Related papers: Don't Trust A Single Gerrymandering Metric
Many democratic societies use district-based elections, where the region under consideration is geographically divided into districts and a representative is chosen for each district based on the preferences of the electors who reside…
We use voting precinct and election data to analyze the political geography of New Hampshire and Maine. We find that the location of dividing line between Congressional districts in both states are significantly different than what we would…
The evaluation of fairness in machine learning systems has become a central concern in high-stakes applications, including biometric recognition, healthcare decision-making, and automated risk assessment. Existing approaches typically rely…
We define a distance metric between partitions of a graph using machinery from optimal transport. Our metric is built from a linear assignment problem that matches partition components, with assignment cost proportional to transport…
Landau, Reid, and Yershov [A Fair Division Solution to the Problem of Redistricting, \textit{Social Choice and Welfare}, 2008] propose a protocol for drawing legislative districts based on a two player fair division process, where each…
In this paper, we develop the metric geometry of ranking statistics, proving that the two major permutation distances in the statistics literature -- Kendall tau and Spearman footrule -- extend naturally to incomplete rankings with both…
Consider the following social choice problem. Suppose we have a set of $n$ voters and $m$ candidates that lie in a metric space. The goal is to design a mechanism to choose a candidate whose average distance to the voters is as small as…
Post-election audits use the discrepancy between machine counts and a hand tally of votes in a random sample of precincts to infer whether error affected the electoral outcome. The maximum relative overstatement of pairwise margins (MRO)…
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…
Our main contribution is the introduction of the map of elections framework. A map of elections consists of three main elements: (1) a dataset of elections (i.e., collections of ordinal votes over given sets of candidates), (2) a way of…
Simulation and bisimulation metrics for stochastic systems provide a quantitative generalization of the classical simulation and bisimulation relations. These metrics capture the similarity of states with respect to quantitative…
In this paper, we study the distortion bounds for voting mechanisms in multi-winner elections in general metric spaces. Our study pertains to the case in which each voter only reports her favorite candidate amongst $m$ possible choices.…
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…
The most prevalent notions of fairness in machine learning are statistical definitions: they fix a small collection of pre-defined groups, and then ask for parity of some statistic of the classifier across these groups. Constraints of this…
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,…
Our main contribution is the introduction of the map of elections framework. A map of elections consists of three main elements: (1) a dataset of elections (i.e., collections of ordinal votes over given sets of candidates), (2) a way of…
Selecting representatives based on voters' preferences is a fundamental problem in social choice theory. While cardinal utility functions offer a detailed representation of preferences, ordinal rankings are often the only available…
A recently proposed graph-theoretic metric, the influence gap, has shown to be a reliable predictor of the effect of social influence in two-party elections, albeit only tested on regular and scale-free graphs. Here, we investigate whether…
Predictions are often probabilities; e.g., a prediction could be for precipitation tomorrow, but with only a 30% chance. Given such probabilistic predictions together with the actual outcomes, "reliability diagrams" help detect and diagnose…
Mean embeddings provide an extremely flexible and powerful tool in machine learning and statistics to represent probability distributions and define a semi-metric (MMD, maximum mean discrepancy; also called N-distance or energy distance),…