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Ranking in Tournaments and Group Decisionmaking

Author

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  • Stephen T. Goddard

    (General Electric Information Services Pty. Ltd., Melbourne, Australia)

Abstract

This paper fully discusses methods for ranking a set of alternatives in the fairest possible way according to a minimum violations criterion. New methods, based on finding paths and circuits in graphs, are presented for ranking participants in round-robin and generalized tournaments, and for consensus and group decisionmaking problems. The objective of the paper is to review existing methods for tackling these problems, and compare them with the new methods, according to a "fairness" criterion, and the amount of computing required to reach a solution. It is shown that the new methods often exceed the existing methods in both fairness and reduced computing requirements. In particular, the new methods are generally more versatile than existing methods. This allows organizations to obtain the fairest ranking of a number of alternatives, according to their managers' or employees' wishes. Particular attention is given to incomplete rankings where insufficient exposure of an individual to some alternatives restricts that individual to ranking only the remaining alternatives.

Suggested Citation

  • Stephen T. Goddard, 1983. "Ranking in Tournaments and Group Decisionmaking," Management Science, INFORMS, vol. 29(12), pages 1384-1392, December.
    • Handle: RePEc:inm:ormnsc:v:29:y:1983:i:12:p:1384-1392
    DOI: 10.1287/mnsc.29.12.1384
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    Cited by:

    1. Zhang, L.P. & Zhou, P., 2018. "A non-compensatory composite indicator approach to assessing low-carbon performance," European Journal of Operational Research, Elsevier, vol. 270(1), pages 352-361.
    2. B. Jay Coleman, 2005. "Minimizing Game Score Violations in College Football Rankings," Interfaces, INFORMS, vol. 35(6), pages 483-496, December.
    3. Siraj, Sajid & Mikhailov, Ludmil & Keane, John, 2012. "A heuristic method to rectify intransitive judgments in pairwise comparison matrices," European Journal of Operational Research, Elsevier, vol. 216(2), pages 420-428.
    4. Funk, Patrick & Davis, Alex & Vaishnav, Parth & Dewitt, Barry & Fuchs, Erica, 2020. "Individual inconsistency and aggregate rationality: Overcoming inconsistencies in expert judgment at the technical frontier," Technological Forecasting and Social Change, Elsevier, vol. 155(C).
    5. Ngwenyama, Ojelanki K. & Bryson, Noel, 1999. "Eliciting and mapping qualitative preferences to numeric rankings in group decision making," European Journal of Operational Research, Elsevier, vol. 116(3), pages 487-497, August.
    6. Dong, Zhi-Long & Ribeiro, Celso C. & Xu, Fengmin & Zamora, Ailec & Ma, Yujie & Jing, Kui, 2023. "Dynamic scheduling of e-sports tournaments," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 169(C).
    7. Mass A. & Bezembinder, T. & Wakker, P., 1996. "On solving intansitivities in repeated pairwise choices," Mathematical Social Sciences, Elsevier, vol. 31(1), pages 53-53, February.
    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. C. Richard Cassady & Lisa M. Maillart & Sinan Salman, 2005. "Ranking Sports Teams: A Customizable Quadratic Assignment Approach," Interfaces, INFORMS, vol. 35(6), pages 497-510, December.
    10. Bryson, Noel & Mobolurin, Ayodele & Ngwenyama, Ojelanki, 1995. "Modelling pairwise comparisons on ratio scales," European Journal of Operational Research, Elsevier, vol. 83(3), pages 639-654, June.
    11. Brozos-Vázquez, Miguel & Campo-Cabana, Marco Antonio & Díaz-Ramos, José Carlos & González-Díaz, Julio, 2008. "Ranking participants in tournaments by means of rating functions," Journal of Mathematical Economics, Elsevier, vol. 44(11), pages 1246-1256, December.

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    Keywords

    tournament rankings; decision making;

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