Related papers: Metric geometry for ranking-based voting: Tools fo…
Performance metrics (error measures) are vital components of the evaluation frameworks in various fields. The intention of this study was to overview of a variety of performance metrics and approaches to their classification. The main goal…
For the problem of aggregating several rankings into one ranking, Kemeny (1959) proposed two methods: the median rule which selects the ranking with the smallest total swap distance to the input rankings, and the mean rule which minimizes…
Recent studies demonstrate that trends in indicators extracted from measured time series can indicate approaching to an impending transition. Kendall's {\tau} coefficient is often used to study the trend of statistics related to the…
The popularity of transformer-based text embeddings calls for better statistical tools for measuring distributions of such embeddings. One such tool would be a method for ranking texts within a corpus by centrality, i.e. assigning each text…
In this work, we leverage a generative data model considering comparison noise to develop a fast, precise, and informative ranking algorithm from pairwise comparisons that produces a measure of confidence on each comparison. The problem of…
We propose a new single-winner election method ("Schulze method") and prove that it satisfies many academic criteria (e.g. monotonicity, reversal symmetry, resolvability, independence of clones, Condorcet criterion, k-consistency,…
The approximate sorting for big data is considered in this paper. The goal of approximate sorting for big data is to generate an approximate sorted result, but using less CPU and I/O cost. For big data, we consider the approximate sorting…
Optimal transport (OT) distances between probability distributions are parameterized by the ground metric they use between observations. Their relevance for real-life applications strongly hinges on whether that ground metric parameter is…
We study the classical metric $k$-median clustering problem over a set of input rankings (i.e., permutations), which has myriad applications, from social-choice theory to web search and databases. A folklore algorithm provides a…
We consider a two-round election model involving $m$ voters and $n$ candidates. Each voter is endowed with a strict preference list ranking the candidates. In the first round, the candidates are partitioned into two subsets, $A$ and $B$,…
We consider the problem of recovering the ground truth ordering (ranking, top-$k$, or others) over a large number of alternatives. The wisdom of crowd is a heuristic approach based on Condorcet's Jury theorem to address this problem through…
Kendall's tau and conditional Kendall's tau matrices are multivariate (conditional) dependence measures between the components of a random vector. For large dimensions, available estimators are computationally expensive and can be improved…
Complex systems are made up of many interacting components. Network science provides the tools to analyze and understand these interactions. Community detection is a key technique in network science for uncovering the structures that shape…
Evolution and geometry generate complexity in similar ways. Evolution drives natural selection while geometry may capture the logic of this selection and express it visually, in terms of specific generic properties representing some kind of…
We explore the Declination, a new metric intended to detect partisan gerrymandering. We consider instances in which each district has equal turnout, the maximum turnout to minimum turnout is bounded, and turnout is unrestricted. For each of…
Order-of-addition experiments arise when the response depends on the order in which a set of components is added. Since the number of possible orders increases factorially with the number of components, full permutation designs are rarely…
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…
The conventional definition of a topological metric over a space specifies properties that must be obeyed by any measure of "how separated" two points in that space are. Here it is shown how to extend that definition, and in particular the…
We reformulate the compatibility condition between a generalized metric and a small (non-maximal rank) Dirac structure in an exact Courant algebroid found in the context of the gauging of strings and formulated by means of two connections…
Van Zuylen et al. [35] introduced the notion of a popular ranking in a voting context, where each voter submits a strict ranking of all candidates. A popular ranking $\pi$ of the candidates is at least as good as any other ranking $\sigma$…