A Bayesian approach to paired comparison rankings based on a graphical model

A Bayesian method for finding an optimal ranking in scalar functions of K population parameters is developed. This is based on the paired comparison experimental arrangement whose results can naturally be represented by a completely oriented graphical model. Introducing posterior preference probabilities satisfying a strong stochastic transitivity condition to the model, a criterion for the optimal ranking is suggested. Necessary theories involved in the method and some computational aspects are provided. As illustrated examples, ranking in generalized variances of K multivariate normal populations and in products of independent normal means are given.