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Maximum Likelihood Paired Comparison Ranking by Linear Programming

John S. deCani
Biometrika
Vol. 56, No. 3 (Dec., 1969), pp. 537-545
Published by: Oxford University Press on behalf of Biometrika Trust
DOI: 10.2307/2334661
Stable URL: http://www.jstor.org/stable/2334661
Page Count: 9
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Maximum Likelihood Paired Comparison Ranking by Linear Programming
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Abstract

The problem of ranking n objects from `best' to `worst', using the results of a paired comparison experiment, is formulated as a linear programming problem with the logarithm of the likelihood as the objective function. The constraints are determined by the transitivity relationships implied in a ranking. The linear program will determine maximum likelihood rankings for the k fold replicated paired comparison experiment with or without the possibility of ties. The method is demonstrated with two examples from recent literature.

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