Related papers: Declination as a Metric to Detect Partisan Gerryma…
American democracy is currently heavily reliant on plurality in single-member districts, or PSMD, as a system of election. But public perceptions of fairness are often keyed to partisan proportionality, or the degree of congruence between…
In representative democracy, a redistricting map is chosen to partition an electorate into districts which each elects a representative. A valid redistricting map must satisfy a collection of constraints such as being compact, contiguous,…
Every representative democracy must specify a mechanism under which voters choose their representatives. The most common mechanism in the United States -- Winner takes all single-member districts -- both enables substantial partisan…
In an election in which each voter ranks all of the candidates, we consider the head-to-head results between each pair of candidates and form a labeled directed graph, called the margin graph, which contains the margin of victory of each…
Geographical considerations such as contiguity and compactness are necessary elements of political districting in practice. Yet an analysis of the problem without such constraints yields mathematical insights that can inform real-world…
Demographic parity is the most widely recognized measure of group fairness in machine learning, which ensures equal treatment of different demographic groups. Numerous works aim to achieve demographic parity by pursuing the commonly used…
Visibility plays an important role for decision making in cluttered, uncertain environments. This paper considers the problem of identifying optimal hiding spots for an agent against line-of-sight detection by an adversary whose location is…
Many people believe that it is disadvantageous for members aligning with a minority party to cluster in cities, as this makes it easier for the majority party to gerrymander district boundaries to diminish the representation of the…
The metric distortion framework posits that n voters and m candidates are jointly embedded in a metric space such that voters rank candidates that are closer to them higher. A voting rule's purpose is to pick a candidate with minimum total…
In this paper, we study the metric distortion of deterministic social choice rules that choose a winning candidate from a set of candidates based on voter preferences. Voters and candidates are located in an underlying metric space. A voter…
The margin of victory of an election is a useful measure to capture the robustness of an election outcome. It also plays a crucial role in determining the sample size of various algorithms in post election audit, polling etc. In this work,…
Gerrymandering is a pervasive problem within the US political system. In the past decade, methods based on Markov Chain Monte Carlo (MCMC) sampling and statistical outlier tests have been proposed to quantify gerrymandering and were used as…
We develop and apply epistemic tests to various decentralized governance methods as well as to study the impact of participation. These tests probe the ability to reach a correct outcome when there is one. We find that partial abstention is…
In recent decades, state legislatures have often drawn U.S. Congressional voting districts that look---to the human eye---to be rather twisted. In this paper, we propose a method to measure how much districts "meander" via a computation of…
We consider models for social choice where voters rank a set of choices (or alternatives) by deliberating in small groups of size at most $k$, and these outcomes are aggregated by a social choice rule to find the winning alternative. We…
Weak gravitational lensing provides a direct statistical measure of the dark matter distribution. The variance is easiest to measure, which constrains the degenerate product \sigma_8\Omega^0.6. The degeneracy is broken by measuring the…
We introduce a novel partial differential equations approach for addressing the problem of partisan gerrymandering. Our method is based on volume preserving curvature flow, a partial differential equation which we adapt to smooth voting…
We consider a setting with agents that have preferences over alternatives and are partitioned into disjoint districts. The goal is to choose one alternative as the winner using a mechanism which first decides a representative alternative…
Affective polarization and increasing social divisions affect social mixing and the spread of information across online and physical spaces, reinforcing social and electoral cleavages and influencing political outcomes. Here, using…
Metrics for rigorously defining a distance between two events have been used to study the properties of the dataspace manifold of particle collider physics. The probability distribution of pairwise distances on this dataspace is unique with…