Undergraduate Summer Research Archives - Institute for Mathematics and Democracy

Summer 2025 Undergraduate Research at IMD

Institute MD — Fri, 13 Jun 2025 17:25:41 +0000

This summer, three Wellesley students will examine various ways mathematics plays a pivotal yet underappreciated role in democracy.

Lydia Byers is part of Wellesley College’s Class of 2028 and a prospective mathematics and classical civilizations major. She is interested in how math can be used to benefit voter representation and help voters make informed decisions about their governments.

Bianca Fiore is a rising sophomore in the class of 2028. She is a prospective double major in Political Science and Mathematics. Bianca is interested in ways math can be applied to political science. As an IMD fellow, she hopes to further explore how mathematical analysis can explain the advantages and disadvantages of different political systems.

Chuming (Mimi) Wu is a member of the class of 2027 in Wellesley College majoring in philosophy and economics. Her favorite parts about the intersection between mathematics and politics are voter theory, game theory and gerrymandering. She is excited to join IMD assisting and learning more about research on democracy and voting systems.

The goal of Lydia, Bianca, and Mimi’s project is to study certain outward-facing aspects of democracy through a mathematical lens and think about our daily interactions with democratic and political processes in an objective way. The main question is whether we are using the best mathematics to design and conduct our democracy, and if not, what should these processes be replaced by.

Some particular topics the students will look at are:

Measuring democracy (quantifying the notion of a “good” and “bad” democracy, representativeness, fairness; democracy indicators and indices; public opinion and polling)
Power and influence (quantifying power of individuals, institutions, and coalitions; measuring centrality and influence in political systems)
Conflict and negotiation (game-theoretic approach to understanding political conflict, war, negotiation, diplomacy, strategy, cooperation, war, and consensus)
Web of democracy (networks, information flow, polarization, opinion dynamics)
Statistics as a political tool (manipulation of stats for political gain, by politicians or media)
Data and algorithms (impact of big data and AI on power dynamics; algorithmic bias)
Digital democracy (new tools for enabling political participation, like sortition, citizen assemblies, participatory budgeting)

Their research will be supervised by Prof. Ismar Volić from Wellesley College.

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Summer 2024 Undergraduate Research at IMD

Institute MD — Sat, 25 May 2024 14:41:07 +0000

This summer, two Wellesley College students will use topological data analysis of Pew political typology data to explore the structure of partisanship and polarization in U.S. politics.

Kamila Lim is a class of 2026 data science and French double major. She is interested in the intersection of cultural communication and data to demonstrate the impact of climate change on public health.

Mira Chandriani is a class of 2026 data science and economics double major. She is excited about her IMD research this summer.

Using the “shape of data” approach of topological analysis, Kami and Mira hope to expose some features of the Pew survey that are not visible to standard statistical techniques. Existence of disjoint components or holes in the data might indicate the likelihood of people coming together on certain political issues or the ability of coalitions being formed along certain topics but not others.

The research will be supervised by Prof. Ismar Volić from Wellesley College in collaboration with Prof. Yuliy Baryshnikov from University of Illinois Urbana-Champaign who had the initial idea for this project.

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Summer 2023 Undergraduate Summer Research at IMD

Institute MD — Tue, 27 Jun 2023 15:26:51 +0000

Undergraduate summer research at IMD is in full swing, with several Wellesley College students continuing their studies into topics at the intersection of mathematics and politics:

Ilinca Drondoe is a member of the Wellesley College Class of 2026. She hopes to major in Peace & Justice Studies and International Relations, and she is passionate about how understanding politics from a mathematical perspective can lead to socially just policy change. Her research began in Fall 2022 when she took Prof. Volić’s Mathematics and Politics class. She is in the process of building upon her final paper, which assesses the political implications of proposed United Nations Security Council reforms, using power indices to determine how they would affect the power balance between permanent and non-permanent members. She is excited to add a quantitative perspective to the conversation around UN reform, which she believes is essential for shaping policies that will improve its ability to respond to global crises and promote peace.
Hanqi Zhu is a member of Wellesley’s class of 2026. She plans to major in Mathematics and Computer Science. She is interested in how mathematics, especially some of its more abstract parts, could be utilized and implemented to analyze politics and demographics. She is currently doing research on simplicial complexes and liquid democracy.
Zixu Wang is a Davis-UWC scholar and a member of the class of 2024 at Wellesley College. While majoring in mathematics and minoring in computer science, she has broad interests and research experience in multiple humanities and social science fields. Her project aims to investigate the relationship between hypergraphs – notions such as clustering coefficient, local and global stability, homology, and contiguity – and political structures, with the objective of enhancing their modeling.

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IMD 2021 Student Summer Research Virtual Event – Videos and Presentations

Institute MD — Tue, 09 Nov 2021 19:37:57 +0000

On November 4, 2021, IMD held a virtual event “Summer Research in Math and Politics. With topics ranging from quantifying power to liquid democracy, four Wellesley students presented their research conducted during the summer of 2021. We are grateful to all who attended.

Below you can find links to both the slide show presentations from each of our speakers and the video of their talk:

– Eliza Zizka ’22: A “Fair” Dictatorship: Social Choice Theory and Category Theory . (Video link)

– Anastasia Brooks ’23: The Geometry of Simplicial Complexes and the Quantification of Power. (Video link)

– Audrey Ballarin ’23 & Heeba Nazeer ’23: Implementing Liquid Democracy. (Video link)

– Hayley Grape ’23: Meeting in the Middle: Choosing a “Typical Map” from Congressional Redistricting Maps. (Video link)

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IMD Student Publishes Paper in Mathematical Social Sciences

Institute MD — Mon, 18 Oct 2021 04:14:05 +0000

Congratulations to IMD student Andrea Mock! Her paper Political structures and the topology of simplicial complexes was accepted for publication in the journal Mathematical Social Sciences.

The paper studies how political structures can be modeled by simplicial complexes and how their topology can be interpreted in terms of political actions like merging structures and introducing mediators. This point of view also allows for the introduction of the notions of the viability of an agent and the stability of a political system, as well as detection of incompatibilities and potential compromises among agents.

You can read the full paper here.

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2021 Summer Research Presentations at IMD

Institute MD — Mon, 13 Sep 2021 05:33:09 +0000

Summer research at IMD has come to a close. To mark the end of the 2021 Wellesley Science Center Summer Research, students presented their findings at a poster session. Here are links to all of their presentations:

Eliza Zizka ’22 – A “Fair” Dictatorship: Social Choice Theory and Category Theory
Anastasia Brooks ’23 & Ava Mock ’23 – Using the Geometry of Simplicial Complexes to Quantify Power in Voting Systems
Hayley Grape ’23 – Meeting in the Middle: Choosing a “Typical Map” from a Set of Congressional Redistricting Maps
Audrey Ballarin ’23 & Heeba Nazeer ’23 – Overcoming the Challenges of Implementing Liquid Democracy

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Undergraduate Research at IMD Returns in Summer 2021

Institute MD — Fri, 25 Jun 2021 19:45:03 +0000

IMD’s second annual summer research program is underway, in collaboration with Wellesley College’s Science Center Summer Research Program. For the next several months, six Wellesley math and computer science students will work on the following projects:

Eliza Zizka ’22 is working on interpreting some standard results in social choice theory, such as Arrow’s Theorem and the Gibbard-Satterthwaite Theorem, in terms of category theory. She will try to establish a framework by which social choice functions can be regarded in terms of functors between certain categories and recast some of the standard criteria and properties of social choice functions in terms of this language.

Anastasia Brooks ’23 and Ava Mock ’23 are working on applications of combinatorial topology to power indices. They will use simplicial complexes to model coalition structures where some of the coalitions are not possible. They are hoping that the topology of simplicial complexes will provide new formulas for the Banzhaf and Shapley-Shubik indices for this generalized setup where not all coalitions are allowed.

Hayley Grape ’23 is working on an algorithm to find an “average” redistricting map out of a set of randomly generated maps. She is experimenting with defining distance metrics to identify a central map within a set.

Audrey Ballarin ’23 and Heeba Nazeer ’23 are identifying properties of a central delegation mechanism for a liquid democracy system. They are exploring algorithmic possibilities for minimizing concentrated power, capping power, and splitting individual votes between delegates.

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Apply for Summer 2021 Research in Math and Politics at Wellesley College

Institute MD — Tue, 30 Mar 2021 14:31:25 +0000

IMD faculty are once again running a research program in math and politics for Wellesley College students in summer ’21. The participants will first be briefly introduced to several topics in mathematics and politics, including voting, apportionment, power index computations, gerrymandering, and game theory, and will then be divided into research groups according to their interests and backgrounds. They will work on several possible projects, including voting and representation theory, combinatorial topology of political structures, comparative power index study, impossibility theorems and category theory, and geometry of gerrymandering.

IMD is grateful to the Science Center Summer Research Program for its support for this program.

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IMD Student featured in Spotlight on Wellesley

Institute MD — Wed, 16 Sep 2020 18:44:09 +0000

During the Science Summer Research this year, Cicely (Cece) Henderson ’23 researched “Trends in Mathematical Language Used in Political Speeches,” with IMD co-founder Professor Ismar Volić.

Her work is featured in Spotlight on Wellesley. Please read the article here.

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Summary of 2020 Summer Activities

Institute MD — Sun, 06 Sep 2020 23:55:42 +0000

We had a busy summer at the Institute for Mathematics and Democracy! Here is a summary of the various activities that took place at the IMD over the last few months:

Summer research

A number of Wellesley College students participated in summer research with IMD. They worked on projects in

Combinatorial topology and political coalition structures
Representation theory and voting
Analysis of power indices with forbidden coalitions
Unicef poverty data and topological data analysis
Spread of coronavirus and topological data analysis

Here are a few highlights.

Yiran Chen ’21 produced visualizations of the U.S. COVID-19 data using Mapper graphs to easily observe and compare the gradual spread of the pandemic across time and space. This unique way of visualizing COVID-19 captures various nuances and conveys its spread in the U.S. in a novel way. You can read more about it in this paper: https://arxiv.org/abs/2008.05989

Annette Belleman ‘23, Helen Chen ‘23, Tantan Dai ‘22, Guadalupe Portillo Deras ‘21, and Jingmiao Zhao ‘23 examined the behavior of positional counting (Borda Count) and pairwise ranking (Condorcet) methods using linear algebra, group theory, and representation theory to study the possible outcome profiles of elections. Their work consisted of three different parts: counting the inconsistencies that arise between Borda Count and Condorcet results, the decomposition of profiles with multiple candidates in an election, and the results of young tableaux multiplication. You can read more about this research here.

Andrea Mock ’22 studied how political structures (coalitions and conflicts among agents such as political parties) can be modeled by simplicial complexes. She is using homology to develop invariants that describe when certain types of coalitions are possible and when power can be delegated. Andrea will continue this work in the fall.

Cece Henderson ’23 examined the evolution of mathematical language in political speeches over the last few decades. She wrote a program that counted the number of certain types of words in hundreds of political speeches in order to quantify the changing relationship between mathematics and politics. In addition to looking at presidential speeches, she also did state-level analysis of governor speeches and will continue to correlate her findings to education trends, especially in STEM fields.

Summer course

Professor Ismar Volić taught a Mathematics and Politics class. For their final projects, the students worked in groups to create a number of teaching modules. covering topics such as the Electoral College, various voting methods, apportionment, and quantification of power. We are very excited that these modules will be used this fall by middle school and high school teachers in California, Pennsylvania, and Texas. If you think these modules might be useful to you or anyone else, please feel free to use them or pass them along.

Lecture

IMD director Ismar Volić delivered an online lecture about the importance of mathematics in democracy at University of Sarajevo’s Center for Interdisciplinary Studies in June. He spoke about voting, apportionment, and gerrymandering with a focus on the upcoming elections in the U.S. and in Bosnia. He is hoping to implement some of IMD’s projects in Bosnia.

For more details on all the summer activities, please visit the IMD webpage.

Let us know if you have any ideas for projects or activities that you think IMD should undertake.

Please help us spread the word about IMD and its activities. We would love to have as many students, educators, researchers, activists, or anyone else who cares about quantitative literacy in democracy involved in IMD’s work.

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