Group:
Monica Moynihan and Anthony Calacino


Topic: Applications of Linear Algebra in Political Science: Candidate Preferences in Elections

Content: In democratic states with liberal elections, voters almost always have multiple candidates to choose from. These candidates typically represent different political parties, ideologies, or voting pacts. Voters have transitive preferences for these multiple candidates. Due to a variety of factors, an individual’s most preferred candidate may not be elected. Electoral rules are often responsible for diverging voting preferences from actual votes cast. Individuals often know that their vote actually counting is contingent on how others vote and electoral rules. As a result, individuals anticipate such electoral rules and potential for certain candidates and adjust their actual vote (which may depart from the individual’s true preference). Linear algebra has been applied to the problem of voting preferences in the past to determine ways that a voter (or group of voters) can change their behavior to elect certain preferred candidates. The voting layout is put into a majority cycle, however, since these circles are complicated to read and understand, they are put into linear combinations, which is where linear algebra comes into the equation. The majority circle is decomposed into a cyclic and acyclic vectors. Through manipulation of the vectors, we can find the basis of the linear combination. Another aspect of linear algebra that is applied in voting, are Markov chains, as well as eigenvectors. This project will discuss, compute and analyze each of these aspects of linear algebra, and how they are applied to the voting system, as well as, investigate and report on the mathematics used to analyze the preferences of voters for candidates in elections.