I am currently working on a project to analyze the 18 districts of Pennsylvania and use the results of the 2018 legislative elections of the House of Representatives. I understand that the transition matrices for Markov chains must be square; However, I do not know how to do it because I currently have an 18×3 matrix (18 districts, 3 parties (Republican, Democrat, Independent).
Here is a more in-depth summary of my project:
we will build a Markov chain X_t whose state space consists of partitions of a real state and whose initial state X_0 is a totally random partition. let f (X_t) denote the
number of seats R for the partition X_t. then 1/1000 * (f (X_1) + … +
f (X_1000)) would be our sense of the number of R seats for this state. Then see where is the fairness version of our model in the graph of the efficiency gap.