Solution of a Ranking Problem from Binary Comparisons

By L. R. Ford. 1957

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Generalized Results for the Existence and Consistency of the MLE in the Bradley-Terry-Luce Model (2021, background): “As proved by Zermelo (1929) and Ford Jr (1957), this is indeed sufficient and necessary for a unique solution.”
Contest functions : theoretical foundations and issues in estimation (2013, methodology): “The Ford condition eliminates these possibilities. Secondly, data sets of individualistic contests (such as tennis, golf, and boxing) are preferred to the ones on team competitions (such as soccer, football, and basketball). In contests among teams, the players act as agents on behalf of the teamwh”
Fast and Accurate Inference of Plackett-Luce Models (2015, methodology): “In the special case of pairwise comparisons, the same iterative algorithm was independently discovered by Zermelo [15], Ford [16] and Dykstra [17].”
Iterative ranking from pair-wise comparisons (2012, methodology): “The ML estimator directly maximizes the likelihood assuming the BTL model [18].”
MM algorithms for generalized Bradley-Terry models (2003, methodology): “The following assumption (Ford, 1957) eliminates these possibilities.”