polarization

Implementation and extension of Flache and Macy (2011) work on cultural polarization.

Introduction

The work by Flache and Macy (2011) showed that more complex cultures less often found themselves in states of high polarization. They also found that high levels of cultural polarization were more likely if agents were connected on a small-world network. At first, I wondered what was the effect of initial conditions on the final polarization an artificial society achieved. Secondly, I wondered what was the effect of communication noise on these artificial societies. So, I implemented the Flache and Macy (2011) model (FM model) in Python and began experimenting. A year later we are submitting this work for review.

Our focus here is on the software that powers our results, and not the social theory. Please see our paper on the arXiv (coming soon) and Flache and Macy's 2011 paper in the Journal of Mathematical Sociology for more information (https://www.tandfonline.com/doi/abs/10.1080/0022250X.2010.532261).

Installation

The best way to install this package is to do the following. First, clone the repository. Then in the root repository directory, create and activate a new virtual environment. To install the package and its dependencies, run

pip install --editable .

You used to be able to download the output, but the files are now missing. I will be re-generating and uploading the data soon, and then you will be able to download the data and run run the accompanying Jupyter notebook. The tarfile is ~14GB, and this is even using built-in HDF5 compression, but it only takes about ten minutes on a good connection.

This will also make available the command-line interface, polexp. To confirm everything went OK, you can run polexp in the console, and you should see

Usage: polexp [OPTIONS] COMMAND [ARGS]...

Options:
  --help  Show this message and exit.

Commands:
  complexity_experiment  Run n_trials for a given maximum initial...
  reproduce_fig11        Create a set of HDF files corresponding to...
  reproduce_fig12        Create a set of HDF files corresponding to...
  rerun_experiment       Re-run an experiment using an hdf from...

More info on the CLI is below.

Unit tests

To run unittests, run

python setup.py nosetests

After you've run that once, you can just run nosetests to run the unit tests.

Experiments

The experiment class we mainly used was the BoxedCaveExperiment, which got its name originally because agent opinions were boxed in between a value of -S and S, where |S| ≤ 1. This experiment is initialized with a conected caveman network structure with n_caves and n_per_cave agents in each cave. Each node in the network is an Agent. The Agent class is simple with just two attributes, opinions and weights.

The minimal example below shows how to initialize a new BoxedCaveExperiment for K=2, run a few iterations of agent updates, and plot the agent coordinates. See scripts/runner.py for how this is used in our large-scale experiments. The sge_scripts/ directory contains job submission scripts for use on the Sun Grid Engine cluster we have on campus. It may just work with other queue management systems.

import matplotlib.pyplot as plt
import numpy as np

from experiments.within_box import BoxedCavesExperiment

n_caves = 20
n_per_cave = 5
S = 0.5
bce = BoxedCavesExperiment(n_caves, n_per_cave, S, K=2)

bce.iterate(5)

init_coords = np.array(bce.history['coords'][0])
final_coords = np.array(bce.history['final_coords'])

xi = init_coords[:, 0]; yi = init_coords[:, 1]
xf = final_coords[:, 0]; yf = final_coords[:, 1]

plt.plot(xi, yi, 'o', label='Initial opinions')
plt.plot(xf, yf, 'o', label='Opinions after five iterations')
lim = [-.55, .55]; plt.xlim(lim); plt.ylim(lim)
plt.axis('equal')
plt.legend()

This script can be run via python simple_readme.py. You should get an image like the one below

Command-line interface

The CLI is called polexp, as in "polarization experiment". The primary subcommand of polexp is complexity_experiment. You can get the help for this by running

polexp complexity_experiment --help

which will print

Usage: polexp complexity_experiment [OPTIONS] S K NOISE_LEVEL OUTPUT_DIR

  Run n_trials for a given maximum initial opinion feature S and cultural
  complexity K.

Options:
  --distance_metric TEXT
  --n_trials INTEGER
  --n_iterations INTEGER
  --n_iter_sync INTEGER
  --help                  Show this message and exit.

See the scripts in sge_scripts for how to use this CLI on a computing cluster.

Data model

To sync experiment data we used the hierarchical data format, HDF5. HDF gives a number of advantages. Data is read from memory on-demand, so loading the file does not load the data, just pointers to the data. HDF is self-describing, meaning that it includes its own metadata. The fact that it is hierarchical is also powerful. So far, we have used this to store agent opinions at various points in time, the network adjacency matrix, and a timeseries of polarization for all 100 trials in a single file, for each network configuration, connected caveman, random short-range, and random long-range conditions.

Reference

Flache, A., & Macy, M. W. (2011). Small Worlds and Cultural Polarization. The Journal of Mathematical Sociology, 35(1-3), 146–176. doi: 10.1080/0022250X.2010.532261