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An extension of Zermelo's model for ranking by paired comparisons

Published online by Cambridge University Press:  01 June 2000

G. R. CONNER  and
C. P. GRANT
G. R. CONNER
Affiliation:
Department of Mathematics, Brigham Young University, Provo, UT 84602, USA. Email: conner@math.byu.edu, grant@math.byu.edu
C. P. GRANT
Affiliation:
Department of Mathematics, Brigham Young University, Provo, UT 84602, USA. Email: conner@math.byu.edu, grant@math.byu.edu
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Abstract

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.

Type
Research Article
Information
European Journal of Applied Mathematics , Volume 11 , Issue 3 , June 2000 , pp. 225 - 247
Copyright
2000 Cambridge University Press

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