Deriving priorities from the Bradley-Terry model

This paper is concerned with the estimation of priorities for n≥ 2 items with respect to a single criterion in the context of the Analytic Hierarchy Process. Following the work of Saaty [1,2], extraction of priority weights has traditionally been based on the normalized eigenvector corresponding to the largest eigenvalue of a reciprocal matrix whose entries are the paired comparisons between the items, expressed on a ratio scale. An alternative, maximum likelihood procedure is presented, proceeding from an interpretation of each paired judgment as a win-to-loss ratio resulting from an instantaneous mental confrontation of the items at hand. The properties of this prioritization technique are presented, and comparisons are made with Saatyʹs scaling method and the logarithmic least squares solution to this problem.