Ronit Banga is a rising senior at Germantown Academy in Pennsylvania with interests in finance, entrepreneurship, and applied mathematics. He is particularly interested in how data and quantitative analysis can be used to better understand economic systems, public policy, and decision-making. At IMD, he looks forward to exploring real-world datasets and using mathematical approaches to analyze democratic systems and the structures that shape them.

Arlan Bartfeld is a rising senior in Miami, Florida, fascinated by Computer Science, Political Science, and Math. He enjoys analyzing polling data, viewing demographic trends, and creating his own election predictions. He is extremely excited to conduct research with like-minded peers at IMD in Political Data Science, an area he is deeply passionate about.

Reese Cartwright is a rising senior at Vanguard High School in Florida. She’s especially interested in how mathematical reasoning can help us understand social and educational policy, and loves thinking about how systems and structures shape real‑world outcomes. She’s excited to explore how data and quantitative tools can support stronger, more equitable democratic processes at IMD this summer.

Cloe Chai is a rising senior at Proof School in San Francisco, California. She’s interested in exploring how theoretical mathematics can become a tool in the fields of social science, electoral politics, and economics. She’s grateful and excited to learn and work at IMD this summer!

Richard Chen is a rising senior from Saratoga High, situated on the California coast. He is interested in political science, especially approaching it using applied research methods. This summer, he hopes to uncover how mathematics can model real-world democratic issues and inform decisions that protect our freedoms.

Jenny Chu is a rising senior at The Hockaday School in Dallas, Texas. She’s broadly interested in patterns of human connection and applied math modeling, and how they can be explored together to inform a more diverse and equitable America. Beyond STEM, she deeply enjoys writing poetry and making Spotify playlists. She’s excited to learn and work with IMD this summer!

Eugenia Evangelinos is a rising senior at Phillips Academy Andover. She is passionate about applied math and how it can be used to improve people’s lives. She has always been an avid reader of the news and is excited to combine her interest in understanding government policies with her love for all things math at IMD this summer!

Raina Gao is a rising senior at Thomas Jefferson High School for Science and Technology in Alexandria, Virginia. She has long been interested in mathematics and human behavior and has become increasingly interested in public policy. At IMD, she is especially excited to use data and mathematical models to study representation and fairness, and she hopes her research can help inform future policy decisions.

Arjun Grandhe is a rising senior from Albuquerque, New Mexico. He first developed an interest in politics through Speech & Debate, and has always been interested in using math to model real world issues. At IMD, he hopes to improve his modeling skills and learn more about the American political system.

Brady Kanter is a rising senior at Phillips Academy Andover in Massachusetts, from San Francisco, CA. He is interested in learning more about the human side of numbers, how math is another lens through which to gain insight into society. He believes that participating in research with IMD will allow his to explore real-world applications of statistics and how they influence various aspects of the political atmosphere, including policy changes, voting patterns, and more.

Siddharth Karuturi is a rising senior from Illinois with a strong passion for economics and mathematics. At IMD, he is excited to explore how these disciplines intersect with democracy, public policy, and government in the United States. He is especially interested in research, competition mathematics, and applying quantitative thinking to real-world societal challenges. Outside of academics, Siddharth enjoys watching comedy films and playing basketball.

Islam Khalaf is a rising senior from Cairo, Egypt. He plans to study data science and machine learning, with a specific interest in how data intersects with finance, politics, and human behavior. Outside of academics, he enjoys weightlifting and training mixed martial arts.

Alexander Kiselgof is a rising senior at Brooklyn Technical High School in New York City. He is passionate about applied mathematics and hopes to pursue it in college and beyond through research. Alex is especially interested in bioinformatics and public health, and he is excited to learn how mathematical tools can be used to better understand real-world issues that affect communities. Through the Institute for Mathematics and Democracy’s summer program, he looks forward to exploring the connection between applied math, public policy, and meaningful social change.

Om Lala is a rising senior at Gretchen Whitney High in Cerritos, California. He’s interested in all walks of mathematics, but he’s currently most interested in Game Theory and Differential Geometry. He’s deeply interested in Machine Learning, where he works specifically on problems in AI Safety. Om is Secretary General of his school’s MUN program, Class President, and actively involved in local policy work. Om is excited to utilize his mathematical and computational toolset to explore interesting problems in Public Policy and Political Science with IMD!

Jason Lee is a rising senior at Dwight-Englewood School in New Jersey. He is interested in how mathematics can help address societal challenges, from public health to institutional fairness in democratic systems. Using quantitative, data-driven approaches, he seeks to identify where such systems fall short and explore reforms that strengthen processes and promote fairness.

Wenhao Lu is a rising senior at Millburn High School in New Jersey. He has always been interested in math, AI, and social good, and is excited to explore their intersection this summer at IMD. He is also interested in AI safety and strengthening democracy by making systems more accessible and less of a black box.

Sasha Ordukhanyan is a rising senior at Stuyvesant High School in New York City. He is a member of both his school’s math team and math modeling team, and is very interested in all the ways in which math can be applied to solve real-world problems. He looks forward to gaining more experience conducting research and modeling real-world issues at IMD. Outside of math, he enjoys playing the piano and is an avid Knicks fan. A fun fact about him is that he also speak Russian, Armenian, and Spanish.

Soham Pradhan is interested in mathematics as a foundation for thinking rigorously about complex systems, especially in areas like probability and optimization that directly connect to machine learning. In ML, he’s drawn to building models that learn from data in meaningful ways, and he’s also interested in how these tools intersect with governance, particularly how data-driven systems can improve decision-making, policy design, and institutional accountability.

Danica Scofield is a rising senior at Blaine High School in Minnesota. She is interested in politics, public policy, and addressing real-world challenges. At IMD, she is very excited to research the intersection of mathematics and political science, particularly how data can contribute to more equitable outcomes for underrepresented communities. Outside of her academic interests, Danica is a competitive pianist who enjoys performing for large audiences.

Taison Scofield is a rising senior from Blaine High School, MN. He is passionate about mathematics (especially combinatorics and probability), and the use of quantitative reasoning to better understand complex societal systems. At IMD, he is excited to explore how mathematical models and data-driven research can increase equality and solve paradoxes in voting systems. Taison enjoys math competitions, cello, and tennis.

Mrinalini Sensarma is a rising senior at Inventure Academy in Bangalore, India. She has always loved both mathematics and the social sciences, and is especially fascinated by the intersection of mathematics, economics, and democratic systems. Curious about how data and quantitative reasoning can be used to better understand societal challenges, she is excited to explore the application of mathematical ideas to real-world political questions at IMD.

Stella Seong is a rising senior at Phillips Academy in MA, but usually resides in the suburbs of Northern NJ. She dedicates her free time to compiling pink noise playlists, buying semi-permanent hair dye, playing Redactle, and doing some occasional math. Her favorite perfect square is 49 or 81.

Pragyan Shukla is a high school researcher from India with a strong focus on pure mathematics, particularly number theory. He is currently engaged in research-oriented learning and mentorship through leading academic environments, including work connected with premier research institutes in India. Pragyan is deeply interested in foundational problems in mathematics and in promoting early research culture among young students, especially from underrepresented regions. He is excited to contribute to and grow within an international summer research community.

Emma Wong is a rising junior from Long Island, New York. She has interests in community advocacy and public policy, and has previously interned on finance and voter outreach branches on political campaigns. She also is passionate about research on social issues and public health disparities. She looks forward to meeting and working with the rest of IMD’s 2026 High School Research cohort!

Andy Zhang is a current junior at Basis Independent Fremont. He is interested in machine learning and linear algebra. Additionally, he enjoys playing badminton with his friends and going for runs.

Zifei Zhao is a rising senior at Langley High School in McLean, VA. She is passionate about using math and computer science to create quantitative models that explore real-world problems. At IMD, she hopes to research how math modelling can address modern issues in democracy.

Zifan Zhao is a rising senior at Langley High School in McLean, Virginia. He is passionate about mathematics, computer science, current events, and history. At IMD, he hopes to apply mathematical modeling to governmental processes to find solutions for the challenges our democracy faces today.

Paige Zhu is a rising senior at Phillips Academy Andover interested in math and statistics. She is excited to get involved with the IMD program and learn more about the applications of math in politics. In her free time, she enjoys reading, playing tennis, and making Spotify playlists.

IMD is excited to host these students and supervise their research this summer. Stay tuned for more updates about the program!

The post Introducing the 2026 High School Summer Research Cohort appeared first on Institute for Mathematics and Democracy.

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!

The post IMD High School Summer Research Program Project Descriptions appeared first on Institute for Mathematics and Democracy.

The workshop included over 40 participants (many of them IMD affiliates) and featured thirteen talks in voting, districting, proportional representation, and other topics. Time was also set aside for collaborative work in small groups and development of new research projects.

IMD is grateful to all who shared their expertise and participated in making the workshop a success!

The post IMD Affiliate-Organized Workshop Recap: “Mathematics of Elections, Fairness, and Representation” at the Banff International Research Station appeared first on Institute for Mathematics and Democracy.

The talk covered how mathematics has been quietly shaping democracy for centuries, from the design of voting systems to the drawing of political maps. Today, with classical results being repurposed in surprising ways and vast computational power at our disposal, it offers powerful new tools for understanding and improving how we govern ourselves. Volić traced the historical role of mathematics in democracy and surveyed current research at their intersection, spanning voting theory, districting, apportionment, proportional representation, and digital democracy. Far from being merely abstract or theoretical, this vibrant interdisciplinary work demonstrates how mathematical expertise speaks directly to the functioning of democratic institutions – challenging the notion that our work has little bearing on civic life. The talk highlighted how mathematical formality can be meaningfully integrated with human realities of politics, a task that feels especially urgent as democracy faces profound strain.

To watch the recording, visit the following link: https://www.youtube.com/watch?v=hm_nBJ_xpAQ 

The post IMD Co-Founder Ismar Volić Gives Talk at the JMM: “Math goes to Washington: The Mathematics of Democracy, from Theory to Practice” appeared first on Institute for Mathematics and Democracy.

See the abstract and link to the publication below:

“This article extends the analysis of Atkinson, Foley, and Ganz in “Beyond the Spoiler Effect: Can Ranked-Choice Voting Solve the Problem of Political Polarization?”. Their work uses a one-dimensional spatial model based on survey data from the Cooperative Election Survey (CES) to examine how instant-runoff voting (IRV) and Condorcet methods promote candidate moderation. Their model assumes an idealized electoral environment in which all voters possess complete information regarding candidates’ ideological positions, all voters provide complete preference rankings, etc. Under these assumptions, their results indicate that Condorcet methods tend to yield winners who are substantially more moderate than those produced by IRV. We construct new models based on CES data which take into account more realistic voter behavior,

such as the presence of partial ballots. Our general finding is that under more realistic models the differences between Condorcet methods and IRV largely disappear, implying that in real-world settings the moderating effect of Condorcet methods may not be nearly as strong as what is suggested by more theoretical models.”

Candidate Moderation Under Instant Runoff and Condorcet Voting: Evidence from the Cooperative Election Survey

The post IMD Team Releases Paper Titled “Candidate Moderation Under Instant Runoff and Condorcet Voting: Evidence from the Cooperative Election Survey” appeared first on Institute for Mathematics and Democracy.

The virtual program runs from the end of June through the beginning of August. Faculty commitment is a few hours per week, working with a group of three or four high school students. IMD can also provide undergraduate teaching assistants. Faculty will receive stipends for their participation.

Projects can be theoretical or empirical, and many involve analysis of real-life data. Some of the past projects include the study of properties of voting methods, the influence of court decisions on measures of gerrymandering, modeling proportional representation in the U.S., and analyzing the effect of alternative sizes and apportionments of House of Representatives on presidential elections. 

If you are interested in being a faculty mentor for this program or to learn more about it, please email us at contact@math-democracy.org.

We look forward to working with you to support student engagement with mathematics and democracy!

The post Seeking Faculty Mentors for 2026 High School Summer Research Program appeared first on Institute for Mathematics and Democracy.

In addition, Prof. Veomett has two articles that were recently published on gerrymandering metrics:  Bounds and Bugs: The Limits of Symmetry Metrics to Detect Partisan Gerrymandering and Don’t Trust a Single Gerrymandering Metric.  The Redistricting Data Hub recently asked her to present this work to their stakeholders (which includes staff from the ACLU, NAACP Legal Defense Fund, Southern Poverty Law Center, and other prominent civil rights organizations). 

The post New Gerrychain Data Resource Available appeared first on Institute for Mathematics and Democracy.

The post IMD Affiliate and Summer Research Students Complete Paper on “Bloc Voting on Single-Peaked Preferences” appeared first on Institute for Mathematics and Democracy.

The post Ranked Choice Voting in Wellesley College Government Elections appeared first on Institute for Mathematics and Democracy.

RSVP Here: https://docs.google.com/forms/d/e/1FAIpQLSdwOA5hTPQ0oXQDCeygaQBKfoRP8f2xz-yDda9J23-dxP2Mxw/viewform

The post IMD Affiliate Talk: The Role of CS and Math in Redistricting and Proportional Multimember Districts as an Electoral Reform appeared first on Institute for Mathematics and Democracy.