Graduation Year

2020

Document Type

Open Access Senior Thesis

Degree Name

Bachelor of Arts

Department

Mathematics

Reader 1

Sarah Cannon

Reader 2

Christopher Towse

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Rights Information

© 2020 Camryn Hollarsmith

Abstract

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.

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