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Evaluating the capacity of paired comparison methods to aggregate rankings of separate groups

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  • Éva Orbán-Mihálykó

    (University of Pannonia)

  • Csaba Mihálykó

    (University of Pannonia)

  • László Gyarmati

    (University of Pannonia)

Abstract

Ranking and rating methods have outstanding significance in sports, mainly due to their capacity to predict results. In this paper we turn to their capacity to aggregate separate groups’ rankings based on a small piece of information. We investigate under which conditions two or more separate groups can be trustworthily interwoven applying Thurstone motivated methods and an AHP based method. A theorem is proved which guarantees adequate unified ranking based on some links between the groups. We also analyse the robustness of the results.

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  • Éva Orbán-Mihálykó & Csaba Mihálykó & László Gyarmati, 2024. "Evaluating the capacity of paired comparison methods to aggregate rankings of separate groups," 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. 32(1), pages 109-129, March.
    • Handle: RePEc:spr:cejnor:v:32:y:2024:i:1:d:10.1007_s10100-023-00839-3
    DOI: 10.1007/s10100-023-00839-3
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    References listed on IDEAS

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    1. Éva Orbán-Mihálykó & Csaba Mihálykó & László Koltay, 2019. "A generalization of the Thurstone method for multiple choice and incomplete 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(1), pages 133-159, March.
    2. 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).
    3. 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.
    4. A. Anderson, 2014. "Maximum likelihood ranking in racing sports," Applied Economics, Taylor & Francis Journals, vol. 46(15), pages 1778-1787, May.
    5. Araki, Kenji & Hirose, Yoshihiro & Komaki, Fumiyasu, 2019. "Paired comparison models with age effects modeled as piecewise quadratic splines," International Journal of Forecasting, Elsevier, vol. 35(2), pages 733-740.
    6. Stern, Hal, 1992. "Are all linear paired comparison models empirically equivalent?," Mathematical Social Sciences, Elsevier, vol. 23(1), pages 103-117, February.
    7. 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.
    8. Csató, László & Tóth, Csaba, 2020. "University rankings from the revealed preferences of the applicants," European Journal of Operational Research, Elsevier, vol. 286(1), pages 309-320.
    9. Julio González-Díaz & Ruud Hendrickx & Edwin Lohmann, 2014. "Paired comparisons analysis: an axiomatic approach to ranking methods," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 42(1), pages 139-169, January.
    10. Éva Orbán-Mihálykó & Csaba Mihálykó & László Koltay, 2019. "Incomplete paired comparisons in case of multiple choice and general log-concave probability density functions," 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 515-532, June.
    11. Alan Agresti, 1992. "Analysis of Ordinal Paired Comparison Data," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 41(2), pages 287-297, June.
    12. Baker, Rose D. & McHale, Ian G., 2017. "An empirical Bayes model for time-varying paired comparisons ratings: Who is the greatest women’s tennis player?," European Journal of Operational Research, Elsevier, vol. 258(1), pages 328-333.
    13. 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.
    14. Lasek, Jan & Gagolewski, Marek, 2021. "Interpretable sports team rating models based on the gradient descent algorithm," International Journal of Forecasting, Elsevier, vol. 37(3), pages 1061-1071.
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    1. Péter Biró & Sándor Bozóki & Tamás Király & Alexandru Kristály, 2024. "Optimization methods and algorithms," 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. 32(1), pages 1-9, March.

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