Remark. Representability, non-identifiability, and heterogeneous preferences [ftip-002S]
Remark. Representability, non-identifiability, and heterogeneous preferences [ftip-002S]
Fitting a Bradley--Terry predictor is an assumption about representation, not a consequence of observing comparisons. Cyclic choices, context effects, and mixtures of judges can fail to agree with one shared scalar ordering.
Even within the model, scores are not identified absolutely: replacing \(r_\phi (x,y)\) by \(r_\phi (x,y)+c(x)\) leaves every pairwise probability and the loss unchanged. Ouyang et al. give one normalization in [ouyang2022training, §3.5; App. C.2]. Other uses must state their own normalization, judge population, and validation law.