I am currently working on a project that involves analyzing the 18 districts of Pennsylvania and using the results of the 2018 House of Representatives Congressional Election.
I understand that transition matrices for Markov chains must be square; however, I am not sure how to do this as I currently have an $18 \times 3$ matrix ( 18 districts, 3 parties (Republican, Democrat, Independent)).
We're going to build a Markov chain $X_t$ whose state space is the partitions for some real state and whose initial state $X_0$ is some totally random partition. let $f(X_t)$ denote the number of R seats for partition $X_t$. then:
$$ \frac{1}{1000}(f(X_1) + \ldots + f(X_{1000}))$$
would be our sense of what is a fair number of $R$ seats for that state. then see where our model's version of fairness lies in the efficiency gap graph.
PA has many D voters packed in its cities which will cause your R-seat distribution not to be Gaussian, but skewed. So you might want to look at both the mean and median seat values. It would be great if you could post your results, or a link, when done. (a histogram of #R seats)