General

Summary of 2020 Summer Activities

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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