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:

• fraction_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, seed=None)

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.
• progress_bar – whether to display a progress bar, default False

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 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 as op

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

# Model selection
model = op.MajorityRuleModel(g)
config = mc.Configuration()
config.add_model_parameter('fraction_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.