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A generalization of the Thurstone method for multiple choice and incomplete paired comparisons

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Listed:
  • Éva Orbán-Mihálykó

    (University of Pannonia)

  • Csaba Mihálykó

    (University of Pannonia)

  • László Koltay

    (University of Pannonia)

Abstract

A ranking method based on paired comparisons is proposed. The object’s characteristics are considered as random variables and the observers judge about their differences. The differences are classified. More than two classes are allowed. Assuming Gauss distributed latent random variables we set up the likelihood function and estimate the parameters by the maximum likelihood method. The rank of the objects is the order of the expectations. We analyse the log-likelihood function and provide reasonable conditions for the existence of the maximum value and the uniqueness of the maximizer. Some illustrative examples are also presented. The method can be applied in case of incomplete comparisons as well. It allows constructing confidence intervals for the probabilities and testing the hypothesis that there are no significant differences between the expectations.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:cejnor:v:27:y:2019:i:1:d:10.1007_s10100-017-0495-6
    DOI: 10.1007/s10100-017-0495-6
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    References listed on IDEAS

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    1. Baker, Rose D. & McHale, Ian G., 2014. "A dynamic paired comparisons model: Who is the greatest tennis player?," European Journal of Operational Research, Elsevier, vol. 236(2), pages 677-684.
    2. 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.
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    6. Frederick Mosteller, 1951. "Remarks on the method of paired comparisons: I. The least squares solution assuming equal standard deviations and equal correlations," Psychometrika, Springer;The Psychometric Society, vol. 16(1), pages 3-9, March.
    7. 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.
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