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Jacek Szybowski

Publications and source records attributed to Jacek Szybowski.

11 recordsLinked to original sources
arXiv2026

Geometric mean-based pairwise comparison method with the reference values -- statistical approach

For many years, pairwise comparison methods have been widely used for eliciting preferences and ranking alternatives in decision-making problems. These methods estimate priority weights from a pairwise comparison matrix and are now standard tools in multi-criteria decision analysis. In this paper, we present a statistical view of the pairwise comparison method using reference values and the geometric mean to calculate alternative priorities. Thanks to this approach, we can simultaneously capture the phenomenon of inconsistency in pairwise comparisons and the preference distance between different alternatives. In this paper, we define indicators that measure the quality of the obtained weight vector, which, thanks to the statistical approach, have an understandable interpretation.

stat.ME↗
arXiv2026

Sufficient conditions for a Heuristic Rating Estimation Method application

A series of papers has introduced the Heuristic Rating Estimation method, which evaluates a set of alternatives based on pairwise comparisons and the weights of reference alternatives. We formulate the conditions under which the HRE method can be applied correctly. The research considers both arithmetic and geometric algorithms for complete and incomplete pairwise comparison methods. The illustrative examples show that the estimations of inconsistency in the arithmetic variant are optimal.

cs.AI↗
arXiv2026

Mean-based incomplete pairwise comparisons method with the reference values

In this article, we propose two quantitative methods for calculating weight vectors for incomplete pairwise comparison matrices using reference values. Both procedures are extensions of arithmetic and geometric heuristic estimation (HRE) methods. The proposed solutions allow flexible selection of the number of reference alternatives and the range of comparisons, from the acceptable minimum to a complete set. In this paper, we prove that the newly introduced geometric HRE method for incomplete data is optimal. For this method, we also prove the existence of a feasible solution. In the paper, we also provide sufficient conditions for the existence of a solution for the second arithmetic variant of the HRE method. We illustrate the presented methods with numerical examples.

cs.AI↗
arXiv2024

My part is bigger than yours -- assessment within a group of peers

A project (e.g., writing a collaborative research paper) is often a group effort. At the end, each contributor identifies their contribution, often verbally. The reward, however, is very frequently financial. It leads to the question of what (percentage) share in the creation of the paper is due to individual authors. Different authors may have various opinions on the matter; even worse, their opinions may have different relevance. In this paper, we present simple models that allow aggregation of experts' views, linking the priority of his preference directly to the assessment made by other experts. In this approach, the more significant the contribution of a given expert, the greater the importance of his opinion. The presented method can be considered an attempt to find consensus among peers involved in the same project. Hence, its applications may go beyond the proposed study example of writing a scientific paper.

cs.DM↗
arXiv2024

Detection of decision-making manipulation in the pairwise comparisons method

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 simple manipulation methods in the pairwise comparison method. We then try to detect these methods using appropriately constructed neural networks. Experimental results accompany the proposed solutions on the generated data, showing a considerable manipulation detection level.

cs.AI↗
arXiv2024

Establishing a leader in a pairwise comparisons method

Abstract Like electoral systems, decision-making methods are also vulnerable to manipulation by decision-makers. The ability to effectively defend against such threats can only come from thoroughly understanding the manipulation mechanisms. In the presented article, we show two algorithms that can be used to launch a manipulation attack. They allow for equating the weights of two selected alternatives in the pairwise comparison method and, consequently, choosing a leader. The theoretical considerations are accompanied by a Monte Carlo simulation showing the relationship between the size of the PC matrix, the degree of inconsistency, and the ease of manipulation. This work is a continuation of our previous research published in the paper (Szybowski et al., 2023)

cs.AI↗
arXiv2023

Almost optimal manipulation of a pair of alternatives

The role of an expert in the decision-making process is crucial, as the final recommendation depends on his disposition, clarity of mind, experience, and knowledge of the problem. However, the recommendation also depends on their honesty. But what if the expert is dishonest? Then, the answer on how difficult it is to manipulate in a given case becomes essential. In the presented work, we consider manipulation of a ranking obtained by comparing alternatives in pairs. More specifically, we propose an algorithm for finding an almost optimal way to swap the positions of two selected alternatives. Thanks to this, it is possible to determine how difficult such manipulation is in a given case. Theoretical considerations are illustrated by a practical example.

cs.AI↗
arXiv2023

Towards secure judgments aggregation in AHP

In decision-making methods, it is common to assume that the experts are honest and professional. However, this is not the case when one or more experts in the group decision making framework, such as the group analytic hierarchy process (GAHP), try to manipulate results in their favor. The aim of this paper is to introduce two heuristics in the GAHP, setting allowing to detect the manipulators and minimize their effect on the group consensus by diminishing their weights. The first heuristic is based on the assumption that manipulators will provide judgments which can be considered outliers with respect to those of the rest of the experts in the group. The second heuristic assumes that dishonest judgments are less consistent than the average consistency of the group. Both approaches are illustrated with numerical examples and simulations.

cs.AI↗
arXiv2018

Towards quantification of incompleteness in the pairwise comparisons method

Alongside consistency, completeness of information is one of the key factors influencing data quality. The objective of this paper is to define ways of treating missing entries in pairwise comparisons (PC) method with respect to inconsistency and sensitivity. Two important factors related to the incompleteness of PC matrices have been identified, namely the number of missing pairwise comparisons and their arrangements. Accordingly, four incompleteness indices have been developed, simple to calculate, each of them take into account both: the total number of missing data and their distribution in the PC matrix. A numerical study of the properties of these indices has been also conducted using a series of Montecarlo experiments. It demonstrated that both incompleteness and inconsistency of data equally contribute to the sensitivity of the PC matrix. Although incompleteness is only just one of the factors influencing sensitivity, a relative simplicity of the proposed indices may help decision makers to quickly estimate the impact of missing comparisons on the quality of final result.

cs.DM↗
arXiv2015

On the Convergence of the Pairwise Comparisons Inconsistency Reduction Process

This study investigates a powerful model, targeted to subjective assessments, based on pairwise comparisons. It provides a proof that a distance-based inconsistency reduction transforms an inconsistent pairwise comparisons (PC) matrix into a consistent PC matrix which is generated by the geometric means of rows of a given inconsistent PC matrix. The distance-based inconsistency indicator was defined in 1993 for pairwise comparisons. Its convergence was analyzed in 1996 (regretfully, with an incomplete proof; finally completed in 2010). However, there was no clear interpretation of the convergence limit which is of considerable importance for applications and this study does so.

cs.DM↗