Abstract
A criterion is presented for the best ranking of items or individuals who have been compared in pairs in an unbalanced fashion. The criterion is to choose the ranking or rankings that minimize the sum over all contestants of the absolute differences between the number of net wins over players ranked above and the number of net losses to players ranked below. A method for reaching the minimum is presented. There are two variations of the criterion. They are illustrated on a small set of 1989 tennis player data.
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References
E. L. Crow. Ranking paired contestants. Commun. Statist. Simula., 19:749–769, 1990.
H.A. David. Ranking from unbalanced paired comparison data. Biometrika, 74:432–436, 1987.
H. A. David. The Method of Paired Comparisons, 2nd ed., Oxford University Press, New York, 1988.
P. Slater. Inconsistencies in a schedule of paired comparisons. Biometrika, 48:303–312, 1961.
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© 1993 Springer-Verlag New York, Inc.
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Crow, E.L. (1993). Ranking From Paired Comparisons by Minimizing Inconsistency. In: Fligner, M.A., Verducci, J.S. (eds) Probability Models and Statistical Analyses for Ranking Data. Lecture Notes in Statistics, vol 80. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-2738-0_16
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DOI: https://doi.org/10.1007/978-1-4612-2738-0_16
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-97920-5
Online ISBN: 978-1-4612-2738-0
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