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We study the computational complexity of the map redistricting problem (gerrymandering). Mathematically, the electoral district designer (gerrymanderer) attempts to partition a weighted graph into $k$ connected components (districts) such…
Recently, a proposal has been advanced to detect unconstitutional partisan gerrymandering with a simple formula called the efficiency gap. The efficiency gap is now working its way towards a possible landmark case in the Supreme Court. This…
Recently, Landau, Reid and Yershov provided a novel solution to the problem of redistricting. Instead of trying to ensure fairness by restricting the shape of the possible maps or by assigning the power to draw the map to nonbiased…
We consider the notions of agreement, diversity, and polarization in ordinal elections (that is, in elections where voters rank the candidates). While (computational) social choice offers good measures of agreement between the voters, such…
We survey a burgeoning and promising new research area that considers the online nature of many practical fair division problems. We identify wide variety of such online fair division problems, as well as discuss new mechanisms and…
Multiwinner voting captures a wide variety of settings, from parliamentary elections in democratic systems to product placement in online shopping platforms. There is a large body of work dealing with axiomatic characterizations,…
Spatial voting models of legislators' preferences are used in political science to test theories about their voting behavior. These models posit that legislators' ideologies as well as the ideologies reflected in votes for and against a…
Over the years, American politics have become increasingly polarized. In the current political landscape, a president cannot easily collaborate with the opposite party and pass legislature. Ideologies between parties have drifted apart to…
The electoral college of voting system for the US presidential election is analogous to a coarse graining procedure commonly used to study phase transitions in physical systems. In a recent paper, opinion dynamics models manifesting a phase…
We provide mechanisms and new metric distortion bounds for line-up elections. In such elections, a set of $n$ voters, $m$ candidates, and $\ell$ positions are all located in a metric space. The goal is to choose a set of candidates and…
There is a tight connection between credit access and voting. We show that uncertainty in access to credit pushes voters toward more conservative candidates in US elections. Using a 1% sample of the US population with valid credit reports,…
Clustering is a foundational problem in machine learning with numerous applications. As machine learning increases in ubiquity as a backend for automated systems, concerns about fairness arise. Much of the current literature on fairness…
We introduce a new Markov Chain called the Cycle Walk for sampling measures of graph partitions where the partition elements have roughly equal size. Such Markov Chains are of current interest in the generation and evaluation of political…
Has ideological polarization actually increased in the last decades, or have voters simply sorted themselves into parties matching their ideology more closely? We present a novel methodology to quantify multidimensional ideological…
We measure polarization in the United States Congress using the network science concept of modularity. Modularity provides a conceptually-clear measure of polarization that reveals both the number of relevant groups and the strength of…
Since the 1960s, Democrats and Republicans in U.S. Congress have taken increasingly polarized positions, while the public's policy positions have remained centrist and moderate. We explain this apparent contradiction by developing a…
We use the United States Supreme Court as an illuminative context in which to discuss three different spatial voting preference models: an instance of the widely used single-peaked preferences, and two models that are more novel in which…
Voter suppression and associated racial disparities in access to voting are long-standing civil rights concerns in the United States. Barriers to voting have taken many forms over the decades. A history of violent explicit discouragement…
Differences in data distributions between demographic groups, known as the problem of infra-marginality, complicate how people evaluate fairness in machine learning models. We present a user study with 85 participants in a hypothetical…
There has been a recent media blitz on a cohort of mathematicians valiantly working to fix America's democratic system by combatting gerrymandering with geometry. While statistics commonly features in the courtroom (forensics, DNA analysis,…