The Math and Democracy Seminar features research on contact points between the mathematical sciences and the structure of democratic society. The purpose of the seminar is to stimulate mathematical activity on problems relating to democracy, and to foster interdisciplinary collaboration between mathematicians and other scholars and democratic stakeholders.
Examples of topics of interest include detection of gerrymandering, fairness and accountability of algorithms used in social decision-making, voting and apportionment theory, applications of statistics to discrimination law and the census, and mathematical modeling of democratic processes. The scope is not limited to these and is expected to expand as further applications emerge.
The seminar is held on select Mondays and Wednesdays at the Center for Data Science at 60 5th Ave.
Contact Ben Blum-Smith (ben@cims.nyu.edu) or Soledad Villar (soledad.villar@nyu.edu) with any questions, including speaker suggestions, or to subscribe to the email list.

Spring 2019

Speaker: Mira Bernstein
Time: Wednesday February 27, 5:30-6:30 pm
Place: 60 5th Avenue, Room 150
Title: Statistical tools for fighting gerrymandering
Abstract: “Gerrymandering is the practice of drawing boundaries of electoral districts in a way that unfairly benefits or hurts a particular group of voters. Common targets of gerrymandering include supporters of a political party (partisan gerrymandering) or members of a racial minority (racial gerrymandering). In the US, these two types of gerrymandering have very different legal status, so the mathematical tools required to combat them are completely different as well. In this talk, I will describe statistical approaches to fighting both types of gerrymandering. In the case of partisan gerrymandering, the main difficulty lies in articulating a quantitative standard of partisan fairness and finding ways to measure deviations from this standard. In contrast, for racial gerrymandering, the legal standard is relatively clear; the challenge is to show that race is a relevant variable at all. Racial gerrymandering can only occur if voters of different races tend to vote differently, which is extremely difficult to prove when we have no way of knowing how any individual voted. I will describe existing statistical tools for detecting racially-polarized voting and conclude with my own work on increasing the power of these techniques by combining data from multiple elections.”
Bio: Mira Bernstein is a founding member of the Metric Geometry and Gerrymandering Group at Tufts. She received her PhD in pure mathematics from Harvard in 1999, but since 2008 her work has focused on using mathematics to solve social problems — from exploring the effects of extending health insurance to low-income populations to combatting slavery and forced labor throughout the world. Mira is also very active in mathematics education. She loves getting her students to see that mathematics, far from being scary and boring, is powerful, fascinating, and highly relevant to their lives.

Past talks

Fall 2018

Speaker: Shira Mitchell (NYC Mayor’s Office)
Time: Wednesday October 31, 5:30-6:30 pm
Place: 60 5th Avenue, Room 150
Title: Prediction-based decisions and fairness: choices, assumptions, and definitions
Abstract: A recent flurry of research activity attempts to define “fairness” quantitatively, especially in decisions based on statistical and machine learning (ML) predictions. The field’s rapid growth has led to wildly inconsistent terminology and notation, presenting a serious challenge for comparing definitions. Our work attempts to bring much-needed order. First, we explicate the various choices and assumptions made—often implicitly—in developing a prediction-based decision system. We then use these to motivate concerns about fairness, and present definitions of fairness from the statistics and ML literature in a notationally consistent catalogue. In doing so, we offer designers of prediction-based decision systems a way to think through choices, assumptions, and fairness considerations.
Bio: Shira Mitchell is a statistician and slow thinker. After her PhD at Harvard and postdoc at Columbia, she spent two years at Mathematica Policy Research working on small area estimation and causal inference for federal agencies (mostly Medicare and Medicaid). Now she is at the NYC Mayor’s Office of Data Analytics (MODA), working with city agencies to both deploy and critique data-driven policy.
 
Speaker: Zajj Daugherty (City College)
Time: Monday November 5, 5:30-6:30pm
Place: 60 5th Ave, Room C10 (note different room)
Title: An algebraic approach to voting theory
Abstract: In voting theory, simple questions can lead to complex and sometimes paradoxical results. Recently, we have been able to use tools from modern algebra to address long-standing arguments over voting and tallying methods that date back to the days of Jean-Charles de Borda and Nicolas de Condorcet. In this talk, we’ll explore how to frame voting methodology in terms of combinatorics and representations of finite groups.
Bio: Zajj Daugherty is an Assistant Professor of Mathematics at the City College of New York. She received her PhD from the University of Wisconsin Madison in 2010, and was a postdoc at Dartmouth College, the Institute for Computational and Experimental Research in Mathematics, and the University of Melbourne. Her research is primarily in combinatorial representation theory, with applications in statistical mechanics. But she got her start in the field via voting theory as an undergraduate researcher at Harvey Mudd College, and has enjoyed revisiting the topic via a recent surge in interest in the topic in her community.
 
Speaker: Steven Brams (NYU)
Time: Monday November 19, 5:30-6:30pm
Place: 60 5th Ave, Room C10
Title:Is There a Better Way to Elect a President?
Abstract: Properties of approval voting—whereby voters can approve of as many candidates as they like in a multi-candidate election, and the candidate with the most approval wins—are compared with properties of (1) plurality voting, in which voters can vote for only one candidate; (2) ranking systems, such as the Borda count and the Hare system of single transferable vote (also called instant runoff or ranked choice voting); and (3) grading systems that have been proposed by several mathematicians. Approval voting, which is used to elect popes, the UN secretary general, and presidents of several professional societies, is a simpler and more practicable alternative that I argue should be used in presidential and other public elections. Extending approval voting to multi-winner elections, such as to a committee or council, will also be discussed.
Bio: Steven J. Brams is Professor of Politics at New York University and the author, co-author, or co-editor of 18 books and about 300 articles. He holds two patents for fair-division algorithms and is chairman of the advisory board of Fair Outcomes, Inc.
Brams has applied game theory and social-choice theory to voting and elections, bargaining and fairness, international relations, and the Bible, theology, and literature. He is a former president of the Peace Science Society (1990-91) and of the Public Choice Society (2004-2006). He is a Fellow of the American Association for the Advancement of Science (1986), a Guggenheim Fellow (1986-87), and was a Visiting Scholar at the Russell Sage Foundation (1998-99).
 

Spring 2018

Speaker: Wesley Pegden (Carnegie Mellon)
Time: Tuesday May 8, 12:00pm
Place: 60 5th Avenue, Room 150
Title: Detecting gerrymandering with mathematical rigor
Abstract: In February of this year, the Pennsylvania Supreme Court found Pennsylvania’s Congressional districting to be an unconstitutional partisan gerrymander. In this talk, I will discuss one of the pieces of evidence which the court used to reach this conclusion. In particular, I will discuss a theorem which allows us to use randomness to detect gerrymandering of Congressional districtings in a statistically rigorous way.