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Ranking by pairwise comparisons for Swiss-system tournaments

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  • László Csató

Abstract

Pairwise comparison matrices are widely used in multicriteria decision making. This article applies incomplete pairwise comparison matrices in the area of sport tournaments, namely proposing alternative rankings for the 2010 Chess Olympiad Open tournament. It is shown that results are robust regarding scaling technique. In order to compare different rankings, a distance function is introduced with the aim of taking into account the subjective nature of human perception. Analysis of the weight vectors implies that methods based on pairwise comparisons have common roots. Visualization of the results is provided by multidimensional scaling on the basis of the defined distance. The proposed rankings give in some cases intuitively better outcome than currently used lexicographical orders. Copyright Springer-Verlag 2013

Suggested Citation

  • László Csató, 2013. "Ranking by pairwise comparisons for Swiss-system tournaments," 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. 21(4), pages 783-803, December.
    • Handle: RePEc:spr:cejnor:v:21:y:2013:i:4:p:783-803
    DOI: 10.1007/s10100-012-0261-8
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    References listed on IDEAS

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    1. Fedrizzi, Michele & Giove, Silvio, 2007. "Incomplete pairwise comparison and consistency optimization," European Journal of Operational Research, Elsevier, vol. 183(1), pages 303-313, November.
    2. Yoram Wind & Thomas L. Saaty, 1980. "Marketing Applications of the Analytic Hierarchy Process," Management Science, INFORMS, vol. 26(7), pages 641-658, July.
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    Cited by:

    1. Ritxar Arlegi & Dinko Dimitrov, 2023. "League competitions and fairness," Journal of Combinatorial Optimization, Springer, vol. 45(4), pages 1-18, May.
    2. Ritxar Arlegi & Institute for Advanced Research in Business and Economics (INARBE) & Dinko Dimitrov, 2018. "Fair Competition Design," Documentos de Trabajo - Lan Gaiak Departamento de Economía - Universidad Pública de Navarra 1803, Departamento de Economía - Universidad Pública de Navarra.
    3. László Csató, 2024. "Club coefficients in the UEFA Champions League: Time for shift to an Elo-based formula," International Journal of Performance Analysis in Sport, Taylor & Francis Journals, vol. 24(2), pages 119-134, March.
    4. Fernandes, Rosário & Furtado, Susana, 2022. "Efficiency of the principal eigenvector of some triple perturbed consistent matrices," European Journal of Operational Research, Elsevier, vol. 298(3), pages 1007-1015.
    5. 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.
    6. Ágoston, Kolos Csaba & Csató, László, 2024. "A lexicographically optimal completion for pairwise comparison matrices with missing entries," European Journal of Operational Research, Elsevier, vol. 314(3), pages 1078-1086.
    7. Csató, László & Petróczy, Dóra Gréta, 2021. "On the monotonicity of the eigenvector method," European Journal of Operational Research, Elsevier, vol. 292(1), pages 230-237.
    8. D'ora Gr'eta Petr'oczy & L'aszl'o Csat'o, 2019. "Revenue allocation in Formula One: a pairwise comparison approach," Papers 1909.12931, arXiv.org, revised Dec 2020.
    9. László Csató, 2017. "On the ranking of a Swiss system chess team tournament," Annals of Operations Research, Springer, vol. 254(1), pages 17-36, July.
    10. L'aszl'o Csat'o & Csaba T'oth, 2018. "University rankings from the revealed preferences of the applicants," Papers 1810.04087, arXiv.org, revised Feb 2020.
    11. Szádoczki, Zsombor & Bozóki, Sándor & Tekile, Hailemariam Abebe, 2022. "Filling in pattern designs for incomplete pairwise comparison matrices: (Quasi-)regular graphs with minimal diameter," Omega, Elsevier, vol. 107(C).
    12. Szádoczki, Zsombor, 2022. "Operációkutatás a sportok profitabilitásáért. László Csató: Tournament Design. How Operations Research Can Improve Sports Rules? Palgrave Pivots in Sports Economics, Palgrave Macmillan, 2021, 175 o," Közgazdasági Szemle (Economic Review - monthly of the Hungarian Academy of Sciences), Közgazdasági Szemle Alapítvány (Economic Review Foundation), vol. 0(2), pages 283-288.
    13. Ágoston, Kolos Csaba & Csató, László, 2022. "Inconsistency thresholds for incomplete pairwise comparison matrices," Omega, Elsevier, vol. 108(C).
    14. L'aszl'o Csat'o, 2024. "Most Swiss-system tournaments are unfair: Evidence from chess," Papers 2410.19333, arXiv.org.
    15. Petróczy, Dóra Gréta, 2021. "An alternative quality of life ranking on the basis of remittances," Socio-Economic Planning Sciences, Elsevier, vol. 78(C).
    16. Csató, László, 2019. "A characterization of the Logarithmic Least Squares Method," European Journal of Operational Research, Elsevier, vol. 276(1), pages 212-216.
    17. László Csató, 2015. "A graph interpretation of the least squares ranking method," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 44(1), pages 51-69, January.
    18. Bozóki, Sándor & Csató, László & Temesi, József, 2016. "An application of incomplete pairwise comparison matrices for ranking top tennis players," European Journal of Operational Research, Elsevier, vol. 248(1), pages 211-218.
    19. 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.
    20. László Csató, 2019. "Axiomatizations of inconsistency indices for triads," Annals of Operations Research, Springer, vol. 280(1), pages 99-110, September.
    21. L'aszl'o Csat'o, 2023. "Club coefficients in the UEFA Champions League: Time for shift to an Elo-based formula," Papers 2304.09078, arXiv.org, revised Oct 2023.
    22. Csató, László, 2016. "Felsőoktatási rangsorok jelentkezői preferenciák alapján [University rankings on the basis of applicants preferences]," Közgazdasági Szemle (Economic Review - monthly of the Hungarian Academy of Sciences), Közgazdasági Szemle Alapítvány (Economic Review Foundation), vol. 0(1), pages 27-61.

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