A computational study of the Kemeny rule for preference aggregation

Abstract We consider from a computational perspective the problem of how to aggregate the ranking preferences of a number of alternatives by a number of different voters into a single consensus ranking, following the majority voting rule. Social welfare functions for aggregating preferences in this way have been widely studied since the time of Condorcet (1785). One drawback of majority voting procedures when three or more alternatives are being ranked is the presence of cycles in the majority preference relation. The Kemeny order is a social welfare function which has been designed to tackle the presence of such cycles. However computing a Kemeny order is known to be NP-hard. We develop a greedy heuristic and an exact branch and bound procedure for computing Kemeny orders. We present results of a computational study on these procedures

Быстрая согласованность по Кемени на основе поиска по стандартным матрицам с минимальным расстоянием до усредненного экспертного ранжирования

Проблематика. Розглядається задача ранжування скінченної множини об’єктів. Мета дослідження. Розробка алгоритму, який дав би змогу пришвидшити пошук узгодженості за Кемені поряд з обґрунтуванням метрики для порівняння ранжувань. Методика реалізації. Пропонується й обґрунтовується підхід щодо об’єднання експертних ранжувань. Також пропонується й обґрунтовується метрика для порівняння ранжувань. Результати дослідження. Розроблений алгоритм знаходить множину ранжувань Кемені значно швидше, ніж класичний прямий пошук. Також ця множина часто містить єдину узгодженість за Кемені, що не вдається за прямого пошуку. Крім цього, єдина узгодженість за Кемені визначається відразу, якщо усереднене експертне ранжування виявляється ациклічним. Так розв’язується задача вибору єдиної узгодженості за Кемені. Висновки. Для 10 і більше об’єктів, де більшість відомих підходів стають незастосовними, алгоритм є реалізовним завдяки пошуку по тільки тих стандартних матрицях, чия відстань до першого ранжування відрізняється від відстані між цим ранжуванням та усередненим експертним ранжуванням на мінімальну величину.Background. The problem of ranking a finite set of objects is considered. Objective. The goal is to develop an algorithm that would let speed up the search of the Kemeny consensus along with substantiation of a metric to compare rankings. Methods. An approach for aggregating experts’ rankings is suggested and substantiated. Also a metric to compare rankings is suggested and substantiated. Results. The developed algorithm finds a set of Kemeny rankings much faster than the classical straightforward search. Also this set often contains a single Kemeny consensus, what fails by the straightforward search. Besides, a single Kemeny consensus is determined at one stroke if the averaged expert ranking turns out acyclic. Thus the problem of selecting a single Kemeny consensus is solved. Conclusions. For 10 objects and more, where most known approaches become intractable, the algorithm still is tractable due to searching over only those standard matrices whose distance to the first ranking differs minimally from the distance between this ranking and the averaged expert ranking.Проблематика. Рассматривается задача ранжирования конечного множества объектов. Цель исследования. Разработка алгоритма, который позволил бы ускорить поиск согласованности по Кемени вместе с обоснованием метрики для сравнения ранжирований. Методика реализации. Предлагается и обосновывается подход относительно объединения экспертных ранжирований. Также предлагается и обосновывается метрика для сравнения ранжирований. Результаты исследования. Разработанный алгоритм находит множество ранжирований Кемени гораздо быстрее, чем классический прямой поиск. Также это множество часто содержит единственную согласованность по Кемени, что не удается при прямом поиске. Кроме этого, единственная согласованность по Кемени определяется сразу, если усредненное экспертное ранжирование оказывается ациклическим. Так решается задача выбора единственной согласованности по Кемени. Выводы. Для 10 и более объектов, где большинство известных подходов становятся неисполнимыми, алгоритм является осуществимым благодаря поиску по только тем стандартным матрицам, чье расстояние к первому ранжированию отличается от расстояния между этим ранжированием и усредненным экспертным ранжированием на минимальную величину

The Complexity of Manipulating kk-Approval Elections

An important problem in computational social choice theory is the complexity of undesirable behavior among agents, such as control, manipulation, and bribery in election systems. These kinds of voting strategies are often tempting at the individual level but disastrous for the agents as a whole. Creating election systems where the determination of such strategies is difficult is thus an important goal. An interesting set of elections is that of scoring protocols. Previous work in this area has demonstrated the complexity of misuse in cases involving a fixed number of candidates, and of specific election systems on unbounded number of candidates such as Borda. In contrast, we take the first step in generalizing the results of computational complexity of election misuse to cases of infinitely many scoring protocols on an unbounded number of candidates. Interesting families of systems include $k$-approval and $k$-veto elections, in which voters distinguish $k$ candidates from the candidate set. Our main result is to partition the problems of these families based on their complexity. We do so by showing they are polynomial-time computable, NP-hard, or polynomial-time equivalent to another problem of interest. We also demonstrate a surprising connection between manipulation in election systems and some graph theory problems

On absolutely and simply popular rankings

Van Zuylen et al. introduced the notion of a popular ranking in a voting context, where each voter submits a strictly-ordered list of all candidates. A popular ranking $\pi$ of the candidates is at least as good as any other ranking $\sigma$ in the following sense: if we compare $\pi$ to $\sigma$, at least half of all voters will always weakly prefer~$\pi$. Whether a voter prefers one ranking to another is calculated based on the Kendall distance. A more traditional definition of popularity -- as applied to popular matchings, a well-established topic in computational social choice -- is stricter, because it requires at least half of the voters \emph{who are not indifferent between $\pi$ and $\sigma$} to prefer~$\pi$. In this paper, we derive structural and algorithmic results in both settings, also improving upon the results by van Zuylen et al. We also point out strong connections to the famous open problem of finding a Kemeny consensus with 3 voters.Comment: full version of the AAMAS 2021 extended abstract 'On weakly and strongly popular rankings

Preference relations based unsupervised rank aggregation for metasearch

Rank aggregation mechanisms have been used in solving problems from various domains such as bioinformatics, natural language processing, information retrieval, etc. Metasearch is one such application where a user gives a query to the metasearch engine, and the metasearch engine forwards the query to multiple individual search engines. Results or rankings returned by these individual search engines are combined using rank aggregation algorithms to produce the final result to be displayed to the user. We identify few aspects that should be kept in mind for designing any rank aggregation algorithms for metasearch. For example, generally equal importance is given to the input rankings while performing the aggregation. However, depending on the indexed set of web pages, features considered for ranking, ranking functions used etc. by the individual search engines, the individual rankings may be of different qualities. So, the aggregation algorithm should give more weight to the better rankings while giving less weight to others. Also, since the aggregation is performed when the user is waiting for response, the operations performed in the algorithm need to be light weight. Moreover, getting supervised data for rank aggregation problem is often difficult. In this paper, we present an unsupervised rank aggregation algorithm that is suitable for metasearch and addresses the aspects mentioned above. We also perform detailed experimental evaluation of the proposed algorithm on four different benchmark datasets having ground truth information. Apart from the unsupervised Kendall-Tau distance measure, several supervised evaluation measures are used for performance comparison. Experimental results demonstrate the efficacy of the proposed algorithm over baseline methods in terms of supervised evaluation metrics. Through these experiments we also show that Kendall-Tau distance metric may not be suitable for evaluating rank aggregation algorithms for metasearch

Оценивание критических факторов трансфера технологий методом агрегирования предпочтений

Объектом исследования является процесс трансфера технологий от вузов к промышленным предприятиям. Целью работы является оценивание критических факторов трансфера технологий методом агрегирования предпочтений на примере процесса внедрения инновационных разработок вузов на промышленных предприятиях. В ходе исследования был составлен перечень барьеров, препятствующих реализации трансфера технологий, где каждый барьер разбит на более мелкие характеризующие его факторы. Были выбраны 15 российских университетов из состава участников Проекта 5-100. На основе имеющейся в открытом доступе информации о деятельности вузов для каждого барьера были составлены профили предпочтения по соответствующим факторам для 15 вузов. Были найдены итоговые ранжирования для каждого барьера, которые составили профиль предпочтения по барьерам для тех же 15 вузов. Методом агрегирования предпочтений было определено результирующее ранжирование вузов, которое дает интегральную характеризацию трансфера технологий в 15 вузах по всему набору пяти барьеров с детализацией по факторам.The object of research is the process of technology transfer from universities to industrial enterprises. The purpose of the assessment is the critical factors of technology transfer by aggregating preferences on the example of the process of introducing innovations universities in industry. The study was drawn up a list of barriers to the implementation of technology transfer, where each barrier is broken into smaller factors which characterize it. They were selected 15 universities from the Russian project participants 5-100. On the basis of publicly available information on higher education activities for each barrier was composed of profiles of preferences on the relevant factors for the 15 universities. Were found the final ranking for each barrier, which amounted to the profile preferences for the barriers for those 15 universities. Method of aggregating preferences has been determined, the resulting ranking of universities, which gives an integral characterization of technology transfer in 15 universities across the set of five barriers, with details on factors

Décision de groupe, Aide à la facilitation : ajustement de procédure de vote selon le contexte de décision

La facilitation est un élément central dans une prise de décision de groupe surtout en faisant l'usage des outils de nouvelle technologie. Le facilitateur, pour rendre sa tâche facile, a besoin des solutions de vote pour départager les décideurs afin d'arriver à des conclusions dans une prise de décision. Une procédure de vote consiste à déterminer à partir d’une méthode le vainqueur ou le gagnant d’un vote. Il y a plusieurs procédures de vote dont certaines sont difficiles à expliquer et qui peuvent élire différents candidats/options/alternatives proposées. Le meilleur choix est celui dont son élection est acceptée facilement par le groupe. Le vote dans la théorie du choix social est une discipline largement étudiée dont les principes sont souvent complexes et difficiles à expliquer lors d’une réunion de prise de décision. Les systèmes de recommandation sont de plus en plus populaires dans tous les domaines de science. Ils peuvent aider les utilisateurs qui n’ont pas suffisamment d’expérience ou de compétence nécessaires pour évaluer un nombre élevé de procédures de vote existantes. Un système de recommandation peut alléger le travail du facilitateur dans la recherche d’une procédure vote adéquate en fonction du contexte de prise de décisions. Le sujet de ce travail de recherche s’inscrit dans le champ de l’aide à la décision de groupe. La problématique consiste à contribuer au développement d’un système d’aide à la décision de groupe (Group Decision Support System : GDSS). La solution devra s’intégrer dans la plateforme logicielle actuellement développée à l’IRIT GRUS : GRoUp Support.Facilitation is a central element in decision-making, especially when using new technology tools. The facilitator, to make his task easy, needs voting solutions to decide between decision-makers in order to reach conclusions in a decision-making process. A voting procedure consists of determining from a method the winner of a vote. There are several voting procedures, some of which are difficult to explain and which may elect different candidate/options/alternatives proposed. The best choice is the one whose election is easily accepted by the group. Voting in social choice theory is a widely studied discipline whose principles are often complex and difficult to explain at a decision-making meeting. Recommendation systems are becoming more and more popular in all fields of science. They can help users who do not have sufficient experience or competence to evaluate large numbers of existing voting procedures. A recommendation system can lighten the facilitator's workload in finding an appropriate voting procedure based on the decision-making context. The objective of this research work is to design such recommendation system. This work is in the field of group decision support. The issue is to contribute to the development of a Group Decision Support System (GDSS). The solution will have to be integrated into the software platform currently being developed at IRITGRUS: GRoUp Support

Parameterized Enumeration of Neighbour Strings and Kemeny Aggregations

In this thesis, we consider approaches to enumeration problems in the parameterized complexity setting. We obtain competitive parameterized algorithms to enumerate all, as well as several of, the solutions for two related problems Neighbour String and Kemeny Rank Aggregation. In both problems, the goal is to find a solution that is as close as possible to a set of inputs (strings and total orders, respectively) according to some distance measure. We also introduce a notion of enumerative kernels for which there is a bijection between solutions to the original instance and solutions to the kernel, and provide such a kernel for Kemeny Rank Aggregation, improving a previous kernel for the problem. We demonstrate how several of the algorithms and notions discussed in this thesis are extensible to a group of parameterized problems, improving published results for some other problems