Internal slackening scoring methods

M. Slikker, P.E.M. Borm, R. van den Brink

Research output: Contribution to journalArticleScientificpeer-review

1 Citation (Scopus)

Abstract

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 λα, consists of the limits of these processes. It is seen that λ0 extends the invariant scoring method, while λ extends the fair bets scoring method. Method λ1 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 λ0 and λ. In particular, an explicit proportionality relation between λα and λ1 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.
Original languageEnglish
Pages (from-to)445-462
JournalTheory and Decision
Volume72
Issue number4
Publication statusPublished - 2012

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