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A Taxation Perspective for Fair Re-ranking

Chen Xu, Xiaopeng Ye, Wenjie Wang, Liang Pang, Jun Xu, Tat-Seng Chua

TL;DR

This work reframes fair re-ranking as a taxation problem to better manage the fairness-accuracy trade-off. It identifies limitations of prior item-level tax policies, notably lack of continuity and controllability, and introduces Tax-rank, a continuous, tunable objective that taxes utility differences between items and optimizes via Sinkhorn-based optimal transport. Theoretical analysis establishes continuity and a bounded price of taxation, while experiments on Yelp and Ipinyou demonstrate that Tax-rank achieves superior Pareto fronts for fairness (Gini@K) and utility (eCN@K/eCPM@K) with efficient inference. The approach offers a principled, scalable mechanism for fair re-ranking applicable to recommendation and advertising tasks, enabling dynamic adjustment of fairness through a single tax-rate parameter $t$.

Abstract

Fair re-ranking aims to redistribute ranking slots among items more equitably to ensure responsibility and ethics. The exploration of redistribution problems has a long history in economics, offering valuable insights for conceptualizing fair re-ranking as a taxation process. Such a formulation provides us with a fresh perspective to re-examine fair re-ranking and inspire the development of new methods. From a taxation perspective, we theoretically demonstrate that most previous fair re-ranking methods can be reformulated as an item-level tax policy. Ideally, a good tax policy should be effective and conveniently controllable to adjust ranking resources. However, both empirical and theoretical analyses indicate that the previous item-level tax policy cannot meet two ideal controllable requirements: (1) continuity, ensuring minor changes in tax rates result in small accuracy and fairness shifts; (2) controllability over accuracy loss, ensuring precise estimation of the accuracy loss under a specific tax rate. To overcome these challenges, we introduce a new fair re-ranking method named Tax-rank, which levies taxes based on the difference in utility between two items. Then, we efficiently optimize such an objective by utilizing the Sinkhorn algorithm in optimal transport. Upon a comprehensive analysis, Our model Tax-rank offers a superior tax policy for fair re-ranking, theoretically demonstrating both continuity and controllability over accuracy loss. Experimental results show that Tax-rank outperforms all state-of-the-art baselines in terms of effectiveness and efficiency on recommendation and advertising tasks.

A Taxation Perspective for Fair Re-ranking

TL;DR

This work reframes fair re-ranking as a taxation problem to better manage the fairness-accuracy trade-off. It identifies limitations of prior item-level tax policies, notably lack of continuity and controllability, and introduces Tax-rank, a continuous, tunable objective that taxes utility differences between items and optimizes via Sinkhorn-based optimal transport. Theoretical analysis establishes continuity and a bounded price of taxation, while experiments on Yelp and Ipinyou demonstrate that Tax-rank achieves superior Pareto fronts for fairness (Gini@K) and utility (eCN@K/eCPM@K) with efficient inference. The approach offers a principled, scalable mechanism for fair re-ranking applicable to recommendation and advertising tasks, enabling dynamic adjustment of fairness through a single tax-rate parameter .

Abstract

Fair re-ranking aims to redistribute ranking slots among items more equitably to ensure responsibility and ethics. The exploration of redistribution problems has a long history in economics, offering valuable insights for conceptualizing fair re-ranking as a taxation process. Such a formulation provides us with a fresh perspective to re-examine fair re-ranking and inspire the development of new methods. From a taxation perspective, we theoretically demonstrate that most previous fair re-ranking methods can be reformulated as an item-level tax policy. Ideally, a good tax policy should be effective and conveniently controllable to adjust ranking resources. However, both empirical and theoretical analyses indicate that the previous item-level tax policy cannot meet two ideal controllable requirements: (1) continuity, ensuring minor changes in tax rates result in small accuracy and fairness shifts; (2) controllability over accuracy loss, ensuring precise estimation of the accuracy loss under a specific tax rate. To overcome these challenges, we introduce a new fair re-ranking method named Tax-rank, which levies taxes based on the difference in utility between two items. Then, we efficiently optimize such an objective by utilizing the Sinkhorn algorithm in optimal transport. Upon a comprehensive analysis, Our model Tax-rank offers a superior tax policy for fair re-ranking, theoretically demonstrating both continuity and controllability over accuracy loss. Experimental results show that Tax-rank outperforms all state-of-the-art baselines in terms of effectiveness and efficiency on recommendation and advertising tasks.
Paper Structure (31 sections, 5 theorems, 15 equations, 8 figures, 1 algorithm)

This paper contains 31 sections, 5 theorems, 15 equations, 8 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Work
  3. Problem Formulation
  4. Taxation Perspective for Fair Re-ranking
  5. Fair Re-ranking as Tax Policy
  6. Re-examine Fair Re-ranking
  7. Non-continuity.
  8. Non-controllability over accuracy loss.
  9. Insights from Taxation Perspective
  10. Tax-rank
  11. Optimization Objective
  12. Optimization Objective Analysis
  13. Geometric explanation for our taxation process
  14. Controllable requirements
  15. Algorithm
  16. ...and 16 more sections

Key Result

Theorem 1

Then optimal fair re-ranking result $\bm{x}(\lambda)$ with specific tax rate $\lambda$ can be achieved as: where $s_{u,i} = \gamma_i w_{u,i} + \bm{\mu}_i,$ and In simpler terms, the ranking score is like the original score $\gamma_i w_{u,i}$ but with the addition of item-level taxation $\bm{\mu}_i$ with the tax rate of $\lambda\in[0,\infty]$. The tax rate $\lambda$ is calculated as where $c_{u,

Figures (8)

  • Figure 1: Sub-figure (a) illustrates that fair re-ranking can be viewed as a taxation process from an economic perspective. Sub-figure (b) illustrates that our taxation process exhibits better continuity compared to previous ones.
  • Figure 2: Geometric explanation for our taxation process, which imposes taxes based on the disparity in utility between two items.
  • Figure 3: Pareto frontier with different top-K ranking under CTR-based settings (i.e., $w_{u,i}$ is the CTR value of user-item pair).
  • Figure 4: Pareto frontier with different top-K ranking under exposure-based settings (i.e., $w_{u,i}=1$).
  • Figure 5: Lorenz Curve Lorenzcurve of three best-performing baselines FairRec, P-MMF and Welf and our model Tax-rank. The distinct curves in each figure are plotted by adjusting various tax rates $t$ or different parameters.
  • ...and 3 more figures

Theorems & Definitions (5)

  • Theorem 1
  • Theorem 2
  • Theorem 3
  • Lemma 1
  • Lemma 2