Using Monte Carlo Markov Chain Methods to Understand the Mathematics and Visualization of Gerrymandering in Politically Competitive Districts

Abstract

Gerrymandering is a technique used to give an unfair advantage to any one political party through the process of manipulating district lines in order to dilute the voting power of an opposing political party. With the advent of recent technology which makes it easy to analyze population dynamics, it has become easier than ever to predict voting outcomes and therefore precisely draw districts in order to engineer specific outcomes. However, it is difficult to isolate cases of deliberate gerrymandering as it is not always evident whether victories in particular areas are due to legislative wrongdoing or a natural political outcome. Commonly thought telltale signs of gerrymandering, such as oddly shaped districts, are not, in fact, an indicator, as gerrymandered districts do not have to be shaped in odd ways in order to be unfair. So how can we isolate cases of gerrymandering?

In this paper, I aim to perform a comprehensive analysis of the redistricting process for the states of Maryland, Pennsylvania and North Carolina. In order to do this, I will firstly use Monte Carlo Markov Chain (MCMC) Modeling techniques to analyze the politically competitive districts in Maryland, North Carolina and Pennsylvania, and determine whether redistricting in the state has provided any one political party with an unfair advantage. I will secondly perform a computational analysis for the recently redistricted states of Pennsylvania and North Carolina by visualizing proposed redistricting plans and comparing them to the enacted plans. Finally, I will analyze and compare policy initiatives and compare their efficacy for the future.