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Biometrika 1969 56(3):537-545; doi:10.1093/biomet/56.3.537
© 1969 by Biometrika Trust
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Maximum likelihood paired comparison ranking by linear programming

JOHN S. DECANI

University of Pennsylvania and Naval Air Development Center Johnsville, Pennsylvania

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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