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PyEI is a Python library for ecological inference. The target audience is the analyst with an interest in the phenomenon called Racially Polarized Voting.

Racially Polarized Voting is a legal concept developed through case law under the Voting Rights Act of 1965; its genesis is in the majority opinion of Thornburg v. Gingles (1982). Considered the “evidentiary linchpin” for vote dilution cases, RPV is a necessary, but not sufficient, condition that plaintiffs must satisfy for a valid claim.

Toward that end, ecological inference uses observed data (historical election results), pairing voting outcomes with demographic information for each precinct in a given polity, to infer voting patterns for each demographic group.

PyEI brings together a variety of ecological inference methods in one place and facilitates reporting and plotting results; quantifying the uncertainty associated with results under a given model; making comparisons between methods; and bringing relevant diagnostic tools to bear on ecological inference methods.

PyEI is relatively new and under active development, so expect rough edges and bugs -- and for additional features and documentation to be coming quickly!

Want to use PyEI? Start here.


You can install the latest release from PyPi with:

pip install pyei

Or, install directly from GitHub for the most up-to-date (but potentially less stable) version:

pip install git+

If you would like to explore PyEI without installation, you can explore this interactive Colab notebook (just note that inference might be slow!)

Example notebooks

Check out the intro notebooks and example notebooks for sample code that shows how to run and adjust the various models in PyEI on datesets.

If you are new to ecological inference generally, start with pyei/intro_notebooks/Introduction_toEI.ipynb.

If you are familiar with ecological inference and want an overview of PyEI and how to use it (with examples), then start with intro_notebooks/PyEI_overview.ipynb.

To explore EI's plotting functionality, check out pyei/intro_notebooks/Plotting_with_PyEI.ipynb.

For more work with two-by-two examples, see in pyei/examples/santa_clara_demo.ipynb.

For more work with r-by-c examples, see pyei/examples/santa_clara_demo_r_by_c.ipynb.

For examples of model comparison and checking steps with PyEI, see pyei/examples/model_eval_and_comparison_demo.ipynb.


Feel free to file an issue if you are running into trouble or if there is a feature you'd particularly like to see, and we will do our best to get to it!

Want to contribute to PyEI? Start here.

Contributions are welcome!

Uses Python>=3.7. After cloning the environment, you should be able to use either virtualenv or conda to run the code. The second (conda) is probably easier for development, but virtualenv is used for the project's CI.

Here is how to create and activate each environment. See the docs for more elaborate details:

Install with virtualenv

virtualenv pyei_venv           # create virtualenv
source pyei_venv/bin/activate  # activate virtualenv
python -m pip install -U pip   # upgrade pip
python -m pip install -e .     # install project locally
python -m pip install -r requirements-dev.txt  # install dev requirements

Install with conda

conda create --name pyei --channel conda-forge python=3.8 --file requirements.txt --file requirements-dev.txt # create conda environment and install requirements
pip install -e . #install project locally


After making changes, make sure everything works by running


This will also run automatically when you make a pull request, so if you have trouble getting that to run, just open the PR, and we can help!


If you are using PyEI, please cite it as:

Knudson et al., (2021). PyEI: A Python package for ecological inference. Journal of Open Source Software, 6(64), 3397,


  doi = {10.21105/joss.03397},
  url = {},
  year = {2021},
  publisher = {The Open Journal},
  volume = {6},
  number = {64},
  pages = {3397},
  author = {Karin C. Knudson and Gabe Schoenbach and Amariah Becker},
  title = {PyEI: A Python package for ecological inference},
  journal = {Journal of Open Source Software}