A branch and bound algorithm for maximum likelihood paired comparison ranking

Abstract

SUMMARY A very simple algorithm for obtaining maximum likelihood rankings of k objects which have been compared pairwise is presented. After some preliminary calculations, only addition and subtraction are required so that it is possible to rank as many as ten objects using only a desk calculator. This is not practical with the linear programming algorithm proposed in an earlier paper, deCani (1969), where ranking ten objects requires the solution of a linear program with 120 constraints in 165 variables in addition to upper bound constraints. The algorithm proposed here is one of a class of algorithms called branch and bound algorithms.