The outflow ranking method for weighted directed graphs
AbstractA 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.
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Bibliographic InfoArticle provided by Elsevier in its journal European Journal of Operational Research.
Volume (Year): 193 (2009)
Issue (Month): 2 (March)
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Decision analysis Weighted directed graph Ranking method Outflow Axiomatization;
Other versions of this item:
- René van den Brink & Robert P. Gilles, 0000. "The Outflow Ranking Method for Weighted Directed Graphs," Tinbergen Institute Discussion Papers 06-044/1, Tinbergen Institute.
- C65 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Miscellaneous Mathematical Tools
- D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
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- Bouyssou, Denis, 1992. "Ranking methods based on valued preference relations: A characterization of the net flow method," European Journal of Operational Research, Elsevier, vol. 60(1), pages 61-67, July.
- Gabrielle Demange, 2014.
"A Ranking Method Based on Handicaps,"
CESifo Working Paper Series
4636, CESifo Group Munich.
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