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Kemeny's rule is one of the most studied and well-known voting schemes with various important applications in computational social choice and biology. Recently, Kemeny's rule was generalized via a set-wise approach by Gilbert et. al. This…
Kemeny Consensus is a well-known rank aggregation method in social choice theory. In this method, given a set of rankings, the goal is to find a ranking $\Pi$ that minimizes the total Kendall tau distance to the input rankings. Computing a…
The central problem in this work is to compute a ranking of a set of elements which is "closest to" a given set of input rankings of the elements. We define "closest to" in an established way as having the minimum sum of Kendall-Tau…
In this paper, we advocate the use of setwise contests for aggregating a set of input rankings into an output ranking. We propose a generalization of the Kemeny rule where one minimizes the number of k-wise disagreements instead of pairwise…
The important Kemeny problem, which consists of computing median consensus rankings of an election with respect to the Kemeny voting rule, admits important applications in biology and computational social choice and was generalized recently…
Aggregating a consensus ranking from multiple input rankings is a fundamental problem with applications in recommendation systems, search engines, job recruitment, and elections. Despite decades of research in consensus ranking aggregation,…
Consensus ranking is a technique used to derive a single ranking that best represents the preferences of multiple individuals or systems. It aims to aggregate different rankings into one that minimizes overall disagreement or distance from…
Rank aggregation is an essential approach for aggregating the preferences of multiple agents. One rule of particular interest is the Kemeny rule, which maximises the number of pairwise agreements between the final ranking and the existing…
The computational study of election problems generally focuses on questions related to the winner or set of winners of an election. But social preference functions such as Kemeny rule output a full ranking of the candidates (a consensus).…
Preference rankings virtually appear in all field of science (political sciences, behavioral sciences, machine learning, decision making and so on). The well-know social choice problem consists in trying to find a reasonable procedure to…
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…
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…
In its most traditional setting, the main concern of optimization theory is the search for optimal solutions for instances of a given computational problem. A recent trend of research in artificial intelligence, called solution diversity,…
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 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…
This article is devoted to the problem of predicting the value taken by a random permutation $\Sigma$, describing the preferences of an individual over a set of numbered items $\{1,\; \ldots,\; n\}$ say, based on the observation of an…
We present a new optimization-based method for aggregating preferences in settings where each voter expresses preferences over pairs of alternatives. Our approach to identifying a consensus partial order is motivated by the observation that…
We study a version of the randomized Kaczmarz algorithm for solving systems of linear equations where the iterates are confined to the solution space of a selected subsystem. We show that the subspace constraint leads to an accelerated…
Aggregating multiple input rankings into a consensus ranking is essential in various fields such as social choice theory, hiring, college admissions, web search, and databases. A major challenge is that the optimal consensus ranking might…
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…