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Monotonicity of ‘ranking by choosing’: A progress report

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  • Denis Bouyssou

Abstract

Procedures designed to select alternatives on the basis of the results of pairwise contests between them have received much attention in literature. The particular case of tournaments has been studied in depth. More recently weak tournaments and valued generalizations thereof have been investigated.The purpose of this paper is to investigate to what extent these choice procedures may be meaningfully used to define ranking procedures via their repeated use, i.e. when the equivalence classes of the ranking are determined by successive applications of the choice procedure. This is what we call “ranking by choosing”. As could be expected, such ranking procedures raise monotonicity problems. We analyze these problems and show that it is nevertheless possible to isolate a large class of well-behaved choice procedures for which failures of monotonicity are not overly serious. The hope of finding really attractive ranking by choosing procedures is however shown to be limited. Our results are illustrated on the case of tournaments. Copyright Springer-Verlag 2004

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  • Denis Bouyssou, 2004. "Monotonicity of ‘ranking by choosing’: A progress report," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 23(2), pages 249-273, October.
    • Handle: RePEc:spr:sochwe:v:23:y:2004:i:2:p:249-273
    DOI: 10.1007/s00355-003-0250-x
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    Cited by:

    1. Sonin, Konstantin & Dagaev, Dmitry, 2013. "Winning by Losing: Incentive Incompatibility in Multiple Qualifiers," CEPR Discussion Papers 9373, C.E.P.R. Discussion Papers.
    2. 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.
    3. 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.
    4. Lainé, Jean, 2015. "Hyper-stable collective rankings," Mathematical Social Sciences, Elsevier, vol. 77(C), pages 70-80.
    5. Gonzalez-Diaz, J. & Hendrickx, R.L.P. & Lohmann, E.R.M.A., 2011. "Paired Comparisons Analysis : An Axiomatic Approach to Rankings in Tournaments," Other publications TiSEM 2dbfd64d-2a1b-445c-86c6-4, Tilburg University, School of Economics and Management.
    6. Horan, Sean & Sprumont, Yves, 2016. "Welfare criteria from choice: An axiomatic analysis," Games and Economic Behavior, Elsevier, vol. 99(C), pages 56-70.
    7. 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.
    8. Bouyssou, Denis & Marchant, Thierry, 2016. "Ranking authors using fractional counting of citations: An axiomatic approach," Journal of Informetrics, Elsevier, vol. 10(1), pages 183-199.
    9. Gonzalez-Diaz, J. & Hendrickx, R.L.P. & Lohmann, E.R.M.A., 2011. "Paired Comparisons Analysis : An Axiomatic Approach to Rankings in Tournaments," Discussion Paper 2011-116, Tilburg University, Center for Economic Research.
    10. Subochev, Andrey & Aleskerov, Fuad & Pislyakov, Vladimir, 2018. "Ranking journals using social choice theory methods: A novel approach in bibliometrics," Journal of Informetrics, Elsevier, vol. 12(2), pages 416-429.
    11. Christian Saile & Warut Suksompong, 2020. "Robust bounds on choosing from large tournaments," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 54(1), pages 87-110, January.

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