IDEAS home Printed from https://ideas.repec.org/a/spr/grdene/v9y2000i1d10.1023_a1008744805975.html
   My bibliography  Save this article

Analyzing Ordinal Data for Group Representation

Author

Listed:
  • Way C.W. Chang

    (National Chiao-Tung University)

  • Po-Young Chu

    (National Chiao-Tung University)

  • Cherng G. Ding

    (National Chiao-Tung University)

  • Soushan Wu

    (National Chiao-Tung University)

Abstract

With n individuals ranking m objects, the exhaustive comparison approach, proposed in this paper, produces a list of order vectors sorted by the relative number of concordant pairs. The exhaustive comparison approach compares all possible order vectors instead of "an" optimal order vector to help the data analyst to consider "practical" solutions rather than a "desired" solution. An overall concordant order ratio is proposed to measure "how well" each order vector may represent the ranking structure of an ordinal data set. And the marginal concordant ratio evaluating the goodness of fit of each object in each order vector is also proposed in this paper. Comparisons among some popular ranking methods are discussed in this article. An empirical survey data regarding how travellers considered various factors for choosing travelling locations are used to illustrate the proposed method and calculations.

Suggested Citation

  • Way C.W. Chang & Po-Young Chu & Cherng G. Ding & Soushan Wu, 2000. "Analyzing Ordinal Data for Group Representation," Group Decision and Negotiation, Springer, vol. 9(1), pages 47-61, January.
    • Handle: RePEc:spr:grdene:v:9:y:2000:i:1:d:10.1023_a:1008744805975
    DOI: 10.1023/A:1008744805975
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1023/A:1008744805975
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1023/A:1008744805975?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
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Wade D. Cook & Lawrence M. Seiford, 1982. "On the Borda-Kendall Consensus Method for Priority Ranking Problems," Management Science, INFORMS, vol. 28(6), pages 621-637, June.
    2. Wade D. Cook & Lawrence M. Seiford, 1978. "Priority Ranking and Consensus Formation," Management Science, INFORMS, vol. 24(16), pages 1721-1732, December.
    Full references (including those not matched with items on IDEAS)

    Citations

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


    Cited by:

    1. Padilla-Hernández, Salvador & Venegas-Martínez, Francisco & Gómez-Monge, Rodrigo (ed.), 2011. "Avances recientes en teoría y práctica económica," Sección de Estudios de Posgrado e Investigación de la Escuela Superios de Economía del Instituto Politécnico Nacional, Escuela Superior de Economía, Instituto Politécnico Nacional, edition 1, volume 2, number 006, January.
    2. Hunter, William Cannon, 2013. "China's Chairman Mao: A visual analysis of Hunan Province online destination image," Tourism Management, Elsevier, vol. 34(C), pages 101-111.
    3. 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.
    4. Hunter, William Cannon, 2011. "Rukai indigenous tourism: Representations, cultural identity and Q method," Tourism Management, Elsevier, vol. 32(2), pages 335-348.

    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. Kelin Luo & Yinfeng Xu & Bowen Zhang & Huili Zhang, 2018. "Creating an acceptable consensus ranking for group decision making," Journal of Combinatorial Optimization, Springer, vol. 36(1), pages 307-328, July.
    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. Sun, Bingzhen & Ma, Weimin, 2015. "An approach to consensus measurement of linguistic preference relations in multi-attribute group decision making and application," Omega, Elsevier, vol. 51(C), pages 83-92.
    5. Jorge Alcalde-Unzu & Marc Vorsatz, 2016. "Do we agree? Measuring the cohesiveness of preferences," Theory and Decision, Springer, vol. 80(2), pages 313-339, February.
    6. I. Contreras, 2012. "Ordered Weighted Disagreement Functions," Group Decision and Negotiation, Springer, vol. 21(3), pages 345-361, May.
    7. Michel Truchon, 2005. "Aggregation of Rankings: a Brief Review of Distance-Based Rules," Cahiers de recherche 0534, CIRPEE.
    8. Jorge Alcalde-Unzu & Marc Vorsatz, 2013. "Measuring the cohesiveness of preferences: an axiomatic analysis," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 41(4), pages 965-988, October.
    9. G. Laffond & J. Lainé, 2013. "Unanimity and the Anscombe’s paradox," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 21(3), pages 590-611, October.
    10. J.C.R. Alcantud & R. de Andrés Calle & J.M. Cascón, 2013. "Consensus and the Act of Voting," Studies in Microeconomics, , vol. 1(1), pages 1-22, June.
    11. Jorge Alcalde-Unzu & Marc Vorsatz, 2008. "The Measurement of Consensus: An Axiomatic Analysis," Working Papers 2008-28, FEDEA.
    12. 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.
    13. Yeşilçimen, Ali & Yıldırım, E. Alper, 2019. "An alternative polynomial-sized formulation and an optimization based heuristic for the reviewer assignment problem," European Journal of Operational Research, Elsevier, vol. 276(2), pages 436-450.
    14. Ignacio Contreras, 2010. "A Distance-Based Consensus Model with Flexible Choice of Rank-Position Weights," Group Decision and Negotiation, Springer, vol. 19(5), pages 441-456, September.
    15. Jabeur, Khaled & Martel, Jean-Marc, 2007. "A collective choice method based on individual preferences relational systems (p.r.s.)," European Journal of Operational Research, Elsevier, vol. 177(3), pages 1549-1565, March.
    16. Andrea Aveni & Ludovico Crippa & Giulio Principi, 2024. "On the Weighted Top-Difference Distance: Axioms, Aggregation, and Approximation," Papers 2403.15198, arXiv.org, revised Mar 2024.
    17. Spyridakos, A. & Siskos, Y. & Yannacopoulos, D. & Skouris, A., 2001. "Multicriteria job evaluation for large organizations," European Journal of Operational Research, Elsevier, vol. 130(2), pages 375-387, April.
    18. 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.
    19. J González-Pachón & C Romero, 2006. "An analytical framework for aggregating multiattribute utility functions," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 57(10), pages 1241-1247, October.
    20. Cascón, J.M. & González-Arteaga, T. & de Andrés Calle, R., 2019. "Reaching social consensus family budgets: The Spanish case," Omega, Elsevier, vol. 86(C), pages 28-41.

    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:spr:grdene:v:9:y:2000:i:1:d:10.1023_a:1008744805975. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.