Open Access Senior Thesis
Bachelor of Arts
© 2020 Camryn Hollarsmith
A gerrymandered political districting plan is used to benefit a group seeking to elect more of their own officials into office. This practice happens at the city, county and state level. A gerrymandered plan can be strategically designed based on partisanship, race, and other factors. Gerrymandering poses a contradiction to the idea of “one person, one vote” ruled by the United States Supreme Court case Reynolds v. Sims (1964) because it values one demographic’s votes more than another’s, thus creating an unfair advantage and compromising American democracy. To prevent the practice of gerrymandering, we must know how to detect a gerrymandered plan. We can use math to quantify districting plans to test if they were gerrymandered. To do this, a widely used method is randomly sampling plans to get a baseline to test if the current or proposed plan is an outlier. If the plan is an outlier, then it can be argued that the plan was gerrymandered. Recombination is a Markov Chain and is one method to sample; however, the distribution it samples from is unknown and therefore presents a problem. In this thesis I examine the four-by-four grid graph and find the stationary distribution of Recombination. I analyze the 117 possible districting plans that arise from a four-by-four grid graph and what each stationary probability means. This new insight will be added to the collective work at understanding gerrymandering and how to mathematically detect and prevent it. Such analysis of Recombination Markov chains has been successfully used in court in Pennsylvania and North Carolina.
Hollarsmith, Camryn, "Stationary Distribution of Recombination on 4x4 Grid Graph as it Relates to Gerrymandering" (2020). Scripps Senior Theses. 1542.
Algebra Commons, American Politics Commons, Applied Mathematics Commons, Law and Politics Commons, Legislation Commons, Other Mathematics Commons, State and Local Government Law Commons, Supreme Court of the United States Commons