Brian Brubach is an Assistant Professor of computer science at Wellesley College. His research focuses on algorithms and theoretical computer science with broad applications in areas such as e-commerce, fairness in automated systems, bioinformatics, and the U.S. electoral system. This is his project description:

“This project will explore measures of how close a set of ranked ballots is to being single-peaked on a line or other graph structure. We will analyze both real and synthetic election data to (1) discover characteristics of real elections, (2) identify patterns indicating electoral anomalies, and (3) check for differences between datasets using different voting rules.”

Mostapha Diss is an Affiliated Professor at Mohammed VI Polytechnic University. He is also a Full Professor of Economics at the University of Franche-Comté in France and a member of the CRESE research center since 2019. His research has focused on microeconomic theory, particularly game theory and social choice theory. This is his project description:

“The objective of this project is to analyze inequalities within the German political system using longitudinal data from the Politbarometer surveys (GESIS), which provide repeated series of public opinion data since 1977. We will develop inequality measures adapted to ordinal preferences derived from these surveys, enabling the assessment of concentration or polarization in political satisfaction rankings across socio-demographic groups, regions, and time periods. This approach will reveal the temporal dynamics of disparities in the representation of collective preferences.”

Natasa Dragovic (University of Saint Thomas) is interested in the intersection of probability and dynamical systems. Her research involves using mathematical models of opinion dynamics to make sense of political phenomena. This is her project description:

“We will explore ranked choice elections in Minneapolis and Saint Paul and look for anomalies.” 

Matt Jones is an assistant professor of Mathematics at Colby College. In the area of mathematics and democracy, his research involves studying the properties of various voting methods using mathematical analysis and computation. This is his project description:

“We will be studying ballot generator models, e.g. impartial culture, Bradley-Terry, Plackett-Luce, spatial models, and compare their outputs to real ranked ballot data. Relevant questions include: What are the statistical markers of “realistic” profiles? What models most closely resemble real elections? How can we modify existing models to account for truncated ballots?”

David McCune received his PhD in geometric group theory and semigroup theory from the University of Nebraska-Lincoln in 2011. He is currently an Associate Professor of Mathematics in the Department of Mathematics and Data Science at William Jewell College. His research interests include apportionment theory and social choice theory, with an emphasis on the computational and empirical aspects of these fields. This is his project description:

“We will study spoiler effects in multiwinner elections where the spoiler candidate is particularly “weak” in some way. How often could a Pareto-dominated candidate be a spoiler for the method of single transferable vote, for example? This project is useful because the spoiler effect is seen as particularly egregious when the spoiler candidate is weak, and Pareto-dominated candidates are weak. We will explore this topic for several different notions of weak candidates, using the Scottish and Australian STV datasets as the main playground.”

Keaton Quinn (Wellesley College) is interested in the geometry of districting. His group will look into multi-winner districts and proportional representation. This is his project description:

“It is claimed that multi-winner districts increase the likelihood that the demographics of those elected more accurately represent the demographics of the voting population. We will investigate these claims using the Markov chain methods that appear in the literature. Do multimember districts always lead to proportional representation? Does it depend on the size of the POC population? Does it depend on the level, size, or location of the election? ”

Andrew Schultz is an Assistant Professor of Mathematics at Wellesley College. Previously, he was a J.L. Doob Professor of Mathematics at the University of Illinois at Urbana-Champaign. He finished his Ph.D. under the direction of Ravi Vakil at Stanford in 2007. His basic research interests are algebraic, though more specifically he’s interested in Galois module structures of ‘interesting’ objects and Hilbert 90-like results. This is his project description:

“Spatial models can be a useful way to understand how voter ideology translates into outcomes for different election types. In this project we use CES data to model elections that first run through a primary selection process before resulting in a general election. What effect does this have on the distance of the elected candidate from the median voter? How might parties act strategically to insert an independent moderate candidate to siphon of votes from their competitor? And how might incumbency or party support be factored into the model to explain persistence or favored status?”

Kristopher Tapp is a Professor in the Department of Mathematics at Saint Joseph’s University. His research areas include Riemannian Geometry, graph algorithms, and combinatorics.  His recent work focuses on applying mathematics to redistricting and election analysis. This is his project description:

“We will study the distribution of ballot lengths in Scottish and other ranked choice elections. How does it depend on the number of candidates and seats? On the number of candidates in one’s preferred party? On the clustering of a profile into blocs of voters? How frequently is it the case that blocs of voters could have obtained a more desirable outcome by extending or shortening their ballots? With respect to which social choice mechanism (STV, Borda, etc) is the outcome most affected by the ballot length distribution?”

Jennifer Wilson is an Associate Professor of Mathematics at The New School.  Her research interests include voting and social choice theory, systems of political representation, resource allocation and cooperative game theory. She has also developed courses in Gerrymandering and Fair Representation, and Fair Division and Politics. This is her project description:

“We will work on one of two projects depending on student background and preferences. The first is to look at the behavior of mult-winner voting methods for a small number of candidates on single-crossing domains. The second is to compare the results by party of the Scottish elections and the results of using a standard apportionment method.”

The undergraduate teaching assistants for this year’s program are Valerie Zhu, Elaine Zhao, Gahan Sabbir, and Erik Hill.

Thank you to all of the mentors and teaching assistants for their integral roles in the program. We look forward to seeing the work their teams will do this summer. Stay tuned for more research updates!

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All students and faculty also meet once a week for guest lectures given by prominent mathematicians and democracy reformers. One session is dedicated to a discussion of the college application process and the final session consists of presentations of the projects (here are some of the presentations from the 2025 program*).

If you’re a high school student interested in participating in IMD’s summer 2026 online research program, visit this page. Linked there is a form you should fill out to apply by March 6, 2026.

If you have any questions, feel free to write to us at contact@math-democracy.org. We are looking forward to reading your application!

The post Apply Now: 2026 IMD Summer High School Research Program appeared first on Institute for Mathematics and Democracy.

Analyzing Swing States in Presidential Elections: The Case of Wisconsin – Michelle Zuo

This paper quantitatively analyzes county-level voting patterns in Wisconsin’s presidential elections from 2000 to 2024. As a pivotal swing state, Wisconsin has alternated between Democratic and Republican candidates since 2012. Using data from the Wisconsin Elections Commission, we examine vote totals across 72 counties and seven election cycles. Pearson correlations measure similarity in county voting trajectories, while choropleth maps visualize spatial shifts. Results show strong clustering of vote changes: Democratic and Republican gains between 2016 and 2020 were concentrated in southeastern urban and suburban counties, with rural areas showing little change. Correlations reveal a north-south divide, as southern counties exhibit similar trends and northern ones diverge. These findings highlight spatial heterogeneity in electoral dynamics and the decisive role of urban mobilization in statewide outcomes.

A Comparison of Precinct and District Voting Data Using Persistent Homology to Identify Gerrymandering in North Carolina – Ananya Shah

Gerrymandering is one of the biggest threats to American democracy. By manipulating district lines, politicians effectively choose their voters rather than the other way around. Current gerrymandering identification methods (namely the Polsby-Popper and Reock scores) focus on the compactness of congressional districts, making them extremely sensitive to physical geography. To address this gap, we extend Feng and Porter’s 2021 paper, which used the level-set method to turn geographic shapefiles into filtered simplicial complexes, in order to compare precinct level voting data to district level voting data. As precincts are regarded as too small to be gerrymandered, we are able to identify discrepancies between precinct and district level voting data to quantify gerrymandering in the United States. By comparing the persistent homologies of Democratic voting regions at the precinct and district levels, we detect when areas have been “cracked” (split across multiple districts) or “packed” (compressed into one district) for partisan gain. This analysis was conducted for North Carolina House of Representatives elections (2012-2024). North Carolina has been redistricted four times in the past ten years, unusually frequent as most states redistrict decennially, making it a valuable case study. By comparing persistence barcodes at the precinct and district levels (using the bottleneck distance), we show that precinct level voting patterns do not significantly fluctuate biannually, while district level patterns do, suggesting that shifts are likely a result of redistricting rather than voter behavior, providing strong evidence of gerrymandering. This research presents a novel application of topological data analysis in evaluating gerrymandering and shows persistent homology can be useful in discerning gerrymandered districts.

The post IMD High School Summer Researchers Release Research Papers appeared first on Institute for Mathematics and Democracy.

Gahan Sabbir is a member of the Wellesley College Class of 2028 who is planning on majoring in mathematics. As an IMD fellow, she is interested in studying how math can help design equitable political systems, and what this math reveals about our power as voters.

Claudia Summers is a member of the Wellesley College Class of 2028 who is a Mathematics and Philosophy double major. As an IMD fellow she is eager to explore how mathematics can play a powerful role in political discussions and influence democratic processes.

Last but not least, Elaine Zhao is a member of the Wellesley College Class of 2027. She is pursuing a double major in Data Science and English on a pre-law track. She is interested in exploring the intersection of law, mathematics, and technology, particularly how mathematical tools can help predict trends and enhance democratic processes. As an IMD fellow, she’s looking forward to studying gerrymandering using geometric knowledge. 

Gahan and Claudia will be researching propositional representation, while Elaine Zhao will pursue a research project on gerrymandering. 

We are also thrilled to have two Wellesley students joining us to support a joint research project on K-12 Math and Civic Education, in partnership with the Center for Applied Research in Education at University of Southern California.

Kate Wepsic is a member of the Wellesley College Class of 2028 and is a prospective math major. She is passionate about mathematics education, especially at the elementary level. At IMD, she is interested in learning more about education in math and civics and how to design and implement K-12 curricula.

Charlotte Chung is a member of the Wellesley College Class of 2027 at Wellesley College, majoring in Education Studies with a minor in Mathematics. She is interested in the intersection of K–12 education and mathematics. At IMD, she is excited to explore the connections between K–12 math and civics education.

For more background on the fellows and their interests, see the IMD website’s students page.

The post Introducing 2025-26 IMD Fellows & Research Students appeared first on Institute for Mathematics and Democracy.

Photo credit: The 2025 Carnegie Young Leaders for Civic Preparedness convene, via Institute for Citizens & Scholars

The post IMD High School Program Alums Win Carnegie Young Leaders Fellowship appeared first on Institute for Mathematics and Democracy.

The first phase of the project will consist of interviews and focus groups with teachers, school leaders, district leaders, and state department of education staff in several states. The second stage will be to develop resources necessary to support teachers (e.g., curriculum, instructional materials, aligned professional learning) who want to implement math and democracy topics in their classrooms (voting, legislative seat allocation, districting and gerrymandering, proportional representation, Electoral College, quantifying political systems, etc.). Research assistants would help create, coordinate, and assess the phase one work. Depending on how this portion progresses, they might also be involved in the development of curricular materials from phase two.

To apply for the position, please fill out this form by the end of the day on Friday, September 19, 2025.

If you have any questions, please reach out to Professor Ismar Volić at ivolic@wellesley.edu. 

The post Research Opportunity: K-12 Math & Civics Education appeared first on Institute for Mathematics and Democracy.

As part of the 16th Days of Bosnian-Herzegovinian American Academy of Arts and Sciences (BHAAAS) conference (June 19-22), the workshop will reach scholars and teachers from around the country. This is an exciting opportunity to help teachers educate their students about applications of mathematics and to continue connecting mathematics and democracy. IMD looks forward to continuing these outreach efforts and integrating democracy into mathematics education.

To learn more and register, please visit this page on the BHAAAS website.

The post 2025 Math and Democracy Workshop for Bosnian High School Teachers appeared first on Institute for Mathematics and Democracy.

The film, which features IMD, highlights the often hidden ways our world runs on math. Through investigating crises like political polarization, inequity, and climate change, it highlights the importance of understanding the mathematical underpinnings of society in order to be empowered to make change. 

Counted Out is being shown across the country, including at the SXSW EDU festival this past week. Don’t miss out on your chance to watch, discuss, and eat pie– please join us on March 13th at 12:45 PM in H105.

The post “Counted Out” Screening at Wellesley College appeared first on Institute for Mathematics and Democracy.

Winnie Zhou presented on ranked choice voting, first giving the audience a rundown of the difference between plurality voting and ranked choice voting. She highlighted the characteristics of a fair election, analyzing different scenarios to compare the relative fairness of a ranked choice system compared to winner-take-all elections. 

In her presentation on “The Problems with the Primaries,” Leah Valentiner walked the audience through the logistics of primary elections, beginning with the allocation of votes in the Republican and Democratic parties. She emphasized the lack of transparency in the primaries and how different the process can be depending on the state and party. Finally, she discussed ranked choice voting and open primaries as ways to make our elections more representative of public interest.

Cianna Salvatora focused on “Gerrymandering: How Redistricting is Reshaping Democracy,” first describing the mechanisms through which gerrymandering happens, before discussing the effects of gerrymandering on elections and what we can do about it. Through both real life and theoretical examples, Cianna illustrated how gerrymandering can change the outcome of elections. She concluded by giving an overview of current efforts to curb gerrymandering and make elections fairer.

Presha Goel shared with the audience the drawbacks of single-member districts in congressional elections and how multi-member districts may help to more accurately reflect the interests of voters and increase diversity of parties and political platforms represented in elections.

Finally, Arial Brookhart discussed the electoral college. She began by explaining the system’s history and how it works, then dove into what makes it an unideal mechanism for our presidential elections. As she noted, there have been five presidential elections where a candidate won the popular vote but was not elected; this most recently occurred in the 2016 election. 

We are proud of our Fellows for their work in conducting research and giving these presentations. Thank you to all who attended! We look forward to continuing these discussions around how our democracy can better serve us and the math underlying our political systems. 

Here are presenters’ slides and recorded talks:

• Slides and video for “Ranked Choice Voting” by Winnie Zhou
• Slides and video for “The Problems with the Primaries” by Leah Valentiner
• Slides and video for “Gerrymandering: How Redistricting is Reshaping Democracy” by Cianna Salvatora
• Slides and video for “Proportional Representation” by Presha Goel
• Slides and video for “Electoral College” by Arial Brookhart

The post Presentation Videos and Slides from “Redesigning our Democracy” by IMD Fellows appeared first on Institute for Mathematics and Democracy.