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 node’s 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.

‘Who Ate All the Pride?’:Patriotic Sentiment and English National Football Support.

The growing popularity of English national insignia in international football tournaments has been widely interpreted as evidence of the emergence of a renewed English national consciousness. However, little empirical research has considered how people in England actually understand football support in relation to national identity. Interview data collected around the time of the Euro 2000 and the 2002 World Cup tournaments fail to substantiate the presumption that support for the England football team maps onto claims to patriotic sentiment in any straightforward way. People with far-right political affiliations did generally use national football support to symbolise a general pride in English national identity. However, other people either claimed not to support the England national team precisely because of its associations with nationalism, or else bracketed the domain of football support from more general connotations of English patriotism.