Scoring of web pages and tournaments—axiomatizations

Slutzki, Giora; Volij, Oscar

doi:10.1007/s00355-005-0033-7

Cited by 50 publications

(40 citation statements)

References 20 publications

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“…In defining the invariant scoring method I and the fair bets scoring method F on the domain D N N , we follow Slutzki and Volij (2006). The invariant scoring method assigns to a digraph D ∈ D N N the unique solution I (D) of the system 1…”

Section: Preliminaries: Invariant Fair Bets and λ-Scoring Methodsmentioning

confidence: 99%

“…Slutzki and Volij (2006)), respectively. As our scoring methods are defined on the set of all connected digraphs, these two extreme internal slackening scoring methods provide natural unique extensions of both fair bets and invariant scoring methods to directed graphs with several top cycles.…”

Section: An Application To Social Choice Situationsmentioning

confidence: 98%

“…In addition, Daniels (1969) proposed a different set of fair scores, based on a procedure that has come to be called the Markov method. A recent detailed comparison between the Markov method and the normalized long path method is given by Slutzki and Volij (2006), who refer to them as the fair bets and invariant scoring method, respectively. Finally, Borm et al (2002) introduced an iterative procedure resulting in the λ-method.…”

Section: Introductionmentioning

confidence: 99%

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Internal slackening scoring methods

2011

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We deal with the ranking problem of the nodes in a directed graph. The bilateral relationships specified by a directed graph may reflect the outcomes of a sport competition, the mutual reference structure between websites, or a group preference structure over alternatives. We introduce a class of scoring methods for directed graphs, indexed by a single nonnegative parameter α. This parameter reflects the internal slackening of a node within an underlying iterative process. The class of so-called internal slackening scoring methods, denoted by λ α , consists of the limits of these processes. It is seen that λ 0 extends the invariant scoring method, while λ ∞ extends the fair bets scoring method. Method λ 1 corresponds with the existing λ-scoring method of Borm et al. (Ann Oper Res 109(1):61-75, 2002) and can be seen as a compromise between λ 0 and λ ∞ . In particular, an explicit proportionality relation between λ α and λ 1 is derived. Moreover, the internal slackening scoring methods are applied to the setting of social choice situations where they give rise to a class of social choice correspondences that refine both the Top cycle correspondence and the Uncovered set correspondence.

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Section: Preliminaries: Invariant Fair Bets and λ-Scoring Methodsmentioning

confidence: 99%

Section: An Application To Social Choice Situationsmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

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Internal slackening scoring methods

2011

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“…In a previous paper, Slutzki and Volij (2004) characterized the fair-bets scoring method for the class of irreducible problems. One of the crucial axioms used there states that all players receive the same score in a particular class of simple problems, namely, the class of strongly balanced problems.…”

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confidence: 99%

Ranking participants in generalized tournaments

Slutzki

Volij

2005

Int J Game Theory

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Consider the problem of ranking social alternatives based on the number of voters that prefer one alternative to the other. Or consider the problem of ranking chess players by their past performance. A wide variety of ranking methods have been proposed to deal with these problems. Using six independent axioms, we characterize the fair-bets ranking method proposed by Daniels [4] and Moon and Pullman [14].

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“…Az aggregált páros összehasonlítási mátrix bizonyos transzformáltjainak domináns sajátvektorát használja az invariáns és a fair bets (Daniels, 1969;Moon és Pullman, 1970), vagy az előbbi egy perturbált változatának megfelelő PageRank módszer (Brin és Page, 1998). Ezeket az eljárásokat, Slutzki és Volij (2005), illetve Slutzki és Volij (2006) karakterizációit részletesen ismertette , bár az invariáns módszer gráfelméleti, ordinális tulajdonságokon alapuló axiomatizációjára (Altman és Tennenholtz, 2005) nem tért ki.…”

Section: A Pontozási Eljárások Axiomatikus Szempontú áTtekintéseunclassified

A páros összehasonlításokon alapuló rangsorolás módszertani és alkalmazási kérdései

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Scoring of web pages and tournaments—axiomatizations

Abstract: Perron–Frobenius theorem, Scoring, Rankings, Tournaments, Web pages, Citations,

Cited by 50 publications

References 20 publications

Internal slackening scoring methods

Internal slackening scoring methods

Ranking participants in generalized tournaments

A páros összehasonlításokon alapuló rangsorolás módszertani és alkalmazási kérdései

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