A bayesian approach to paired comparison experimentation

We have formulated a Bayesian approach to paired comparison experimentation under the multi-binomial and Bradley-Terry models and have provided two estimators of the model parameters (assuming a natural conjugate prior distribution) for each model. Furthermore, in the Bradley-Terry case, if the experimental design and prior distribution satisfy the criterion of posterior balance, then for a large class of acceptable loss functions, a Bayes ranking of the worth parameters is explicitly calculated and shown to coincide with the ranking determined by each of the two estimators. Thus, if the objective is ranking the worth parameters by their estimates, which are not easily calculated, one can easily calculate the Bayes ranking with the assurance that it agrees with the ranking provided by these estimates