Mathematical Aspects of Gerrymandering

Abstract

Every 10 years the United States performs a census, and this census determines how many members of congress will represent each state. Then begins an unfortunate battle, as cartographers manipulate the boundaries for political power in a process called gerrymandering. A city can become one strong Democratic hold out, or divided up creating multiple more moderate districts. A previously strong Republican district can be changed to include some more Democratically leaning districts, resulting in a competitive race where previously none existed. These fights can expose the worst of the political system, and have driven many researchers to try to find ways to prevent these power grabs. Researchers have suggested ways of measuring the districts to detect Gerrymandering by looking at the boundaries of the districts for irregularity, or by looking at the results over time to detect a bias towards one party, or even ways to generate the maps automatically, free of human intervention. In this thesis, I give an overview of some of these approaches, how to implement them using the R mapping packages, and the innate limitations of the analysis.