinions ±1, just like the Voter model. At each time step a group of r agents is selected randomly and they all take the majority opinion within the group.

The group size can be fixed or taken at each time step from a specific distribution. If r is odd, then the majority opinion is always defined, however if r is even there could be tied situations. To select a prevailing opinion in this case, a bias in favour of one opinion (+1) is introduced.

This idea is inspired by the concept of social inertia [2].

Statuses¶

During the simulation a node can experience the following statuses:

Name Code
Susceptible 0
Infected 1

Parameters¶

Name Type Value Type Default Mandatory Description
q Model int in [0, V(G)]   True Number of neighbours

The initial infection status can be defined via:

• percentage_infected: Model Parameter, float in [0, 1]
• Infected: Status Parameter, set of nodes

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.MajorityRuleModel.MajorityRuleModel(graph)
MajorityRuleModel.__init__(graph)

Model Constructor

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

Set the initial model configuration

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

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

Describe¶

MajorityRuleModel.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
MajorityRuleModel.get_status_map(self)

Specify the statuses allowed by the model and their numeric code

Returns: a dictionary (status->code)

Execute Simulation¶

MajorityRuleModel.iteration(self)

Execute a single model iteration

Returns: Iteration_id, Incremental node status (dictionary node->status)
MajorityRuleModel.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. 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 Majority Rule 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.MajorityRuleModel as mr

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

# Model selection
model = mr.MajorityRuleModel(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] S.Galam, “Minority opinion spreading in random geometry.” Eur.Phys. J. B, vol. 25, no. 4, pp. 403–406, 2002.
 [2] R.Friedman and M.Friedman, “The Tyranny of the Status Quo.” Orlando, FL, USA: Harcourt Brace Company, 1984.