Ranking via Arrow-Debreu Equilibrium

TL;DR

This paper links ranking algorithms like PageRank to economic market equilibria, introduces a new CES ranking method with desirable fairness and monotonicity properties, and provides an economic interpretation of existing ranking methods.

Contribution

It establishes a novel connection between ranking theory and equilibrium market models, and proposes a new ranking method with specific fairness and invariance features.

Findings

PageRank corresponds to a Cobb-Douglas market equilibrium

Introduces CES ranking with minimal fairness and strict monotonicity

CES ranking is invariant to reference intensity

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.