The project also studied single-peakedness, social utility, and statistical fingerprinting of real elections. Although real voter preferences rarely satisfy perfect single-peakedness, many elections come surprisingly close. Condorcet methods perform well on social utility under idealized assumptions, but their advantage weakens with more realistic voter behavior. Statistical fingerprinting helps assess whether synthetic elections resemble real ones.

To read the report, access our data and visualizations, and check out our repository of datasets and code, visit the project webpage.

The post Empirical Analysis of Ranked Choice Voting Methods: Phase 2 Report Now Available appeared first on Institute for Mathematics and Democracy.

Baigali Nyamdulam and Jordyn Barger will work with Prof. David McCune (William Jewell College) to study the spoiler effect in multiwinner ranked choice elections. They will examine which proportional voting rules are most susceptible to “weak” spoiler candidates, using several different notions of weakness.

Madeline Ashton will work with Prof. Kristopher Tapp (St. Joseph’s University) on a project around computational redistricting algorithms. The mathematical core of all such algorithms involves the generation and splitting of random spanning trees. This project will explore old and new methods of generating random spanning trees, and compare their effectiveness at generating ensembles of voting maps.

Mai Li McGhee will work with Prof. Ellen Veomett (University of San Francisco) to use machine learning techniques to estimate the impact of proposed legal or policy changes on voter registration and turnout. In particular, they will look at the SAVE act and the mail-in-ballot executive order (and potentially other proposed legal or policy changes).

Brendan White will work with Prof. Jeff Wheeler (University of Pittsburgh) to further elucidate the underlying mechanism of Duncan Watts’ “model of global cascades on random networks” in a 2002 paper that determined the factors causing a narrow “cascade window” that differentiated between whether a contagion caused a “global cascade” or merely fizzled out locally in the originating subnetwork. The model relies on binary states of nodes that are flipped from zero to one by an arbitrary threshold of its neighbors being in the one state – and form a connection to case studies in social choice theory (e.g. spread of preferences, surge in candidate popularity, etc.).

At Wellesley College, Farah Rajeh and Nyamal Bangoang Riek will work with Prof. Karamatou Yacoubou Djima on a project integrating mathematical tools like Applied Harmonic Analysis (specifically shearlets) with graph-based methods and machine learning to develop affordable computational biomarkers for early autism detection. Democratic systems rely on equal opportunity and civic participation. Early detection using low-cost, low-tech placental imaging offers a universally beneficial, non-partisan approach to public health. Because placental imaging requires no expensive genetic sequencing hardware and can analyze lower-quality images taken under non-optimal conditions, it is uniquely suited for low-income and rural communities. Bridging the healthcare gap between well-funded urban centers and under-resourced regions strengthens equal access to fundamental healthcare infrastructure, which is a key pillar of a fair and inclusive democracy.

Kate Wepsic and Charlotte Chung will work with Prof. Ismar Volić on a joint project between IMD and the University of South California. The goal of the project is to understand whether topics in the intersection of math and civics are taught in K-12 schools and to what extent, and then develop instructional materials in partnership with a curriculum provider and pilot them in several schools.

IMD is grateful to all our faculty mentors for their support. We are excited about the diversity in projects and student interests with the expansion of the fellows program. Stay tuned for more research updates!

The post Introducing 2026-2027 IMD Fellows appeared first on Institute for Mathematics and Democracy.

Until now, the program has primarily supported undergraduate research at Wellesley College. Beginning this year, we would like to extend this opportunity to faculty at other colleges and universities who are interested in supervising their own undergraduate students on research projects related to mathematics and democracy. IMD has funding available to support both the students and the faculty supervising these projects.

Projects can span a broad range of topics at the intersection of mathematics (and related disciplines like statistics, computer science, and data science) and democracy.  Theoretical, empirical, and computational projects in voting and social choice, proportional representation, districting, deliberative democracy, and related areas are all welcome.

For faculty interested in participating in the Fellows Program, please write to contact@math-democracy.org with a brief description of the project you have in mind. You should also feel free to pass this information along to anyone you feel might be a good fit for this program.

The post IMD Fellows Program Expands for 2026-27 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.

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.

Find out more about the program here: https://drive.google.com/file/d/162xqjHqKQMvoRQ6qEdgm2fSnneQaSeuB/view?usp=drive_link

The post Electoral Innovation Lab: 2026 Summer Fellowship Program appeared first on Institute for Mathematics and Democracy.

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.

The post IMD Team Shares RCV Research in The Conversation appeared first on Institute for Mathematics and Democracy.