arXiv subjects

László Csató

Publications and source records attributed to László Csató.

87 records · Page 5Linked to original sources

arXiv2018

An impossibility theorem for paired comparisons

In several decision-making problems, alternatives should be ranked on the basis of paired comparisons between them. We present an axiomatic approach for the universal ranking problem with arbitrary preference intensities, incomplete and multiple comparisons. In particular, two basic properties -- independence of irrelevant matches and self-consistency -- are considered. It is revealed that there exists no ranking method satisfying both requirements at the same time. The impossibility result holds under various restrictions on the set of ranking problems, however, it does not emerge in the case of round-robin tournaments. An interesting and more general possibility result is obtained by restricting the domain of independence of irrelevant matches through the concept of macrovertex.

cs.GT↗

arXiv2018

Some impossibilities of ranking in generalized tournaments

In a generalized tournament, players may have an arbitrary number of matches against each other and the outcome of the games is measured on a cardinal scale with a lower and upper bound. An axiomatic approach is applied to the problem of ranking the competitors. Self-consistency requires assigning the same rank for players with equivalent results, while a player showing an obviously better performance than another should be ranked strictly higher. According to order preservation, if two players have the same pairwise ranking in two tournaments where the same players have played the same number of matches, then their pairwise ranking is not allowed to change in the aggregated tournament. We reveal that these two properties cannot be satisfied simultaneously on this universal domain.

cs.GT↗

arXiv2018

Was Zidane honest or well-informed? How UEFA barely avoided a serious scandal

UEFA European Championship 1996 qualification is known to violate strategy-proofness. It has been proved recently that a team could be better off by exerting a lower effort: it might be optimal to concede some goals in order to achieve a better position among runners-up, and hence avoid a hazardous play-off. We show that it is not only an irrelevant scenario with a marginal probability since France had an incentive to kick two own goals on its last match against Israel.

physics.soc-ph↗

arXiv2017

Distance-based accessibility indices

The paper attempts to develop a suitable accessibility index for networks where each link has a value such that a smaller number is preferred like distance, cost, or travel time. A measure called distance sum is characterized by three independent properties: anonymity, an appropriately chosen independence axiom, and dominance preservation, which requires that a node not far to any other is at least as accessible. We argue for the need of eliminating the independence property in certain applications. Therefore generalized distance sum, a family of accessibility indices, will be suggested. It is linear, considers the accessibility of vertices besides their distances and depends on a parameter in order to control its deviation from distance sum. Generalized distance sum is anonymous and satisfies dominance preservation if its parameter meets a sufficient condition. Two detailed examples demonstrate its ability to reflect the vulnerability of accessibility to link disruptions.

cs.SI↗

arXiv2017

Between plurality and proportionality: an analysis of vote transfer systems

The paper considers a general model of electoral systems combining district-based elections with a compensatory mechanism in order to create any outcome between strictly majoritarian and purely proportional seat allocation. It contains vote transfer and allows for the application of three different correction formulas. Analysis in a two-party system shows that a trade-off exists for the dominant party between its expected seat share and its chance of obtaining majority. Vote transfer rules are also investigated by focusing on the possibility of manipulation. The model is applied to the 2014 Hungarian parliamentary election. Hypothetical results reveal that the vote transfer rule cannot be evaluated in itself, only together with the share of constituency seats. With an appropriate choice of the latter, the three mechanisms may be functionally equivalent.

cs.GT↗

arXiv2017

A mathematical evaluation of vote transfer systems

The paper builds a general model of vote transfer systems on the basis of the current Hungarian electoral rules. It combines single-seat districts and list mandates with three possible compensation rule for 'wasted' votes in constituencies: no compensation (direct vote transfer, DVT), compensation for votes cast for losing party candidates (positive vote transfer, PVT) and compensation for all votes that are not necessary to win the district (negative vote transfer, NVT). The model is studied in the case of two parties. When the number of votes for the majority party follows a uniform distribution in each district, DVT results in the greatest expected seat share, however, application of PVT, and, especially, NVT increases the probability of winning the election. The trade-off between vote transfer formulas and the number of list mandates reveals that the majority party should use an appropriately calibrated NVT system if it focuses on these two variables.

cs.GT↗

arXiv2017

On the ranking of a Swiss system chess team tournament

The paper suggests a family of paired comparison-based scoring procedures for ranking the participants of a Swiss system chess team tournament. We present the challenges of ranking in Swiss system, the features of individual and team competitions as well as the failures of the official rankings based on lexicographical order. The tournament is represented as a ranking problem such that the linearly-solvable row sum (score), generalized row sum, and least squares methods have favourable axiomatic properties. Two chess team European championships are analysed as case studies. Final rankings are compared by their distances and visualized with multidimensional scaling (MDS). Differences to the official ranking are revealed by the decomposition of the least squares method. Rankings are evaluated by prediction power, retrodictive performance, and stability. The paper argues for the use of least squares method with a results matrix favouring match points on the basis of its relative insensitivity to the choice between match and board points, retrodictive accuracy, and robustness.

stat.AP↗

arXiv2017

Eigenvector Method and rank reversal in group decision making revisited

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 are derived from the aggregated group comparison matrix. We give a minimal counterexample and prove that this negative result is a consequence of the difference of the rankings induced by the right and inverse left eigenvectors.

math.OC↗

arXiv2017

Characterization of an inconsistency ranking for pairwise comparison matrices

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 deviation from this ideal case. We axiomatically characterize the inconsistency ranking induced by the Koczkodaj inconsistency index: six independent properties are presented such that they determine a unique linear order on the set of all pairwise comparison matrices.

cs.AI↗

arXiv2017

Measuring centrality by a generalization of degree

Network analysis has emerged as a key technique in communication studies, economics, geography, history and sociology, among others. A fundamental issue is how to identify key nodes, for which purpose a number of centrality measures have been developed. This paper proposes a new parametric family of centrality measures called generalized degree. It is based on the idea that a relationship to a more interconnected node contributes to centrality in a greater extent than a connection to a less central one. Generalized degree improves on degree by redistributing its sum over the network with the consideration of the global structure. Application of the measure is supported by a set of basic properties. A sufficient condition is given for generalized degree to be rank monotonic, excluding counter-intuitive changes in the centrality ranking after certain modifications of the network. The measure has a graph interpretation and can be calculated iteratively. Generalized degree is recommended to apply besides degree since it preserves most favourable attributes of degree, but better reflects the role of the nodes in the network and has an increased ability to distinguish among their importance.

cs.SI↗

arXiv2016

An application of incomplete pairwise comparison matrices for ranking top tennis players

Pairwise comparison is an important tool in multi-attribute decision making. Pairwise comparison matrices (PCM) have been applied for ranking criteria and for scoring alternatives according to a given criterion. Our paper presents a special application of incomplete PCMs: ranking of professional tennis players based on their results against each other. The selected 25 players have been on the top of the ATP rankings for a shorter or longer period in the last 40 years. Some of them have never met on the court. One of the aims of the paper is to provide ranking of the selected players, however, the analysis of incomplete pairwise comparison matrices is also in the focus. The eigenvector method and the logarithmic least squares method were used to calculate weights from incomplete PCMs. In our results the top three players of four decades were Nadal, Federer and Sampras. Some questions have been raised on the properties of incomplete PCMs and remains open for further investigation.

cs.AI↗

arXiv2015

On the additivity of preference aggregation methods

The paper reviews some axioms of additivity concerning ranking methods used for generalized tournaments with possible missing values and multiple comparisons. It is shown that one of the most natural properties, called consistency, has strong links to independence of irrelevant comparisons, an axiom judged unfavourable when players have different opponents. Therefore some directions of weakening consistency are suggested, and several ranking methods, the score, generalized row sum and least squares as well as fair bets and its two variants (one of them entirely new) are analysed whether they satisfy the properties discussed. It turns out that least squares and generalized row sum with an appropriate parameter choice preserve the relative ranking of two objects if the ranking problems added have the same comparison structure.

cs.GT↗

arXiv2015

A graph interpretation of the least squares ranking method

The paper aims at analyzing the least squares ranking method for generalized tournaments with possible missing and multiple paired comparisons. The bilateral relationships may reflect the outcomes of a sport competition, product comparisons, or evaluation of political candidates and policies. It is shown that the rating vector can be obtained as a limit point of an iterative process based on the scores in almost all cases. The calculation is interpreted on an undirected graph with loops attached to some nodes, revealing that the procedure takes into account not only the given object's results but also the strength of objects compared with it. We explore the connection between this method and another procedure defined for ranking the nodes in a digraph, the positional power measure. The decomposition of the least squares solution offers a number of ways to modify the method.

cs.GT↗

arXiv2015

Ranking by pairwise comparisons for Swiss-system tournaments

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 Open tournament. It is shown that results are robust regarding scaling technique. In order to compare different rankings, a distance function is introduced with the aim of taking into account the subjective nature of human perception. Analysis of the weight vectors implies that methods based on pairwise comparisons have common roots. Visualization of the results is provided by Multidimensional Scaling on the basis of the defined distance. The proposed rankings give in some cases intuitively better outcome than currently used lexicographical orders.

stat.AP↗

arXiv2015

Incomplete pairwise comparison matrices and weighting methods

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. A weighting method satisfies the linear order preservation property if it always results in a ranking such that an alternative directly preferred to another does not have a lower rank. We study whether two procedures, the Eigenvector Method and the Logarithmic Least Squares Method meet this axiom. Both weighting methods break linear order preservation, moreover, the ranking according to the Eigenvector Method depends on the incomplete pairwise comparison representation chosen.

math.OC↗