Date of Completion

Spring 5-1-2021

Thesis Advisor(s)

Myron Minn-Thu-Aye

Honors Major





Voting is in integral part of any functioning democracy, but there exist more than just one way to count votes. Some voting methods use only a voter’s top-choice candidate, while others require a ranking of all candidates, most-preferred to least-preferred, from each voter. We examine some of these ranked-choice voting methods, including the anti-plurality method, Hare’s method, and Coomb’s method.

Because of the variety of voting methods, we introduce criteria, which allow for an evaluation of the advantages and disadvantages of each method. The criteria give various definitions for what “good” or “bad” voting methods look like, depending on context. Some important criteria include the monotonicity, independence, and decisiveness criteria. Arrow’s theorem then gives us restrictions on which criteria can coexist and which are incompatible.

Next, we explore how the state of Maine uses ranked-choice voting, specifically Hare’s method, for both state and federal primaries and general federal elections. Hare’s violation of the monotonicity and independence criteria is explored and proved.

Finally the results of the 2020 United States presidential election are dissected. The apportionment of congressional seats and thus Electoral College votes is cause for complaint from some citizens, and reapportionment may allow fairer representation for citizens through the Electoral College. This reapportionment of electoral votes, as well as a reallocation of electoral votes within each state is investigated.

Included in

Mathematics Commons