The outflow ranking method for weighted directed graphs
A ranking method assigns to every weighted directed graph a (weak) ordering of the nodes. In this paper we axiomatize the ranking method that ranks the nodes according to their outflow using four independent axioms. Besides the well-known axioms of anonymity and positive responsiveness we introduce outflow monotonicity  meaning that in pairwise comparison between two nodes, a node is not doing worse in case its own outflow does not decrease and the other nodes outflow does not increase  and order preservation  meaning that adding two weighted digraphs such that the pairwise ranking between two nodes is the same in both weighted digraphs, then this is also their pairwise ranking in the sum weighted digraph. The outflow ranking method generalizes the ranking by outdegree for directed graphs, and therefore also generalizes the ranking by Copeland score for tournaments.
outflow ranking method weighted directed graph axiomatization decision analysis