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 rankings. However, Kemeny rankings are NP-hard to compute. This has resulted in the development of various algorithms. Fortunately, NP-hardness may not reflect the difficulty of solving problems that arise in practice. As a result, we aim to demonstrate that the Kemeny consensus can be computed efficiently when aggregating different rankings in real case. In this paper, we extend a dynamic programming algorithm originally for Kemeny scores. We also provide details on the implementation of the algorithm. Finally, we present results obtained from an empirical comparison of our algorithm and two other popular algorithms based on real world and randomly generated problem instances. Experimental results show the usefulness and efficiency of the algorithm in practical settings.
As a method for answer aggregation in crowdsourced data management, rank aggregation aims to combine different agents' answers or preferences over the given alternatives into an aggregate ranking which agrees the most with the preferences. However, since the aggregation procedure relies on a data curator, the privacy within the agents' preference data could be compromised when the curator is untrusted. Existing works that guarantee differential privacy in rank aggregation all assume that the data curator is trusted. In this paper, we formulate and address the problem of locally differentially …
In social choice theory, (Kemeny) rank aggregation is a well-studied problem where the goal is to combine rankings from multiple voters into a single ranking on the same set of items. Since rankings can reveal preferences of voters (which a voter might like to keep private), it is important to aggregate preferences in such a way to preserve privacy. In this work, we present differentially private algorithms for rank aggregation in the pure and approximate settings along with distribution-independent utility upper and lower bounds. In addition to bounds in the central model, we also present uti…
A top-list is a possibly incomplete ranking of elements: only a subset of the elements are ranked, with all unranked elements tied for last. Top-list aggregation, a generalization of the well-known rank aggregation problem, takes as input a collection of top-lists and aggregates them into a single complete ranking, aiming to minimize the number of upsets (pairs ranked in opposite order in the input and in the output). In this paper, we give simple approximation algorithms for top-list aggregation. * We generalize the footrule algorithm for rank aggregation. * Using inspiration from approval vo…
We study fixed parameter algorithms for three problems: Kemeny rank aggregation, feedback arc set tournament, and betweenness tournament. For Kemeny rank aggregation we give an algorithm with runtime O*(2^O(sqrt{OPT})), where n is the number of candidates, OPT is the cost of the optimal ranking, and O* hides polynomial factors. This is a dramatic improvement on the previously best known runtime of O*(2^O(OPT)). For feedback arc set tournament we give an algorithm with runtime O*(2^O(sqrt{OPT})), an improvement on the previously best known O*(OPT^O(sqrt{OPT})) (Alon, Lokshtanov and Saurabh 2009…
University of Bergen（卑尔根大学）；University of Trier（特里尔大学）；University of California Santa Barbara（加州大学圣巴巴拉分校）
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, has focused on the development of notions of optimality that may be more appropriate in settings where subjectivity is essential. The idea is that instead of aiming at the development of algorithms that output a single optimal solution, the goal is to investigate algorithms that output a small set of sufficiently good solutions that are sufficiently diverse f…
University of Patras（帕特雷大学）；University of Essex（埃塞克斯大学）
Ordinal peer grading has been proposed as a simple and scalable solution for computing reliable information about student performance in massive open online courses. The idea is to outsource the grading task to the students themselves as follows. After the end of an exam, each student is asked to rank -- in terms of quality -- a bundle of exam papers by fellow students. An aggregation rule then combines the individual rankings into a global one that contains all students. We define a broad class of simple aggregation rules, which we call type-ordering aggregation rules, and present a theoretic…
We introduce a framework to approximate a Markov Decision Process that stands on two pillars: state aggregation -- as the algorithmic infrastructure; and central-limit-theorem-type approximations -- as the mathematical underpinning of optimality guarantees. The theory is grounded in recent work Braverman et al (2020} that relates the solution of the Bellman equation to that of a PDE where, in the spirit of the central limit theorem, the transition matrix is reduced to its local first and second moments. Solving the PDE is $\textit{not}$ required by our method. Instead, we construct a "sister" …
