  The Bradley-Terry model assigns probabilities for the outcome of paired
comparison experiments based on strength parameters associated with the objects
being compared. We consider different proposed choices of prior parameter
distributions for Bayesian inference of the strength parameters based on the
paired comparison results. We evaluate them according to four desiderata
motivated by the use of inferred Bradley-Terry parameters to rate teams on the
basis of outcomes of a set of games: invariance under interchange of teams,
invariance under interchange of winning and losing, normalizability and
invariance under elimination of teams. We consider various proposals which fail
to satisfy one or more of these desiderata, and illustrate two proposals which
satisfy them. Both are one-parameter independent distributions for the
logarithms of the team strengths: 1) Gaussian and 2) Type III generalized
logistic.
