Ranking via Arrow-Debreu Equilibrium

Abstract

In this paper, we establish a connection between ranking theory and general equilibrium theory. First of all, we show that the ranking vector of PageRank or Invariant method is precisely the equilibrium of a special Cobb-Douglas market. This gives a natural economic interpretation for the PageRank or Invariant method. Furthermore, we propose a new ranking method, the CES ranking, which is minimally fair, strictly monotone and invariant to reference intensity, but not uniform or weakly additive.