α-Rank: Unified Item-Fair Ranking from A Cooperative Game Theory View

TL;DR — We introduced the α-rank framework, utilizing Optimal Transport (OT), to optimize a smooth fairness objective for effectively balancing various item fairness concepts.

Abstract

Driven by economic and systematic considerations, the pursuit of item fairness in ranking has emerged as a prominent topic in recommendation and advertising applications. Prior research has suggested various fairness aspects can be aligned with the concept of distributive justice in sociology, such as utilitarianism, dealism, and egalitarianism. However, they fail to distinguish the distinctions and relationships among these fairness dimensions in ranking. In fact, item fairness can be viewed as a unified challenge of fairly allocating the constrained and fluctuating resources, from the perspective of cooperative game theory. In our work, we introduce the smooth α-fairness objective for different fairness and unify item fairness as a cooperative game problem. In such games, items are considered as the players dividing the cake of user attention. In such games, we analyze the α-fairness objective from a theoretical way and introduce an efficient approach called α-rank. Firstly, we re-form several important axioms in cooperative games to tell us how item fairness principles exhibit when the resource ``cake'' changes in ranking. Then we designed α-rank, which applies the optimal transport to conduct item fairness. Theoretical analysis provides an upper bound, showcasing the maximum total utility loss across different fairness degrees. we conducted experiments in two ranking applications: recommendation and advertising. The experimental results demonstrate that α-rank effectively and efficiently outperforms the baseline methods.