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Fairness in Ranking under Disparate Uncertainty

Richa Rastogi, Thorsten Joachims

TL;DR

Equal-Opportunity Ranking (EOR) is proposed as a new fairness criterion for ranking and it is shown that it corresponds to a group-wise fair lottery among the relevant options even in the presence of disparate uncertainty.

Abstract

Ranking is a ubiquitous method for focusing the attention of human evaluators on a manageable subset of options. Its use as part of human decision-making processes ranges from surfacing potentially relevant products on an e-commerce site to prioritizing college applications for human review. While ranking can make human evaluation more effective by focusing attention on the most promising options, we argue that it can introduce unfairness if the uncertainty of the underlying relevance model differs between groups of options. Unfortunately, such disparity in uncertainty appears widespread, often to the detriment of minority groups for which relevance estimates can have higher uncertainty due to a lack of data or appropriate features. To address this fairness issue, we propose Equal-Opportunity Ranking (EOR) as a new fairness criterion for ranking and show that it corresponds to a group-wise fair lottery among the relevant options even in the presence of disparate uncertainty. EOR optimizes for an even cost burden on all groups, unlike the conventional Probability Ranking Principle, and is fundamentally different from existing notions of fairness in rankings, such as demographic parity and proportional Rooney rule constraints that are motivated by proportional representation relative to group size. To make EOR ranking practical, we present an efficient algorithm for computing it in time $O(n \log(n))$ and prove its close approximation guarantee to the globally optimal solution. In a comprehensive empirical evaluation on synthetic data, a US Census dataset, and a real-world audit of Amazon search queries, we find that the algorithm reliably guarantees EOR fairness while providing effective rankings.

Fairness in Ranking under Disparate Uncertainty

TL;DR

Equal-Opportunity Ranking (EOR) is proposed as a new fairness criterion for ranking and it is shown that it corresponds to a group-wise fair lottery among the relevant options even in the presence of disparate uncertainty.

Abstract

Ranking is a ubiquitous method for focusing the attention of human evaluators on a manageable subset of options. Its use as part of human decision-making processes ranges from surfacing potentially relevant products on an e-commerce site to prioritizing college applications for human review. While ranking can make human evaluation more effective by focusing attention on the most promising options, we argue that it can introduce unfairness if the uncertainty of the underlying relevance model differs between groups of options. Unfortunately, such disparity in uncertainty appears widespread, often to the detriment of minority groups for which relevance estimates can have higher uncertainty due to a lack of data or appropriate features. To address this fairness issue, we propose Equal-Opportunity Ranking (EOR) as a new fairness criterion for ranking and show that it corresponds to a group-wise fair lottery among the relevant options even in the presence of disparate uncertainty. EOR optimizes for an even cost burden on all groups, unlike the conventional Probability Ranking Principle, and is fundamentally different from existing notions of fairness in rankings, such as demographic parity and proportional Rooney rule constraints that are motivated by proportional representation relative to group size. To make EOR ranking practical, we present an efficient algorithm for computing it in time and prove its close approximation guarantee to the globally optimal solution. In a comprehensive empirical evaluation on synthetic data, a US Census dataset, and a real-world audit of Amazon search queries, we find that the algorithm reliably guarantees EOR fairness while providing effective rankings.
Paper Structure (41 sections, 11 theorems, 27 equations, 14 figures, 1 table, 1 algorithm)

This paper contains 41 sections, 11 theorems, 27 equations, 14 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Works
  3. Un-fairness due to Disparate Uncertainty in Rankings
  4. Illustrative Example
  5. Sources of Disparate Uncertainty
  6. Equality of Opportunity in Ranking
  7. Cost Burden to Candidate Groups and the Principal
  8. Equality of Opportunity Ranking (EOR) Criterion
  9. Computing EOR-Fair Rankings
  10. Extension to $G$ Groups
  11. Experimental Evaluation
  12. Synthetic Data
  13. How does $\pi^{EOR}$ compare against the baselines under varying amounts of disparate uncertainty?
  14. At which positions in the rankings do the policies incur unfairness?
  15. How do the ranking policies distribute the costs between the stakeholders?
  16. ...and 26 more sections

Key Result

Theorem 5.1

The EOR fair ranking $\sigma^{EOR}$ produced by Algorithm alg:EOR_alg is at least $\phi\delta(\sigma^{EOR}_k)$ cost optimal for any prefix $k$, where $\phi = \frac{2}{nRel(A)+nRel(B)}\left| \frac{p_{A}-p_{B} }{q_{A}+q_{B}}\right|$, $q_{A}=\frac{p_{A}}{nRel(A)}$, and $q_{B}=\frac{p_{B}}{nRel(B)}$. Fu

Figures (14)

  • Figure 1: The expected probability of relevance $p_i$ and their true relevance $r_i$ for all candidates in both groups.
  • Figure 2: Top-4 ranking for Probability Ranking Principle (PRP), Demographic Parity (DP), and our proposed EOR for the example in \ref{['fig:expected_probs']}. Selected relevant number of candidates in expectation and total relevant number of candidates in expectation are shown corresponding to each ranking.
  • Figure 3: An illustration of disparate uncertainty between groups from a Bayesian perspective for all the candidates of \ref{['fig:expected_probs']}. The candidates in group A have peaky posteriors, while those in group B have relatively flat posteriors.
  • Figure 4: Left: EOR criterion $\delta(\sigma_k)$, Middle: group costs according to \ref{['eq:subgroup_cost']}, Right: the principal's total cost according to \ref{['eq:total_cost']} of the ranking policies for the synthetic dataset with high disparate uncertainty shown in top right of \ref{['tab:vary_disp_unc']}. Group A consists of 30 candidates with sharp probabilities with $p_i \sim \text{Beta}(1/20, 1/20)$. This provides $nRel(A)=14.96$ expected number of relevant candidates. Group B also has similar candidates, in particular, it has 31 candidates, with relatively flat probabilities $p_i \sim \text{Beta}(5,5)$, providing $nRel(B)=14.94$ expected number of relevant candidates.
  • Figure 5: US Census Dataset: EOR criterion $\delta(\sigma_k)$ and cost of the ranking policies computed with true relevance labels from the test subset for the US Census dataset. Top: Two groups setting using the White and Black/African American racial groups for the state of Alabama. Bottom: Multiple (four groups) setting using White, Black/African American, Asian, and Other for the state of NY.
  • ...and 9 more figures

Theorems & Definitions (12)

  • Definition 4.1: $\delta$-EOR Fair Ranking
  • Theorem 5.1: Cost Approximation Guarantee at $k$
  • Theorem 5.2: Global Cost and Fairness Guarantee
  • Proposition 5.1: Costs from EOR vs. Uniform Policy
  • Theorem 6.1: Global Cost and Fairness Guarantee for multiple groups
  • Lemma 5.1
  • Lemma 5.2
  • Lemma 5.3
  • Lemma 6.1
  • Lemma 6.2
  • ...and 2 more