Invited Paper Session Abstracts - Quantitative Justice: Incorporating Social Justice in Research, the Classroom, and More

An Introduction to Quantitative Justice

8:00 a.m. - 8:20 a.m.
Ranthony A.C. Edmonds, Duke University
AJ Stewart, AAAS Science and Technology Executive Fellow

Quantitative Justice is the application of techniques from quantitative sciences in the social sciences to study existing social systems and derive potential tools to improve social justice, fairness, and equality. The intersection between quantitative techniques and social sciences is not new, but research by mathematicians in quantitative justice has experienced significant growth during the last five years with an increased interest in topics such as gerrymandering, voting methods, using data science to study bias in healthcare and the arts, as well as the study of algorithmic fairness. In this talk we will define quantitative justice, discuss its recent growth, and give current examples of how mathematics is being used today to shift societal systems.

Quantifying Communities of Interest in Electoral Redistricting

8:30 a.m. - 8:50 a.m.
Parker Edwards, Florida Atlantic University

Communities of interest are groups of people, such as ethnic, racial, and economic groups, with common sets of concerns that may be affected by legislation. Many states have requirements to preserve communities of interest as part of their redistricting process. While some states collect data about communities of interest in the form of public testimony, there are no states to our knowledge which systematically collect, aggregate, and summarize spatialized testimony on communities of interest when drawing new districting plans. During the 2021 redistricting cycle, our team worked to quantify communities of interest by collecting and synthesizing thousands of community maps in partnership with grassroots organizations and/or government offices. In most cases, the spatialized testimony collected included both geographic and semantic data—a spatial representation of a community as a polygon, as well as a written narrative description of that community. In this talk, we outline our aggregation pipeline that started with spatialized testimony as input, and output processed community clusters for a given state with geographic and semantic cohesion.

Topological and Geometric Methods in Redistricting

9:00 a.m. - 9:20 a.m.
Tom Needham, Florida State University

I will discuss some novel mathematical approaches to study the redistricting problem; i.e., the problem of recognizing and characterizing political districting plans which were designed for political advantage at the cost of fair representation. In particular, I’ll introduce methods from the fields of topological data analysis and optimal transport, which are able to give new insights into the ‘shape’ of the space of all districting plans.

Topological Data Analysis of U.S. City Demographics

9:30 a.m. - 9:50 a.m.
Jakini Kauba, Clemson University

In recent years, Topological Data Analysis (TDA) has been used to analyze complex data and provide insights that other research techniques cannot. TDA is a newer form of data analysis which analyzes trends of data from a topological perspective by way of the main visualization tool of persistence diagrams. TDA has been used to measure breast cancer transcriptional DNA, voting patterns in precincts, gerrymandering, and even texture representation.

In this paper, we apply TDA to geospatial data from the census to more accurately describe racial segregation among the Black and Hispanic demographics across one hundred cities in America. Our goal was to complete city to city comparisons in 2010 and 2020 as well as compare city similarities over the course of ten years for each race and note the respective trends. We were able to find seven clusters of cities in the black population that shared common characteristics and five for the Hispanic population. After doing a comparison of cities across the span of a decade, we also found commonalities of each racial demographic. In summary, this project represents a first step in uncovering trends in demographic data using TDA. We hope to continue exploring this data set in an effort to expand our understanding of various demographic patterns in America.

Accelerating and Scaling Community Centered Research

10:00 a.m. - 10:20 a.m.
Carrie Diaz-Eaton, Bates College

Nuevas Voces is a program run by the Woonasqatucket River Watershed Council in Providence, RI. Nuevas Voces creates a leadership cohort from a low-income, primarily immigrant neighborhood along the river to understand environmental issues such as neighborhood flooding and water contamination. Researchers at ICERM in Providence at Brown and IMSI at Chicago began a partnership with Nuevas Voces to provide some tools they might need to help advocate for their communities. In this talk we focus on how we developed this partnership, choices we made to center community needs, and resulting data projects.

#Metamath: The Mathematics of Mathematics

10:30 a.m. - 10:50 a.m.
Ron Buckmire, Occidental College

We present and discuss a curated selection of recent literature related to the application of quantitative techniques, tools, and topics from mathematics and data science that have been used to analyze the mathematical sciences community. We engage in this project with a focus on including research that highlights, documents, or quantifies (in)equities that exist in the mathematical sciences, specifically, and STEM (science, technology, engineering, and mathematics) more broadly. We seek to enhance social justice in the mathematics and data science communities by providing numerous examples of the ways in which the mathematical sciences fails to meet standards of equity, equal opportunity and inclusion. We call our project the “mathematics of Mathematics,” explicitly building upon the growing, interdisciplinary field known as “Science of Science” to interrogate, investigate, and identify the nature of mathematical sciences itself. We aim to promote, provide, and posit sources of productive collaborations and we invite interested researchers to contribute to this developing body of work.