Related papers: Understanding Distance Measures Among Elections
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…
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…
We form a "map of tournaments" by adapting the map framework from the world of elections. By a tournament we mean a complete directed graph where the nodes are the players and an edge points from a winner of a game to the loser (with no…
The map of elections framework is a methodology for visualizing and analyzing election datasets. So far, the framework was restricted to elections that have equal numbers of candidates, equal numbers of voters, and where all the (ordinal)…
We introduce and study isomorphic distances between ordinal elections (with the same numbers of candidates and voters). The main feature of these distances is that they are invariant to renaming the candidates and voters, and two elections…
The purpose of this paper is to give a survey on the notions of distance between subsets either of a metric space or of a measure space, including definitions, a classification, and a discussion of the best-known distance functions, which…
Measuring the distance between data points is fundamental to many statistical techniques, such as dimension reduction or clustering algorithms. However, improvements in data collection technologies has led to a growing versatility of…
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,…
In recent years, in an effort to promote fairness in the election process, a wide variety of techniques and metrics have been proposed to determine whether a map is a partisan gerrymander. The most accessible measures, requiring easily…
Recently, Szufa et al. [AAMAS 2020] presented a "map of elections" that visualizes a set of 800 elections generated from various statistical cultures. While similar elections are grouped together on this map, there is no obvious…
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…
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…
Distance queries are a basic tool in data analysis. They are used for detection and localization of change for the purpose of anomaly detection, monitoring, or planning. Distance queries are particularly useful when data sets such as…
We give an overview of different approaches to measuring the similarity of, or the distance between, two graphs, highlighting connections between these approaches. We also discuss the complexity of computing the distances.
We present several natural notions of distance between spectral density functions of (discrete-time) random processes. They are motivated by certain filtering problems. First we quantify the degradation of performance of a predictor which…
The concepts of similarity and distance are crucial in data mining. We consider the problem of defining the distance between two data sets by comparing summary statistics computed from the data sets. The initial definition of our distance…
Recent works in the information science literature have presented cases of using patent databases and patent classification information to construct network maps of technology fields, which aim to aid in competitive intelligence analysis…
We compare and contrast fourteen measures that have been proposed for the purpose of quantifying partisan gerrymandering. We consider measures that, rather than examining the shapes of districts, utilize only the partisan vote distribution…
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…
Geometric graphs appear in many real-world data sets, such as road networks, sensor networks, and molecules. We investigate the notion of distance between embedded graphs and present a metric to measure the distance between two geometric…