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Paired Comparisons Analysis: An Axiomatic Approach to Rankings in Tournaments

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  • Gonzalez-Diaz, J.
  • Hendrickx, R.L.P.
  • Lohmann, E.R.M.A.

    (Tilburg University, Center for Economic Research)

Abstract

In this paper we present an axiomatic analysis of several ranking methods for tournaments. We find that two of them exhibit a very good behaviour with respect to the set of properties under consideration. One of them is the maximum likelihood ranking, the most common method in statistics and psychology. The other one is a new ranking method introduced in this paper: recursive Buchholz. One of the most widely studied methods in social choice, the fair bets ranking, also performs quite well, but fails to satisfy some arguably important properties.

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Bibliographic Info

Paper provided by Tilburg University, Center for Economic Research in its series Discussion Paper with number 2011-116.

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Date of creation: 2011
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Handle: RePEc:dgr:kubcen:2011116

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Web page: http://center.uvt.nl

Related research

Keywords: Tournament; ranking; paired comparisons; fair bets; maximum likelihood;

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  1. Ignacio Palacios-Huerta & Oscar Volij, 2002. "The Measurement of Intellectual Influence," Economic theory and game theory 015, Oscar Volij.
  2. Borm, Peter & Fiestras-Janeiro, Gloria & Hamers, Herbert & Sanchez, Estela & Voorneveld, Mark, 2002. "On the convexity of games corresponding to sequencing situations with due dates," European Journal of Operational Research, Elsevier, vol. 136(3), pages 616-634, February.
  3. Giora Slutzki & Oscar Volij, 2005. "Ranking participants in generalized tournaments," International Journal of Game Theory, Springer, vol. 33(2), pages 255-270, 06.
  4. Bhaskar Dutta & Jean-Francois Laslier, 1999. "Comparison functions and choice correspondences," Social Choice and Welfare, Springer, vol. 16(4), pages 513-532.
  5. 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.
  6. P. Herings & Gerard Laan & Dolf Talman, 2005. "The positional power of nodes in digraphs," Social Choice and Welfare, Springer, vol. 24(3), pages 439-454, 06.
  7. Denis Bouyssou, 2004. "Monotonicity of ‘ranking by choosing’: A progress report," Social Choice and Welfare, Springer, vol. 23(2), pages 249-273, October.
  8. Marco Slikker & Peter Borm & René Brink, 2012. "Internal slackening scoring methods," Theory and Decision, Springer, vol. 72(4), pages 445-462, April.
  9. Liebowitz, S J & Palmer, J P, 1984. "Assessing the Relative Impacts of Economic Journals," Journal of Economic Literature, American Economic Association, vol. 22(1), pages 77-88, March.
  10. Giora Slutzki & Oscar Volij, 2006. "Scoring of web pages and tournaments—axiomatizations," Social Choice and Welfare, Springer, vol. 26(1), pages 75-92, January.
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