Issue: 2016/Vol.26/No.2, Pages 107-125
POWER ON DIGRAPHS
Hans Peters
, Judith Timmer, Rene van den Brink
Cite as: H. Peters, J. Timmer, R. v. d. Brink. Power on digraphs. Operations Research and Decisions 2016: 26(2), 107-125. DOI 10.5277/ord160207
Abstract
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,and apex type indices.
Keywords: digraph, power index, transfer property, link addition
Received: 24 April 2016 Accepted: 11 July 2016