Related papers: Pairwise ranking: choice of method can produce arb…
There are many priority deriving methods for pairwise comparison matrices. It is known that when these matrices are consistent all these methods result in the same priority vector. However, when they are inconsistent, the results may vary.…
Pairwise comparisons are a well-known method for modelling of the subjective preferences of a decision maker. A popular implementation of the method is based on solving an eigenvalue problem for M - the matrix of pairwise comparisons. This…
The pairwise comparisons method is a convenient tool used when the relative order among different concepts (alternatives) needs to be determined. One popular implementation of the method is based on solving an eigenvalue problem for the…
This paper examines the problem of ranking a collection of objects using pairwise comparisons (rankings of two objects). In general, the ranking of $n$ objects can be identified by standard sorting methods using $n log_2 n$ pairwise…
Pairwise comparisons between alternatives are a well-known method for measuring preferences of a decision-maker. Since these often do not exhibit consistency, a number of inconsistency indices has been introduced in order to measure the…
A classical proposal to derive weights from a pairwise comparison matrix is the right eigenvector. The literature has identified some potential weaknesses of this method in previous decades. This chapter discusses five of these issues.…
A common problem in machine learning is to rank a set of n items based on pairwise comparisons. Here ranking refers to partitioning the items into sets of pre-specified sizes according to their scores, which includes identification of the…
Owing to the advancement of deep learning, artificial systems are now rival to humans in several pattern recognition tasks, such as visual recognition of object categories. However, this is only the case with the tasks for which correct…
The task of ranking individuals or teams, based on a set of comparisons between pairs, arises in various contexts, including sporting competitions and the analysis of dominance hierarchies among animals and humans. Given data on which…
Recommender systems are one of the most pervasive applications of machine learning in industry, with many services using them to match users to products or information. As such it is important to ask: what are the possible fairness risks,…
Pairwise comparisons are used in a wide variety of decision situations where the importance of alternatives should be measured on a numerical scale. One popular method to derive the priorities is based on the right eigenvector of a…
The pairwise comparisons method is a convenient tool used when the relative order of preferences among different concepts (alternatives) needs to be determined. There are several popular implementations of this method, including the…
A special class of preferences, given by a directed acyclic graph, is considered. They are represented by incomplete pairwise comparison matrices as only partial information is available: for some pairs no comparison is given in the graph.…
Pairwise comparison matrices are widely used in Multicriteria Decision Making. This article applies incomplete pairwise comparison matrices in the area of sport tournaments, namely proposing alternative rankings for the 2010 Chess Olympiad…
It has been shown recently that the Eigenvector Method may lead to strong rank reversal in group decision making, that is, the alternative with the highest priority according to all individual vectors may lose its position when evaluations…
We consider sequential or active ranking of a set of n items based on noisy pairwise comparisons. Items are ranked according to the probability that a given item beats a randomly chosen item, and ranking refers to partitioning the items…
This paper examines the differences in ordinal rankings obtained from a pairwise comparison matrix using the eigenvalue method and the geometric mean method. First, we introduce several propositions on the (dis)similarity of both rankings…
Chess championships are often organised as a Swiss-system tournament, causing great challenges in ranking the participants due to the different strength of schedules and possible circular triads. The paper suggests that pairwise comparison…
We attack the problem of getting a strict ranking (i.e. a ranking without equally ranked items) of $n$ items from a pairwise comparisons matrix. Basic structures are described, a first heuristical approach based on a condition, the…
Most decision-making models, including the pairwise comparison method, assume the decision-makers honesty. However, it is easy to imagine a situation where a decision-maker tries to manipulate the ranking results. This paper presents three…