BAYESIAN-ANALYSIS OF CONSISTENT PAIRED COMPARISONS

A general Bayesian model for paired comparisons is formulated and applied in some special cases, in which the comparisons are assumed to be consistent. Further, a class of expert models having interesting properties connected with the calibration and bias of the expert and the independence of irrelevant variables is constructed. The asymptotic behaviour of the two-dimensional model is studied: it is observed that the posterior variance cannot be made arbitrarily small by increasing the number of experts. In addition to exactly stated expert models, the case with unknown parameters is also described. The use of models is illustrated with numerical examples, where the posterior distributions are generated by a sampling procedure.