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The paper aims at analyzing the least squares ranking method for generalizedtournaments with possible missing and multiple paired comparisons. Thebilateral relationships may reflect the outcomes of a sport competition,product comparisons, or evaluation of political candidates and policies. It isshown that the rating vector can be obtained as a limit point of an iterativeprocess based on the scores in almost all cases. The calculation is interpretedon an undirected graph with loops attached to some nodes, revealing that theprocedure takes into account not only the given object's results but also thestrength of objects compared with it. We explore the connection between thismethod and another procedure defined for ranking the nodes in a digraph, thepositional power measure. The decomposition of the least squares solutionoffers a number of ways to modify the method.

A graph interpretation of the least squares ranking method