The Majority Rule model is a discrete model of opinion dynamics, proposed to describe public debates
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].
During the simulation a node can experience the following statuses:
| Name | Code |
|---|---|
| Susceptible | 0 |
| Infected | 1 |
| 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.
The following class methods are made available to configure, describe and execute the simulation:
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.
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) |
|---|
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: |
|
|---|---|
| Returns: |
a list containing for each iteration a dictionary {“iteration”: iteration_id, “status”: dictionary_node_to_status} |
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. |
The Majority Rule model is a discrete model of opinion dynamics, proposed to describe public debates.
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