CPSC 532L Project Development and Axiomatization of a Ranking System

Ranking systems are central to many internet applications including, notably, Google’s PageRank algorithm for ranking web pages. Ranking systems are a special case of a social choice problem in which the set of agents and the set of outcomes coincide. In this paper we consider PageRank as a particular ranking system and we present two axiomatizations that allow PageRank to be studied from a social choice perspective. The first axiomatization is normative and leads to the theory that no ranking system can simultaneously satisfy two desirable properties. Despite this discouraging result, PageRank is nonetheless highly successful and the second, descriptive, axiomatization characterizes PageRank uniquely among ranking systems. We conclude by suggesting areas for further research, including axioms describing vulnerability to manipulation and preferences submitted directly by human users.