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In two-player competitions,let pij denote the probability that player i defeats player j.Suppose that p,j + Pji =1 for all pairs; that is,a tie cannot occur.Bradley-Terry (1952) proposed the model pij=δ,=(δ,+ δj).There are several ways to obtain this model.Lehmann (1953) considered distributional models for alternative hypotheses which were themselves distribution free in a sense and parameter-dependent.