Scholarship

I received my PhD in algebra in 2011 under the supervision of Susan Hermiller and John Meakin at the University of Nebraska-Lincoln. Around 2015, I switched my research focus to mathematical political science, broadly defined. I started by doing work in the theory of apportionment, mostly focusing on the apportionment of delegates in US presidential primaries. Currently I work in social choice theory and voting theory, focusing on the methods of instant runoff voting (aka "ranked choice voting") for single-winner elections and single transferable vote for multiwinner elections. My favorite type of work is searching for voting paradoxes in real-world ranked-choice elections, although I also like generating theoretical results. This work lies in the intersection of mathematics, political science, data science, and computer science.

Highlights of my work include: 

• my book about presidential primaries, Delegate Apportionment in the US Presidential Primaries: A Mathematical Analysis, co-authored with Michael Jones and Jennifer Wilson, and published by Springer.

• my paper Monotonicity Anomalies in Scottish Local Government Elections, co-authored with Adam Graham-Squire, which appeared in Social Choice and Welfare. This paper contains the first empirical examination of monotonicity paradoxes in real-world multiwinner single transferable vote elections. For this work I collected and cleaned ballot data from approximately 1100 ranked-choice elections; that data is now publicly available at https://github.com/mggg/scot-elex.

• my paper Proportional Representation in Practice: Quantifying Proportionality in Ordinal Elections, co-authored with Tuva Bardal, Markus Brill, and Jannik Peters, which was accepted at the AAAI 2025 conference. The paper uses various measures of proportionality to analyze how well the voting method of single transferable vote achieves proportionality in Scottish local government elections.

• I greatly enjoy mentoring student research projects. Five of the peer-reviewed articles listed below have student coauthors.

1. M. Jones, D. McCune, and J. Wilson (Editors). Mathematical Analyses of Decisions, Voting, and Games. Contemporary Mathematics Series 795 (2024). American Mathematical Society. Providence, RI.

2. M. Jones, D. McCune, and J. Wilson. Delegate Apportionment in the US Presidential Primaries: A Mathematical Analysis. Springer, (2023). Studies in Choice and Welfare.

1. D. McCune and J. Wilson. The Negative Participation Paradox in Three-Candidate Instant Runoff Elections, forthcoming in Theory and Decision. arxiv version

2. D. McCune. Single Transferable Vote and Paradoxes of Negative and Positive Involvement, forthcoming in Mathematics Magazine. arxiv version

3. A. Graham-Squire and D. McCune. Paradoxical Oddities in Two Multiwinner Elections from Scotland, The
   Mathematical Gazette 108 (2024), no. 573: 492-506. arxiv version

4. D. McCune and A. Graham-Squire. Monotonicity Anomalies in Scottish Local Government Elections, Social Choice and Welfare (2024), https://doi.org/10.1007/s00355-024-01522-5. arxiv version

5. D. McCune and L. McCune. Does the Choice of Preferential Voting Method Matter? An Empirical Study Using Ranked Choice Elections in the United States, Representation 60 (2024), no. 1: 1-16. https://doi. org/10.1080/00344893.2022.2133003.

6. M. Jones, D. McCune, and J. Wilson. An iterative procedure for apportionment and its use in the 2016 Georgia Republican primary. In M. Jones, D. McCune, and J. Wilson (Eds.). Mathematical Analyses of Decisions, Voting, and Games. Contemporary Mathematics 795 (2024). American Mathematical Society. Providence, RI.

7. D. McCune, E. Martin, G. Latina, and K. Simms. A Comparison of Sequential Ranked-Choice Voting and Single Transferable Vote. The Journal of Computational Social Science (2024), https://doi.org/10.1007/ s42001-024-00249-8. arxiv version

8. G. Chambers-Wall and D. McCune. An Issue of Guaranteed Representation in a Variant of Hamilton’s Method. Involve 17 (2024), no. 3: 373-396.

9. M. Dickerson, E. Martin, and D. McCune. An Empirical Analysis of the Effect of Ballot Truncation on Ranked-Choice Electoral Outcomes. The PUMP Journal of Undergraduate Research 7 (2024): 79-95. arxiv version

10. A. Graham-Squire and D. McCune. Ranked Choice Wackiness in Alaska. Math Horizons 31 (2024), no. 1: 24-27. arxiv version

11. A. Graham-Squire and D. McCune. An Examination of Ranked-Choice Voting in the United States, 2004-2022. Representation (2023), https://doi.org/10.1080/00344893.2023.2221689.

12. D. McCune and L. McCune. The Curious Case of the 2021 Minneapolis Ward 2 City Council Election. The College Mathematics Journal (2023), https://doi.org/10.1080/07468342.2023.2212548. arxiv version

13. D. McCune and J. Wilson. Ranked-choice voting and the spoiler effect. Public Choice (2023), https: //doi.org/10.1007/s11127-023-01050-3.

14. D. McCune. A Simple Algorithm for Drawing Apportionment Diagrams. The College Mathematics Journal 54 (2023), no. 1: 22-32.

15. D. McCune. The Many Apportionment Paradoxes of the 2020 Iowa Democratic Presidential Caucuses. The Mathematical Intelligencer 45 (2023): 55-63.

16. B. Groharing and D. McCune. Benford’s Law and County-Level Votes in US Presidential Elections. CHANCE 35 (2022), no. 2: 4-10.

17. M. Jones, D. McCune, and J. Wilson. New Quota-based Apportionment Methods: The Allocation of Delegates in the Republican Presidential Primary. Mathematical Social Sciences 108 (2020): 122-137.

18. D. McCune, L. McCune, and D. Nelson. The Cutoff Paradox in the Kansas Presidential Caucuses. UMAP Journal 40 (2019), no. 1: 21-45.

19. D. McCune and L. McCune. Counting Your Chickens with Markov Chains. Mathematics Magazine 92 (2019), no. 3: 163-172.

20. M. Jones, D. McCune, and J. Wilson. The Elimination Paradox: Apportionment in the Democratic Party. Public Choice 178 (2019), no. 1: 53-65.

21. D. McCune and S. Tunstall. Calculated Democracy: Explorations in Gerrymandering. Teaching Statistics 41 (2019), no. 2: 1-7. Winner: 2019 C. George Oswald Prize

22. D. McCune and L. McCune. How Can we Compare Voting Mehotds? A Voting Theory Project. PRIMUS 29 (2019), no. 5: 487-501.

23. D. McCune. Semigroups Arising from Asynchronous Automata. Groups, Geometry, and Dynamics 8 (2014): 199-223.

24. K. Bryan, J. Haugh, and D. McCune. Fast Imaging of Partially Conductive Linear Cracks Using Impedance Data. Inverse Problems 22 (2006): 1337-1358.

1. T. Bardal, M. Brill, D. McCune, and J. Peters. (2025). Proportional Representation in Practice: Quantifying Proportionality in Ordinal Elections. In Proceedings of the 39th AAAI Conference on Artificial Intelligence (AAAI). AAAI Press. Forthcoming.

2. M. Jones, D. McCune, and J. Wilson. (2025). Proportional Consistency of Apportionment Methods. In Proceedings of the 6th AMMCS International Conference. Springer. Forthcoming. arxiv version

1. J. Clelland, M. Duchin, and D. McCune. (2025). Study of the 2024 STV City Council Election in Portland, Oregon. Report commissioned by Building Power for Communities of Color Oregon. Report available here.

2. D. McCune, A. Schultz, and I. Volić. (2025). An Empirical Investigation of Ranked Voting Methods. Report commissioned by Freedman Consulting.

1. D. McCune. Vector Calculus. In Calculus Volume 3, pp. 647-836. Chapter 6, 1st Edition. Austin, TX: OpenStax College, 2016.

1. Schwab Charitable ($383,628), 2025.
   Project Title: An empirical analysis of ranked choice voting methods
   Principal Investigators: David McCune, Andy Schultz, Ismar Volić

2. International Centre for Mathematical Sciences (£30,000), 2024.
   The grant funded the conference "Mathematics of Voting and Representation", hosted by the Edinburgh Futures Institute.
   Conference Organizers: Jeanne Clelland, David McCune, Michael Singer, and Ismar Volić
   
   

1. Lead organizer of the workshop The Mathematics of Elections, Fairness, and Representation. (2026)
   Banff International Research Station
   Co-organizers: Jeanne Clelland, Natasa Dragovic, Ismar Volić
   Workshop webpage 

2. Mathematics of Voting and Representation conference (2024),  hosted by the Edinburgh Futures Institute
   International Centre for Mathematical Sciences
   Conference Organizers: Jeanne Clelland, David McCune, Michael Singer, and Ismar Volić
   Conference webpage 

3. As program chair of the Missouri Section of the MAA, I organized the 2024 section meeting.

1. AMS Special Session on the Mathematics of Decisions, Elections and Games
   Joint Mathematics Meetings, 2026
   Co-organizers: Michael Jones and Jennifer Wilson

2. AMS Special Session on the Mathematics of Decisions, Elections and Games
   Joint Mathematics Meetings, 2025
   Co-organizers: Michael Jones and Jennifer Wilson

3. Session on Voting Methods and Fairness Criteria
   Public Choice Society Meeting, 2024

4. AMS Special Session on the Mathematics of Decisions, Elections and Games
   Joint Mathematics Meetings, 2024
   Co-organizers: Michael Jones and Jennifer Wilson

5. AMS Special Session on the Mathematics of Decisions, Elections and Games
   Joint Mathematics Meetings, 2022
   Co-organizers: Michael Jones and Jennifer Wilson

6. AMS Special Session on the Mathematics of Decisions, Elections and Games
   Fall Central Section Meeting of the AMS, 2018
   Co-organizer: Michael Jones