Related papers: Understanding Distance Measures Among Elections
To improve our understanding of connected systems, different tools derived from statistics, signal processing, information theory and statistical physics have been developed in the last decade. Here, we will focus on the graph comparison…
We derive distributional limits for empirical transport distances between probability measures supported on countable sets. Our approach is based on sensitivity analysis of optimal values of infinite dimensional mathematical programs and a…
We define a (pseudo-)distance between graphs based on the spectrum of the normalized Laplacian, which is easy to compute or to estimate numerically. It can therefore serve as a rough classification of large empirical graphs into families…
By assigning a probability measure via the spectrum of the normalized Laplacian to each graph and using L^p Wasserstein distances between probability measures, we define the corresponding spectral distances d_p on the set of all graphs.…
Here we present \texttt{electoral\_sim}, an open-source Python framework for simulating and comparing electoral systems across diverse voter preference distributions. The framework represents voters and candidates as points in a…
We report on experimental measurement of the Hilbert-Schmidt distance between two two-qubit states by many-particle interference. We demonstrate that our three-step method for measuring distances in Hilbert space is far less complex than…
We study maximal distances in the commuting graphs of matrix algebras defined over algebraically closed fields. In particular, we show that the maximal distance can be attained only between two nonderogatory matrices. We also describe…
We provide a simple method and relevant theoretical analysis for efficiently estimating higher-order lp distances. While the analysis mainly focuses on l4, our methodology extends naturally to p = 6,8,10..., (i.e., when p is even).…
The distance from a given position toward one or more destinations, exits, and way points is a more or less important input variable in most models of pedestrian dynamics. Except for the special case when there are no obstacles in a concave…
Metrics on the space of sets of trajectories are important for scientists in the field of computer vision, machine learning, robotics, and general artificial intelligence. However, existing notions of closeness between sets of trajectories…
In this paper, we present a new metric distance for comparing two large graphs to find similarities and differences between them based on one of the most important graph structural properties, which is Node Adjacency Information, for all…
Gerrymandering voting districts is one of the most salient concerns of contemporary American society, and the creation of new voting maps, along with their subsequent legal challenges, speaks for much of our modern political discourse. The…
With historic misses in the 2016 and 2020 US Presidential elections, interest in measuring polling errors has increased. The most common method for measuring directional errors and non-sampling excess variability during a postmortem for an…
We present a computational study of finite-time mixing of a line segment by cutting and shuffling. A family of one-dimensional interval exchange transformations is constructed as a model system in which to study these types of mixing…
We consider a classical problem in choice theory -- vote aggregation -- using novel distance measures between permutations that arise in several practical applications. The distance measures are derived through an axiomatic approach, taking…
In previous work cite{Ha98:Towards} we presented a case-based approach to eliciting and reasoning with preferences. A key issue in this approach is the definition of similarity between user preferences. We introduced the probabilistic…
We study the multifaceted question of how to sample approval elections in a meaningful way. Our analysis aims to discern the properties of various statistical cultures (both established and new ones). Based on the map-of-elections framework…
In this paper, we experimentally compare major approval-based multiwinner voting rules. To this end, we define a measure of similarity between two equal-sized committees subject to a given election. Using synthetic elections coming from…
In the context of functional data analysis, we propose new two sample tests for homogeneity. Based on some well-known depth measures, we construct four different statistics in order to measure distance between the two samples. A simulation…
We provide an implementation to compute the flat metric in any dimension. The flat metric, also called dual bounded Lipschitz distance, generalizes the well-known Wasserstein distance $W_1$ to the case that the distributions are of unequal…