# Algorithmic Bias¶

The Algorithmic Bias model considers a population of individuals, where each individual holds a continuous opinion in the interval [0,1]. Individuals are connected by a social network, and interact pairwise at discrete time steps. The interacting pair is selected from the population at each time point in such a way that individuals that have close opinion values are selected more often, to simulate algorithmic bias. The parameter gamma controls how large this effect is. Specifically, the first individual in the interacting pair is selected randomly, while the second individual is selected based on a probability that decreases with the distance from the opinion of the first individual, i.e. directly proportional with the distance raised to the power -gamma.

After interaction, the two opinions may change, depending on a so called bounded confidence parameter, epsilon. This can be seen as a measure of the open-mindedness of individuals in a population. It defines a threshold on the distance between the opinion of the two individuals, beyond which communication between individuals is not possible due to conflicting views. Thus, if the distance between the opinions of the selected individuals is lower than epsilon, the two individuals adopt their average opinion. Otherwise nothing happens.

Note: setting gamma=0 reproduce the results for the Deffuant model.

## Statuses¶

Node statuses are continuous values in [0,1].

## Parameters¶

Name Type Value Type Default Mandatory Description
epsilon Model float in [0, 1]   True Bounded confidence threshold
gamma Model int in [0, 100]   True Algorithmic bias

## Methods¶

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

### Configure¶

class ndlib.models.opinions.AlgorithmicBiasModel.AlgorithmicBiasModel(graph, seed=None)

Model Parameters to be specified via ModelConfig

Parameters: epsilon – bounded confidence threshold from the Deffuant model, in [0,1] gamma – strength of the algorithmic bias, positive, real

Node states are continuous values in [0,1].

The initial state is generated randomly uniformly from the domain [0,1].

AlgorithmicBiasModel.__init__(graph)

Model Constructor

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

Override behaviour of methods in class DiffusionModel. Overwrites initial status using random real values.

AlgorithmicBiasModel.reset(self)

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

### Describe¶

AlgorithmicBiasModel.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
AlgorithmicBiasModel.get_status_map(self)

Specify the statuses allowed by the model and their numeric code

Returns: a dictionary (status->code)

### Execute Simulation¶

AlgorithmicBiasModel.iteration(self)

Execute a single model iteration

Returns: Iteration_id, Incremental node status (dictionary node->status)
AlgorithmicBiasModel.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 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 AlgorithmicBiasModel 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.AlgorithmicBiasModel(g)

# Model configuration
config = mc.Configuration()