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Ranking participants in tournaments by means of rating functions

Author

Listed:
  • Brozos-Vázquez, Miguel
  • Campo-Cabana, Marco Antonio
  • Díaz-Ramos, José Carlos
  • González-Díaz, Julio

Abstract

In this paper we bring a novel approach to the theory of tournament rankings. We combine two different theories that are widely used to establish rankings of populations after a given tournament. First, we use the statistical approach of paired comparison analysis to define the performance of a player in a natural way. Then, we determine a ranking (and rating) of the players in the given tournament. Finally, we show, among other properties, that the new ranking method is the unique one satisfying a natural consistency requirement.

Suggested Citation

  • Brozos-Vázquez, Miguel & Campo-Cabana, Marco Antonio & Díaz-Ramos, José Carlos & González-Díaz, Julio, 2008. "Ranking participants in tournaments by means of rating functions," Journal of Mathematical Economics, Elsevier, vol. 44(11), pages 1246-1256, December.
    • Handle: RePEc:eee:mateco:v:44:y:2008:i:11:p:1246-1256
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    References listed on IDEAS

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    1. AMIR, Rabah, 2002. "Impact-adjusted citations as a measure of journal quality," LIDAM Discussion Papers CORE 2002074, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. Iqbal Ali & Wade D. Cook & Moshe Kress, 1986. "On the Minimum Violations Ranking of a Tournament," Management Science, INFORMS, vol. 32(6), pages 660-672, June.
    3. Ignacio Palacios-Huerta & Oscar Volij, 2004. "The Measurement of Intellectual Influence," Econometrica, Econometric Society, vol. 72(3), pages 963-977, May.
    4. Michael Stob, 1985. "Note---Rankings from Round-Robin Tournaments," Management Science, INFORMS, vol. 31(9), pages 1191-1195, September.
    5. Giora Slutzki & Oscar Volij, 2005. "Ranking participants in generalized tournaments," International Journal of Game Theory, Springer;Game Theory Society, vol. 33(2), pages 255-270, June.
    6. Stephen T. Goddard, 1983. "Ranking in Tournaments and Group Decisionmaking," Management Science, INFORMS, vol. 29(12), pages 1384-1392, December.
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    Cited by:

    1. Mehmet Mars Seven, 2024. "Performance Rating Equilibrium," Papers 2410.19006, arXiv.org, revised Nov 2025.
    2. 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.
    3. 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.
    4. 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.
    5. 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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