IDEAS home Printed from https://ideas.repec.org/a/inm/ormnsc/v28y1982i6p638-645.html
   My bibliography  Save this article

Priority Ranking and Consensus Formation: The Case of Ties

Author

Listed:
  • Ronald D. Armstrong

    (University of Georgia)

  • Wade D. Cook

    (University of Texas, Austin)

  • Lawrence M. Seiford

    (York University)

Abstract

This paper investigates the problem of obtaining a compromise/consensus from a set of ordinal rankings of n objects supplied by m committee members. Earlier work by Cook and Seiford (Cook, Wade D., Lawrence M. Seiford. 1978. Priority ranking and consensus formation. Management Sci. 24 (16) 1721--1732.) dealt with the problem of consensus when attention was restricted to complete rankings only. That is, no ties were permitted. This paper examines the general problem which allows for tied preferences. A convex polyhedral representation is given of the feasible solution space, and a branch-and-bound procedure is developed for determining an optimal ranking. Computational results for various problem sizes are presented. Generalizations, and directions for further research are discussed.

Suggested Citation

  • Ronald D. Armstrong & Wade D. Cook & Lawrence M. Seiford, 1982. "Priority Ranking and Consensus Formation: The Case of Ties," Management Science, INFORMS, vol. 28(6), pages 638-645, June.
    • Handle: RePEc:inm:ormnsc:v:28:y:1982:i:6:p:638-645
    DOI: 10.1287/mnsc.28.6.638
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/mnsc.28.6.638
    Download Restriction: no
    File URL: https://libkey.io/10.1287/mnsc.28.6.638?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Gilbert Laffond & Jean Lainé & M. Remzi Sanver, 2020. "Metrizable preferences over preferences," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 55(1), pages 177-191, June.
    2. Hanna Bury & Dariusz Wagner, 2009. "Group judgement with ties. A position-based approach," Operations Research and Decisions, Wroclaw University of Technology, Institute of Organization and Management, vol. 4, pages 9-26.
    3. Cook, Wade D. & Kress, Moshe & Seiford, Lawrence M., 1997. "A general framework for distance-based consensus in ordinal ranking models," European Journal of Operational Research, Elsevier, vol. 96(2), pages 392-397, January.
    4. Patricia Jaramillo & Ricardo Smith & JoaquÍn Andréu, 2005. "Multi-Decision-Makers Equalizer: A Multiobjective Decision Support System for Multiple Decision-Makers," Annals of Operations Research, Springer, vol. 138(1), pages 97-111, September.
    5. Fujun Hou, 2015. "A Consensus Gap Indicator and Its Application to Group Decision Making," Group Decision and Negotiation, Springer, vol. 24(3), pages 415-428, May.
    6. Hou, Fujun & Triantaphyllou, Evangelos, 2019. "An iterative approach for achieving consensus when ranking a finite set of alternatives by a group of experts," European Journal of Operational Research, Elsevier, vol. 275(2), pages 570-579.
    7. Yucheng Dong & Yao Li & Ying He & Xia Chen, 2021. "Preference–Approval Structures in Group Decision Making: Axiomatic Distance and Aggregation," Decision Analysis, INFORMS, vol. 18(4), pages 273-295, December.
    8. Cook, Wade D., 2006. "Distance-based and ad hoc consensus models in ordinal preference ranking," European Journal of Operational Research, Elsevier, vol. 172(2), pages 369-385, July.
    9. Slim Ben Khelifa & Jean-Marc Martel, 2001. "A Distance-Based Collective Weak Ordering," Group Decision and Negotiation, Springer, vol. 10(4), pages 317-329, July.
    10. Hanna Bury & Dariusz Wagner, 2009. "Group judgment with ties. A position-based approach," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 19(4), pages 7-26.
    11. Tino Werner, 2022. "Elicitability of Instance and Object Ranking," Decision Analysis, INFORMS, vol. 19(2), pages 123-140, June.
    12. Fujun Hou, 2018. "Mutual Conversion Between Preference Maps And Cook-Seiford Vectors," Papers 1812.03566, arXiv.org.
    13. Saaty, Thomas L. & Shang, Jen S., 2007. "Group decision-making: Head-count versus intensity of preference," Socio-Economic Planning Sciences, Elsevier, vol. 41(1), pages 22-37, March.
    14. Fujun Hou, 2016. "The Prametric-Based GDM Procedure Under Fuzzy Environment," Group Decision and Negotiation, Springer, vol. 25(5), pages 1071-1084, September.

    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:inm:ormnsc:v:28:y:1982:i:6:p:638-645. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.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.