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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.

The program is a one-year commitment and averages to about 3 hours per week of required work in addition to a 1-hour weekly meeting (total 4 hours). The program is not stipended but students may discuss with the directors the option of receiving independent study credit for one semester. 

If you are a Wellesley student interested in learning more about the intersection of math and politics and conducting original research, please complete this application to become an IMD Fellow. The application deadline is September 12, 2024. Although priority is given to juniors, we encourage anyone interested to apply. If you have any questions, you can reach out to contact@math-democracy.com.

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We initiate the study of simple games from the point of view of combinatorial topology. The starting premise is that the losing coalitions of a simple game can be identified with a simplicial complex. Various topological constructions and results from the theory of simplicial complexes then carry over to the setting of simple games. Examples are cone, join, and the Alexander dual, each of which have interpretations as familiar game-theoretic objects. We also provide some new topological results about simple games, most notably in applications of homology of simplicial complexes to weighted simple games. The exposition is introductory and largely self-contained, intended to inspire further work and point to what appears to be a wealth of potentially fruitful directions of investigation bridging game theory and topology.

Congratulations, Leah!

If you are a student interested in being involved in IMD research when opportunities arise, please fill out this form.

The post IMD Fellow Leah Valentiner Publishes Paper on the Topology of Simple Games appeared first on Institute for Mathematics and Democracy.

The PIs on the project are David McCune, Andy Schultz, and Ismar Volić. Three Wellesley students – Khyatee Atolia, Belle See, and Karen Xiao – are also a part of the project team.

The post IMD Researchers Begin a Study of Ranked Choice Methods 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.

Join us in the Pendleton East Atrium on 12/05 at 6:00 pm, exactly one month after the election. The event will be recorded and released on YouTube.

The fellows’ talks will be as follows:

Winnie Zhou – Ranked choice voting
Leah Valentiner – Primary elections
Cianna Salvatora – Gerrymandering
Presha Goel – Proportional representation
Arial Brookhart – Electoral College

RSVP required: https://forms.gle/eJgdhkP4LeFn8sYHA

The post Redesigning our Democracy – an IMD Event at Wellesley College appeared first on Institute for Mathematics and Democracy.

Arial Brookhart and Winnie Zhou will try to use category theory to reframe certain foundational constructions and results from game theory, specifically simple games and weighted voting games. 

Presha Goel will study the relationship between apportionment methods that have been used in the U.S. to allocate seats in the U.S. House of Representatives and two popular multi-winner methods of seat apportionment used in many democracies around the world.

Cianna Salvatora will examine some common proportional representation systems and see how applicable they would be to the setting of the U.S. if we switched from single-winner to multi-winner districts. In particular, she will study the effects of such a change on the implementation of the Voting Rights Act and the distribution of legislative seats for minority populations.

Leah Valentiner will work on topological modeling of political systems, namely using simplicial complexes to capture coalition structures. She hopes to understand how attaching probabilities that certain coalitions will form might add richness to the topology of the resulting complexes.

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

The post Introducing the 2024-2025 IMD Fellows appeared first on Institute for Mathematics and Democracy.

See the abstract below.

We analyze various proposals for reforming the United Nations Security Council from the game-theoretic viewpoint of quantification of power. We calculate the decision-making power of the UNSC members under each proposal using Banzhaf and Shapley-Shubik indices. Utilizing these measures, we assess how seven different reform proposals would influence the power distribution among permanent and non-permanent members and find that Weak Veto proposal is the most effective in giving non-permanent members increased influence while the African Union proposal is the best for achieving equity among regional blocs. We also provide a self-contained mathematical exposition of Banzhaf and Shapley-Shubik power indices.

The post IMD Intern Ilinca Drondoe’s Paper on Power Distribution in the UN Security Council appeared first on Institute for Mathematics and Democracy.

The program is a one-year commitment and averages to about 3 hours per week of required work in addition to a 1-hour weekly meeting (total 4 hours). The program is not stipended but students may discuss with the directors the option of receiving independent study credit for one semester. 

If you are a Wellesley student interested in learning more about the intersection of math and politics and conducting original research, please complete this application to become an IMD Fellow. The application deadline is September 13, 2024. Although priority is given to juniors, we encourage anyone interested to apply. If you have any questions, you can reach out to contact@math-democracy.com.

The post IMD Fellows Program, 2024-25 appeared first on Institute for Mathematics and Democracy.