Zermelo, paired comparisons, ranking
In 1929, Zermelo proposed a probabilistic model for ranking by paired comparisons and showed that this model produces a unique ranking of the objects under consideration when the outcome matrix is irreducible. When the matrix is reducible, the model may yield only a partial ordering of the objects. In this paper, we analyse a natural extension of Zermelo's model resulting from a singular perturbation. We show that this extension produces a ranking for arbitrary (nonnegative) outcome matrices and retains several of the desirable properties of the original model. In addition, we discuss computational techniques and provide examples of their use.
Original Publication Citation
European Journal of Applied Mathematics, 11(2), pp 225-247.
BYU ScholarsArchive Citation
Grant, Christopher P. and Conner, Gregory R., "An Extension of Zermelo's Model for Ranking by Paired Comparisons" (2000). Faculty Publications. 605.
Cambridge University Press, http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=47589
Physical and Mathematical Sciences
© 2000 Cambridge University Press.
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