Theory and Decision 72 (4):445-462 (2012)

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 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 λ α 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
Keywords Digraphs  Scoring methods  Invariant method  Fair bets method  Social choice correspondences
Categories (categorize this paper)
DOI 10.1007/s11238-011-9281-4
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

PhilArchive copy

Upload a copy of this paper     Check publisher's policy     Papers currently archived: 64,229
Through your library

References found in this work BETA

Digraph Competitions and Cooperative Games.René van Den Brink & Peter Borm - 2002 - Theory and Decision 53 (4):327-342.

Add more references

Citations of this work BETA

No citations found.

Add more citations

Similar books and articles

Simple 'Might's, Indicative Possibilities and the Open Future.K. DeRose - 1998 - Philosophical Quarterly 48 (190):67-82.
Internal and External Method in the Study of Law.Richard L. Schwartz - 1992 - Law and Philosophy 11 (3):179 - 199.
A New Way of Scoring Moral Judgement Interviews.Peter E. Langford & J. Vin D'Cruz - 1989 - Journal of Moral Education 18 (2):118-130.


Added to PP index

Total views
75 ( #144,856 of 2,455,478 )

Recent downloads (6 months)
1 ( #449,205 of 2,455,478 )

How can I increase my downloads?


My notes