Does the Choice of Preferential Voting Method Matter? An Empirical Study Using Ranked Choice Elections in the United States

ABSTRACT

In an election which uses preference ballots, there exist many different voting methods for choosing a winner of the election given the voters’ preference data. We analyse the extent to which the choice of voting method matters in American ranked-choice elections. To this end, we compiled a database of over 200 American elections which used preference ballots and, for each election, calculated the winner under the methods of plurality, instant runoff voting, plurality runoff, Condorcet, Bucklin voting, and two versions of Borda count. We find that the choice of voting method matters less frequently than what is suggested by much of the theoretical literature.

KEYWORDS:

• Ranked choice voting
• empirical results
• voting theory

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 Whenever we refer to the number of candidates in an election, we do not include write-in candidates.

2 There are other ways to adapt the Borda count method to partial ballots, but we would argue that the two adaptations in this article are the most natural.

3 These are limiting probabilities, where the number of voters approaches infinity.

4 RCV elections occurred in America before 1997, but as far as we know none of the complete vote data survived for any of those elections.

5 The election is the 2021 Minneapolis Ward 2 city council election.

6 Two elections, the 2021 New York City Democratic primary elections for the city council seats in districts 27 and 32, contained a Condorcet winner but also contained a Condorcet cycle among other, non-winning candidates.

7 We use simulation because, as mentioned above, there is very little theoretical literature addressing these questions for elections with four or more candidates.

Additional information

Notes on contributors

David McCune

David McCune is an Associate Professor of Mathematics at William Jewell College, where has has taught for the last ten years. He received his PhD in mathematics from the University of Nebraska-Lincoln in 2011. His research interests include voting theory and questions of fair representation.

Lori McCune

Lori McCune received her Ph.D. in commutative algebra from the University of Nebraska-Lincoln in 2011. She is an associate professor of mathematics at Missouri Western State University, where she has taught since 2012. E-mail: [email protected]