Internal slackening scoring method

Internal slackening scoring method

By: jacobsadm

June 5, 2013

  • Author(s):
    Slikker, M., Borm, P.E.M. & Brink, J.R. den

  • Appeared In: Theory and decision : an international journal for philosophy and methodology of the social sciences
  • Volume: 21, 2012
  • Issue: 4
  • Pages: 403 – 421


  • 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^sup α^, consists of the limits of these processes. It is seen that λ^sup 0^ extends the invariant scoring method, while λ^sup ∞^ extends the fair bets scoring method. Method λ^sup 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^sup 0^ and λ^sup ∞^. In particular, an explicit proportionality relation between λ^sup α^ and λ^sup 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.