Opinion formation model with social identity and in-group bias

This is an agent-based model to study the effect of social identity and in-group bias on consensus formation in virtual societies.

The schematic below shows the main processes and parameters of the model. For a detailed model description see [todo:insert link to manuscript]

The model produces opinion patterns that may look as follows for a society $U_2$ of agents unaffected or a society $B$ of agents affected by in-group biases.

Usage

For a single run, use

python model.py 

Run time (on a normal laptop): ca. 20 sec

Batch runs

For batch simulations use

.\run.sh n k k_in k_out delta_0 kappa communication_frequency sig_op_0 p_rewire T resolution seed 

where T is the time horizon and resolution can be "high" for the full range of in- and out-group perception parameters $\alpha_{\rm in/out} \in [0,1[$ or "low" for $\alpha_{\rm in/out} \in { {\rm U1}(0.25, 0.25), \ {\rm U2}(0.5,0.5), \ {\rm U3}(0.75,0.75), \ {\rm B}(0.75,0.25)}$.

To reproduce the results in the main article run:

.\run.sh 100 10 8 2 0.0 0.0002 0.2 0.2 0.0 5000 low 420 

In the article, we vary `p_rewire' between 0 and 1 and use 1000 random seeds.

Parameters

Parameter	Description	Default value
n_agents	number of agents	100
k	average node degree per agent	10
k_in	average number of in-group links per agent $k_{\rm in}$. This determines the degree of homophily $^{*}$	8
k_out	average number of out-group links per agent $k_{\rm out}$	2
a_ins	in-group perception values	0.1,0.2,0.3,...,0.8,0.9,0.99
a_outs	out-group perception values. Note, only values smaller or equal than in-group perception are simulated	0.1,0.2,0.3,...,0.8,0.9,0.99
sig_op_0	fixed initial opinion uncertainty of the agents	0.2
communication_frequency	probability to interact and be socially influenced at each time step	0.2
kappa	diffusion strength during non-interaction	0.0002
delta_0	predisposition for a social identity group to have an opinion in the upper half of the opinion space. This is not used in the main manuscript	0.0
p_rewire	the randomness in the network	0.0
track_times	times at which the simulation tracks the agent mean opinions, the standard deviation. Consensus time and mean consensus opinion are stored regardless of this.	[0,5000]
seed	random seed

• $^{*}$ One can summarise $k_{in}$ and $k_{out}$ as the degree of homophily $h=\frac{k_{\rm in} - k_{\rm out} }{k}=0.6$

Python Libraries and Dependencies

Package	Version
python	3.9.5
see environment.yml

Netlogo

For interested people who prefer netlogo over python, we have also implemented a version in netlogo. Disclaimer: Unlike the python version, this has not been thoroughly tested and should be used with caution.