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Incomplete paired comparisons in case of multiple choice and general log-concave probability density functions

Author

Listed:
  • Éva Orbán-Mihálykó

    (University of Pannonia)

  • Csaba Mihálykó

    (University of Pannonia)

  • László Koltay

    (University of Pannonia)

Abstract

A scoring method based on paired comparison allowing multiple choice is investigated. We allow general log-concave probability density functions for the random variables describing the difference of the objects. This case involves Bradley–Terry models and Thurstone models as well. A sufficient condition is proved for the existence and uniqueness of the maximum likelihood estimation of the parameters in case of incomplete comparisons. The axiomatic properties of the method are also investigated.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:cejnor:v:27:y:2019:i:2:d:10.1007_s10100-018-0568-1
    DOI: 10.1007/s10100-018-0568-1
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    References listed on IDEAS

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    1. 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.
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    6. Stern, Hal, 1992. "Are all linear paired comparison models empirically equivalent?," Mathematical Social Sciences, Elsevier, vol. 23(1), pages 103-117, February.
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