Understanding Accuracy-Fairness Trade-offs in Re-ranking through Elasticity in Economics

TL;DR

This paper reframes the fairness-accuracy trade-off in re-ranking as a commodity tax transfer problem, using elasticity theory to analyze how fairness constraints influence user utility and item-group utilities. It introduces the EF-Curve as a comprehensive evaluation framework and ElasticRank as a fairness-aware re-ranking algorithm that adjusts inter-group distances in a curved, elasticity-informed space. Empirical results on three large ranking datasets show ElasticRank consistently improves fairness (EF) while maintaining near-stateful accuracy (NDCG) and running with the efficiency of standard sorting. The work provides a principled lens to compare fair-re-ranking methods across different elasticity regimes and offers practical guidance for deploying fair algorithms in real systems.

Abstract

Fairness is an increasingly important factor in re-ranking tasks. Prior work has identified a trade-off between ranking accuracy and item fairness. However, the underlying mechanisms are still not fully understood. An analogy can be drawn between re-ranking and the dynamics of economic transactions. The accuracy-fairness trade-off parallels the coupling of the commodity tax transfer process. Fairness considerations in re-ranking, similar to a commodity tax on suppliers, ultimately translate into a cost passed on to consumers. Analogously, item-side fairness constraints result in a decline in user-side accuracy. In economics, the extent to which commodity tax on the supplier (item fairness) transfers to commodity tax on users (accuracy loss) is formalized using the notion of elasticity. The re-ranking fairness-accuracy trade-off is similarly governed by the elasticity of utility between item groups. This insight underscores the limitations of current fair re-ranking evaluations, which often rely solely on a single fairness metric, hindering comprehensive assessment of fair re-ranking algorithms. Centered around the concept of elasticity, this work presents two significant contributions. We introduce the Elastic Fairness Curve (EF-Curve) as an evaluation framework. This framework enables a comparative analysis of algorithm performance across different elasticity levels, facilitating the selection of the most suitable approach. Furthermore, we propose ElasticRank, a fair re-ranking algorithm that employs elasticity calculations to adjust inter-item distances within a curved space. Experiments on three widely used ranking datasets demonstrate its effectiveness and efficiency.

Figures (7)

• Figure 1: Parallels between (a) the commodity tax transfer process and (b) the accuracy-fairness trade-off in re-ranking.
• Figure 2: (a) The EF-Curve, where the x-axis is tax base $t$ and the y-axis is the fairness metric $f(\bm{v};t)$. EF-Curve describes the restrict/support degree for different item groups. (b) The specific fairness metrics corresponding to particular $t$ values.
• Figure 3: (a) The Elasticity curve when optimizing Jain's index and objective without fairness constraint. (b) Illustration of how the commodity tax (item fairness) is being transferred to users (accuracy loss).
• Figure 4: Pareto frontier with different size $K$ under Steam.
• Figure 5: EF-Curve for different models with cut-off size $K=10$ under Steam.

Theorems & Definitions (3)

• Theorem 1
• Theorem 2
• Theorem 3