Related papers: Space reduction techniques for the $3$-wise Kemeny…
Many hardness results in computational social choice make use of the fact that every directed graph may be induced as the pairwise majority relation of some preference profile. However, this fact requires a number of voters that is almost…
We introduce the $(j,k)$-Kemeny rule -- a generalization of Kemeny's voting rule that aggregates $j$-chotomous weak orders into a $k$-chotomous weak order. Special cases of $(j,k)$-Kemeny include approval voting, the mean rule and Borda…
Kemeny (1959) introduced a topologically complete metric space to study ordinal random variables, particularly in the context of Condorcet's paradox and the measurability of ties. Building on this, Emond & Mason (2002) reformulated Kemeny's…
We introduce a correlation coefficient that is designed to deal with a variety of ranking formats including those containing non-strict (i.e., with-ties) and incomplete (i.e., unknown) preferences. The correlation coefficient is designed to…
The computational study of elections generally assumes that the preferences of the electorate come in as a list of votes. Depending on the context, it may be much more natural to represent the list succinctly, as the distinct votes of the…
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 $\sigma$…
We consider the following well-studied problem of metric distortion in social choice. Suppose we have an election with $n$ voters and $m$ candidates located in a shared metric space. We would like to design a voting rule that chooses a…
Winner selection by majority, in an election between two candidates, is the only rule compatible with democratic principles. Instead, when the candidates are three or more and the voters rank candidates in order of preference, there are no…
When scheduling public works or events in a shared facility one needs to accommodate preferences of a population. We formalize this problem by introducing the notion of a collective schedule. We show how to extend fundamental tools from…
In this article we develop a new method for summarizing a ranking distribution, \textit{i.e.} a probability distribution on the symmetric group $\mathfrak{S}_n$, beyond the classical theory of consensus and Kemeny medians. Based on the…
The Kemeny method is one of the popular tools for rank aggregation. However, computing an optimal Kemeny ranking is NP-hard. Consequently, the computational task of finding a Kemeny ranking has been studied under the lens of parameterized…
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…
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…
May's Theorem [K. O. May, Econometrica 20 (1952) 680-684] characterizes majority voting on two alternatives as the unique preferential voting method satisfying several simple axioms. Here we show that by adding some desirable axioms to…
The computational complexity of winner determination is a classical and important problem in computational social choice. Previous work based on worst-case analysis has established NP-hardness of winner determination for some classic voting…
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…
Ranking and comparing items is crucial for collecting information about preferences in many areas, from marketing to politics. The Mallows rank model is among the most successful approaches to analyse rank data, but its computational…
The main idea of the {\em distance rationalizability} approach to view the voters' preferences as an imperfect approximation to some kind of consensus is deeply rooted in social choice literature. It allows one to define ("rationalize")…
We consider the algorithmic question of choosing a subset of candidates of a given size $k$ from a set of $m$ candidates, with knowledge of voters' ordinal rankings over all candidates. We consider the well-known and classic scoring rule…
In this work we study the metric distortion problem in voting theory under a limited amount of ordinal information. Our primary contribution is threefold. First, we consider mechanisms which perform a sequence of pairwise comparisons…