IDEAS home Printed from https://ideas.repec.org/p/mse/cesdoc/19009.html
   My bibliography  Save this paper

The Degree Ratio Ranking Method for Directed Networks

Author

Listed:

Abstract

One of the most famous ranking methods for digraphs is the ranking by Copeland score. The Copeland score of a node in a digraph is the difference between its outdegree (i.e. its number of outgoing arcs) and its indegree (i.e. its number of ingoing arcs). In the ranking by Copeland score, a node is ranked higher, the higher is its Copeland score. In this paper, we deal with an alternative to rank nodes according to their out– and indegree, namely ranking the nodes according to their degree ratio, i.e. the outdegree divided by the indegree. To avoid dividing by a zero indegree, we implicitly take the out– and indegree of the reflexive digraph. We provide an axiomatization of the ranking by degree ratio using a sibling neutrality axiom, which says that the entrance of a sibling (i.e. a node that is in some sense similar to the original node) does not change the ranking among the original nodes. We also provide a new axiomatization of the ranking by Copeland score using the same axioms except that this method satisfies a different sibling neutrality. Finally, we modify the ranking by degree ratio by not considering the reflexive digraph, but by definition assume nodes with indegree zero to be ranked higher than nodes with a positive indegree. We provide an axiomatization of this ranking by modified degree ratio using yet another sibling neutrality and a maximal property. In this way, we can compare the three ranking methods by their respective sibling neutrality

Suggested Citation

  • René van den Brink & Agnieszka Rusinowska, 2019. "The Degree Ratio Ranking Method for Directed Networks," Documents de travail du Centre d'Economie de la Sorbonne 19009, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    • Handle: RePEc:mse:cesdoc:19009
    as

    Download full text from publisher

    File URL: ftp://mse.univ-paris1.fr/pub/mse/CES2019/19009.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Gabrielle Demange, 2012. "On the influence of a ranking system," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 39(2), pages 431-455, July.
    2. Ignacio Palacios-Huerta & Oscar Volij, 2004. "The Measurement of Intellectual Influence," Econometrica, Econometric Society, vol. 72(3), pages 963-977, May.
    3. de Clippel, Geoffroy & Moulin, Herve & Tideman, Nicolaus, 2008. "Impartial division of a dollar," Journal of Economic Theory, Elsevier, vol. 139(1), pages 176-191, March.
    4. Woeginger, Gerhard J., 2008. "An axiomatic characterization of the Hirsch-index," Mathematical Social Sciences, Elsevier, vol. 56(2), pages 224-232, September.
    5. 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.
    6. 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.
    7. D. Bouyssou & P. Perny, 1992. "Ranking methods for valued preference relations," Post-Print hal-02920156, HAL.
    8. 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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Brink, René van den & Rusinowska, Agnieszka, 2021. "The degree ratio ranking method for directed graphs," European Journal of Operational Research, Elsevier, vol. 288(2), pages 563-575.
    2. 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.
    3. van den Brink, René & Rusinowska, Agnieszka, 2022. "The degree measure as utility function over positions in graphs and digraphs," European Journal of Operational Research, Elsevier, vol. 299(3), pages 1033-1044.
    4. ,, 2014. "A ranking method based on handicaps," Theoretical Economics, Econometric Society, vol. 9(3), September.
    5. Daniela Bubboloni & Michele Gori, 2018. "The flow network method," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 51(4), pages 621-656, December.
    6. Csató, László, 2019. "A characterization of the Logarithmic Least Squares Method," European Journal of Operational Research, Elsevier, vol. 276(1), pages 212-216.
    7. 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.
    8. P. Herings & A. Predtetchinski & A. Perea, 2006. "The Weak Sequential Core for Two-Period Economies," International Journal of Game Theory, Springer;Game Theory Society, vol. 34(1), pages 55-65, April.
    9. Demange, Gabrielle, 2017. "Mutual rankings," Mathematical Social Sciences, Elsevier, vol. 90(C), pages 35-42.
    10. P. Jean-Jacques Herings & Gerard van der Laan & Dolf Talman, 2000. "Cooperative Games in Graph Structure," Tinbergen Institute Discussion Papers 00-072/1, Tinbergen Institute.
    11. László Csató, 2019. "An impossibility theorem for paired comparisons," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 27(2), pages 497-514, June.
    12. G Özerol & E Karasakal, 2008. "Interactive outranking approaches for multicriteria decision-making problems with imprecise information," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 59(9), pages 1253-1268, September.
    13. Chen, Xuqi & Gao, Zhifeng & House, Lisa, 2015. "Willingness to Pay for Niche Fresh Produce across the States: Why Are Consumers Willing to Pay More for the Less Favorite?," 2015 Annual Meeting, January 31-February 3, 2015, Atlanta, Georgia 196901, Southern Agricultural Economics Association.
    14. Zhiwei Cui & Yan-An Hwang & Ding-Cheng You, 2021. "Axiomatizations of the $$\beta $$ β and the score measures in networks," International Journal of Game Theory, Springer;Game Theory Society, vol. 50(2), pages 399-418, June.
    15. Csató, László, 2013. "Rangsorolás páros összehasonlításokkal. Kiegészítések a felvételizői preferencia-sorrendek módszertanához [Paired comparisons ranking. A supplement to the methodology of application-based preferenc," Közgazdasági Szemle (Economic Review - monthly of the Hungarian Academy of Sciences), Közgazdasági Szemle Alapítvány (Economic Review Foundation), vol. 0(12), pages 1333-1353.
    16. Herings, P.J.J. & van der Laan, G. & Talman, A.J.J., 2001. "Measuring the Power of Nodes in Digraphs," Other publications TiSEM 8ad1bdb1-a602-4674-b737-2, Tilburg University, School of Economics and Management.
    17. Vincke, Ph., 1999. "Robust and neutral methods for aggregating preferences into an outranking relation," European Journal of Operational Research, Elsevier, vol. 112(2), pages 405-412, January.
    18. Yazidi, Anis & Ivanovska, Magdalena & Zennaro, Fabio M. & Lind, Pedro G. & Viedma, Enrique Herrera, 2022. "A new decision making model based on Rank Centrality for GDM with fuzzy preference relations," European Journal of Operational Research, Elsevier, vol. 297(3), pages 1030-1041.
    19. Monsuur, Herman, 2005. "Characterizations of the 3-cycle count and backward length of a tournament," European Journal of Operational Research, Elsevier, vol. 164(3), pages 778-784, August.
    20. Mario Martín-Gamboa & Luis C. Dias & Paula Quinteiro & Fausto Freire & Luís Arroja & Ana Cláudia Dias, 2019. "Multi-Criteria and Life Cycle Assessment of Wood-Based Bioenergy Alternatives for Residential Heating: A Sustainability Analysis," Energies, MDPI, vol. 12(22), pages 1-17, November.

    More about this item

    Keywords

    group decisions and negotiations; directed graph; ranking method; degree ratio; Copeland score;
    All these keywords.

    JEL classification:

    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
    • D85 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Network Formation
    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:mse:cesdoc:19009. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Lucie Label (email available below). General contact details of provider: https://edirc.repec.org/data/cenp1fr.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.