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The outflow ranking method for weighted directed graphs

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  • van den Brink, René
  • Gilles, Robert P.

Abstract

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.

Suggested Citation

  • van den Brink, René & Gilles, Robert P., 2009. "The outflow ranking method for weighted directed graphs," European Journal of Operational Research, Elsevier, vol. 193(2), pages 484-491, March.
  • Handle: RePEc:eee:ejores:v:193:y:2009:i:2:p:484-491
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    References listed on IDEAS

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    1. 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.
    2. Bouyssou, D. & Perny, P., 1992. "Ranking methods for valued preference relations : A characterization of a method based on leaving and entering flows," European Journal of Operational Research, Elsevier, vol. 61(1-2), pages 186-194, August.
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    Cited by:

    1. René Van den Brink & Agnieszka Rusinowska, 2017. "The degree measure as utility function over positions in networks," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-01592181, HAL.
    2. Demange, Gabrielle, 2017. "Mutual rankings," Mathematical Social Sciences, Elsevier, vol. 90(C), pages 35-42.
    3. Csató, László, 2017. "European qualifiers to the 2018 FIFA World Cup can be manipulated," MPRA Paper 82652, University Library of Munich, Germany.
    4. Rene (J.R.) van den Brink & Agnieszka Rusinowska, 2017. "The Degree Measure as Utility Function over Positions in Networks," Tinbergen Institute Discussion Papers 17-065/II, Tinbergen Institute.
    5. Demange, Gabrielle, 2014. "A ranking method based on handicaps," Theoretical Economics, Econometric Society, vol. 9(3), September.
    6. René van den Brink & Agnieszka Rusinowska, 2017. "The degree measure as utility function over positions in networks," Documents de travail du Centre d'Economie de la Sorbonne 17035, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    7. Gabrielle Demange, 2016. "Mutual rankings," Working Papers halshs-01353825, HAL.

    More about this item

    Keywords

    Decision analysis Weighted directed graph Ranking method Outflow Axiomatization;

    JEL classification:

    • 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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