Power on digraphs

Hans Peters, Judith B. Timmer, René van den Brink

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It is assumed that relations between $n$ players are represented by a directed graph or digraph. Such a digraph is called invariant if there is a link (arc) between any two players between whom there is also a directed path. We characterize a class of power indices for invariant digraphs based on four axioms: Null player, Constant sum, Anonymity, and the Transfer property. This class is determined by $2n-2$ parameters. By considering additional conditions about the effect of adding a directed link between two players, we single out three different, one-parameter families of power indices, reflecting several well-known indices from the literature: the Copeland score, $\beta$- and apex type indices.
Original languageUndefined
Pages (from-to)107-125
Number of pages19
JournalOperations research and decisions
Issue number2
Publication statusPublished - 2016


  • Link addition
  • Transfer property
  • Power index
  • Digraph
  • METIS-318515
  • IR-101441
  • EWI-27207

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