Methods of ranking nodes in directed graphs by excellence, importance, or other values have become integral to modern processes of social learning. For the case that each directed edge (u,v) signifies a preference for ranking v over u, there are many natural examples: ranking products and services from pairwise consumer preferences, ranking educational institutions based on pairwise comparisons, ranking web content from pairwise judgments of relevance, ranking sports teams based on pairwise wins and losses, ranking political candidates given pairwise voter preferences, and so on. In this talk, I will present a new mathematical approach for obtaining such a ranking.
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