RunDMCMC

This code implements Monte-Carlo exploration of districting plans, exploring the space around an initial districting plan to give some idea of the degree of gerrymandering. It is a Python rewrite of the chain C++ program (https://github.com/gerrymandr/cfp_mcmc), originally by Maria Chikina, Alan Frieze and Wesley Pegden, for their paper, "Assessing significance in a Markov chain without mixing" (http://www.pnas.org/content/114/11/2860)

Installation

To install RunDMCMC, we currently recommend cloning the repository and installing manually:

git clone https://github.com/gerrymandr/RunDMCMC.git
cd RunDMCMC
python3 setup.py install

Using in an interactive python session

Here's how you can use RunDMCMC in an interactive python session. Navigate to the RunDMCMC/rundmcmc folder in a terminal, and then run an ipython or python command to open an interactive session. Alternatively, this should work in the terminal window in Spyder.

Now we can start playing with Markov chains! First we'll import some things.

from rundmcmc.grid import Grid

The Grid class is a little helper class for playing around with grid examples.

grid = Grid((20,20))    # Make a 20x20 grid
print(grid)

You should see a grid made out of 0's, 1's, 2's, and 3's. By default, the Grid is partitioned into four equal quadrants.

Running a chain

Now we can configure and run a MarkovChain.

from rundmcmc.chain import MarkovChain
from rundmcmc.proposals import propose_random_flip
from rundmcmc.validity import Validator, contiguous
from rundmcmc.accept import always_accept

is_valid = Validator([contiguous])

We'll configure a chain starting with grid, using the regular boundary flip proposal, validating that the districts are connected, and always accepting if the proposal is valid.

chain = MarkovChain(propose_random_flip, is_valid, always_accept, grid, total_steps=1000)

The MarkovChain in RunDMCMC is just a python generator. This means we can do a simple for loop over all the states in the chain.

for partition in chain:
    print(partition)

This should output a bunch of grids like before, but with the districts changing over time.

Making a histogram

Now we can make a histogram! The Grid class comes with a fake 'population' attribute. This attribute can be accessed as grid['population']. It is a dictionary from the districts to their populations. We'll make a histogram of the minimum district population at each step in the chain.

We'll import matplotlib to make the histogram, but feel free to use your favorite alternative.

import matplotlib.pyplot as plt

We can generate the data for our histogram using a simple list comprehension:

data = [min(partition['population'].values()) for partition in chain]

plt.hist(data)
plt.show()

The histogram should pop up in a new window. Yay!