Source-linked AI summary
Equity of Attention: Amortizing Individual Fairness in Rankings
Asia J. Biega, Krishna P. Gummadi, Gerhard Weikum
TL;DR
Rankings can distribute attention unfairly because position bias gives lower-ranked subjects less exposure, affecting opportunities and resources. This paper defines individual equity-of-attention measures and amortizes fairness across consecutive rankings through constrained online optimization, finding substantial attention discrepancies while preserving high ranking quality.
Problem
Position bias can make received attention disproportionate to individual relevance, potentially distorting opportunities and resources in ranked platforms.
Method
The paper measures individual equity-of-attention and reorders subjects across consecutive rankings using an online integer linear program constrained by ranking-quality loss.
Results
Experiments with synthetic and real-world data show substantial discrepancies between received and deserved attention, while improving equity can often preserve high ranking quality.
Takeaways & Limitations
Amortizing attention fairness over time offers a way to improve individual fairness in rankings, especially where ranking exposure affects economic livelihood.
Takeaways & Limitations
The online ILP has a quadratic number of binary variables in the number of subjects, creating a scalability bottleneck for systems with millions of subjects.
Abstract
from arXiv · showhide
Rankings of people and items are at the heart of selection-making, match-making, and recommender systems, ranging from employment sites to sharing economy platforms. As ranking positions influence the amount of attention the ranked subjects receive, biases in rankings can lead to unfair distribution of opportunities and resources, such as jobs or income. This paper proposes new measures and mechanisms to quantify and mitigate unfairness from a bias inherent to all rankings, namely, the position bias, which leads to disproportionately less attention being paid to low-ranked subjects. Our approach differs from recent fair ranking approaches in two important ways. First, existing works measure unfairness at the level of subject groups while our measures capture unfairness at the level of individual subjects, and as such subsume group unfairness. Second, as no single ranking can achieve individual attention fairness, we propose a novel mechanism that achieves amortized fairness, where attention accumulated across a series of rankings is proportional to accumulated relevance. We formulate the challenge of achieving amortized individual fairness subject to constraints on ranking quality as an online optimization problem and show that it can be solved as an integer linear program. Our experimental evaluation reveals that unfair attention distribution in rankings can be substantial, and demonstrates that our method can improve individual fairness while retaining high ranking quality.
1 INTRODUCTION
Rankings distribute attention through position bias, potentially creating unfair economic outcomes for lower-ranked subjects. The paper introduces individual equity-of-attention measures and online amortization mechanisms that preserve ranking quality.
- Motivation and Problem: Position bias makes searchers pay most attention to top-ranked subjects, so lower-ranked subjects may receive less attention than their relevance warrants.Repeatedly displaying an unchanged ranking can systematically disadvantage lower-ranked subjects.
- Motivation and Problem: Ranking positions can translate into financial gains or losses on platforms such as LinkedIn, Uber, Amazon, and Spotify.The paper highlights possible economic starvation for lower-exposed drivers and reduced royalty opportunities for low-ranked artists.
- Problem Statement: A single ranking cannot generally make received attention approximately equal deserved attention while preserving relevance-based ranking quality.The paper therefore formulates fairness over a series of rankings rather than one ranking.
- Approach and Contribution: The paper formalizes individual equity-of-attention fairness by measuring discrepancies between subjects’ deserved and received attention.This individual-level formulation differs from prior group-based approaches and subsumes group fairness as a special case.
- Approach and Contribution: Online mechanisms amortize attention fairly over consecutive rankings, while an integer linear program permutes subjects subject to ranking-quality constraints.Filters prune the ILP’s combinatorial search space so the optimization can be solved in an online system.
- Approach and Contribution: Experiments with synthetic and real-world data investigate the proposed mechanisms’ properties and behavior.The contribution statement identifies experimental evaluation across both data types.
2 EQUITY-OF-ATTENTION FAIRNESS
Equity of attention treats relevance as the basis for deserved attention and seeks proportional allocation at the individual level. Because position bias prevents this in one ranking, the paper amortizes fairness across a sequence while distinguishing it from equality and group fairness.
- Defining Equity of Attention: Equity of attention requires each ranked subject to receive attention proportional to its relevance, using relevance as a proxy for task-specific worthiness.The notion is framed as individual fairness because relevance represents suitability for the ranking task.
- Defining Equity of Attention: Position bias makes exact equity of attention unlikely in a single ranking, especially when similarly relevant subjects cannot share one position.Relevance is determined by data and query, whereas views or clicks are strongly influenced by position.
- Amortized Attention: Equity of amortized attention distributes cumulative attention proportional to cumulative relevance across a sequence of rankings.A subject’s attention deficiency in one ranking can be compensated by placing it higher in a later ranking.
- Amortized Attention: The amortized definition permits reordering individual rankings so fairness requirements can be satisfied over time.The mechanism changes consecutive rankings rather than requiring every ranking to be individually fair.
- Alternative Fairness Objectives: Equality of attention is a separate fairness objective for settings where equal exposure is preferred regardless of relevance.The paper gives biased relevance estimates and non-query informational lists as examples of such settings.
- Relation to Prior Fairness Work: Individual equity of attention differs from prior group-based ranking approaches because position bias affects individuals independently of group membership.Prior diversification methods target one-time rankings and can accumulate equity-of-attention unfairness over time.
3 RANKINGS WITH EQUITY OF ATTENTION
The paper measures unfairness as the distance between cumulative attention and relevance, then reorders rankings online to reduce this discrepancy while constraining ranking-quality loss.
- Measuring (un)fairness: Unfairness is measured as the L1 distance between cumulative attention and relevance distributions across subjects.A value of 0 satisfies the paper’s fairness criterion, although the cumulative measure does not reveal how unfairness is distributed among individuals.
- Measuring ranking quality: Ranking quality is assessed by divergence from the original relevance-based ranking using NDCG, which emphasizes highly relevant subjects at top positions.NDCG is normalized against an ideal relevance-ordered ranking and equals 1 when rankings differ only through ties or not at all.
- Constrained optimization: The mechanism permutes each ranking to minimize cumulative unfairness while imposing per-ranking NDCG-quality constraints.An alternative formulation can constrain average quality loss across the sequence rather than loss in each individual ranking.
- Online amortization: In the online setting, the current ranking is reordered using attention and relevance accumulated from rankings seen so far, without future query information.The optimization updates cumulative values for each subject as the current ranking is processed.
- ILP formulation: The optimization is formulated as an ILP with n^2 binary assignment variables mapping subjects bijectively to ranking positions.The variables indicate whether subject ui is assigned to position j; constraints bound NDCG loss and enforce one-to-one assignments.
- Quality–fairness tradeoff: The quality threshold controls permissible reordering: θ = 1 allows only quality-preserving changes, while θ = 0 permits any permutation.At θ = 1, subjects may still be reordered within relevance ties to reduce unfairness.
- Limitations and extensions: The ILP has a quadratic number of binary variables, creating a scalability bottleneck for systems with millions of subjects.The paper identifies LP relaxations and greedy heuristics as directions for further research.
- Candidate filtering: Prefiltering selects reranking candidates using high relevance and attention deficits, but relevance-only or objective-only filtering can limit fairness gains or feasibility.The strategy includes the k most relevant subjects to help satisfy quality constraints while targeting subjects with the largest fair-share deficits.
4 EXPERIMENTS
The experiments use controlled synthetic relevance distributions and real-world rankings from Airbnb and StackExchange-derived workloads to evaluate amortized ranking fairness.
- Datasets: Three synthetic datasets contain 100 subjects each and use uniform, linear, or exponential relevance distributions.These distributions provide controlled settings for analyzing model behavior under different relevance shapes.
- Datasets: The real-world Airbnb datasets contain 3944 Boston, 1728 Geneva, and 4529 Hong Kong subjects.Rankings use apartment identifiers as subjects and review ratings as relevance scores.
- Datasets: Airbnb rankings represent a platform where exposure and attention can affect subjects’ financial success.The study uses freely available data from three cities in different parts of the world.
- Experimental settings: The evaluation compares single-query sequences, where one ranking repeats, with multi-query sequences, where rankings with different relevance distributions repeat.The multi-query Airbnb setup uses seven rating attributes to construct distinct rankings.
- Datasets: A StackExchange-derived dataset contains about 20K timestamp-ordered queries, with Indri retrieving 500 answers per query and answer authors treated as ranked subjects.The workload is built from a synthesized query log and document collection based on a public dump.
4.2 Position bias
The study models position bias through geometric and singular attention distributions, with attention weights determined by the application and potentially estimated from click data.
- Attention models: Attention-position weights depend on the platform and may be estimated from historical click data.The experiments instead study generic attention distributions.
- Geometric attention: The geometric model assigns geometrically distributed weights through position k and zero weight below k.It corresponds to a cascade model in which each subject has click probability p, while uninspected low-ranked subjects receive no attention.
- Singular attention: The singular model assigns all attention to the top-ranked subject.It is the geometric special case p = 1, k = 1 and reflects systems that show only top-1 matches by default.
- Scope: The attention weights are rescaled to sum to 1, while more complex attention models remain future work.The paper therefore evaluates position bias under a limited family of generic distributions.
4.3 Implementation and parameters
The implementation solves the amortization ILP with Gurobi, reranks prefiltered candidates, and evaluates singular and geometric attention under repeated ranking sequences.
- Implementation: The ILP is implemented with Gurobi, using a feasibility threshold of 1e-7 and 100 reranking candidates per iteration.Candidate prefiltering follows the strategy described for the online mechanism.
- Attention parameters: The singular model constrains NDCG-quality at k = 1, whereas the geometric model uses p = 0.5, k = 5 and constrains quality at k = 5.These settings align the quality constraint with the number of positions receiving modeled attention.
- Experimental parameters: Single-query experiments run for 20K iterations, while multi-query experiments repeat a seven-ranking sequence 3K times for 21K total rankings.The two modes measure amortization under repeated identical or varying rankings.
- Relevance normalization: Relevance scores are normalized into a distribution by linearly rescaling ratings, under the assumption that relevance directly proxies worthiness.Other transformations are possible when the platform has additional knowledge about relevance and worthiness.
4.4 Mechanisms under comparison
The evaluation compares relevance-only ranking, an objective-driven fairness heuristic, and the ILP-based online mechanism against Airbnb relevance distributions and position-biased attention.
- Mechanisms under comparison: The experiments compare the ILP-based online mechanism with relevance-only and objective-driven ranking heuristics.The relevance heuristic ignores fairness, while the objective heuristic targets strong fairness amortization without quality constraints.
- Mechanisms under comparison: The relevance distributions differ across Boston, Geneva, and Hong Kong Airbnb datasets, partly because Geneva assigns individuals a larger average fraction of total relevance.Boston and Hong Kong appear flatter because their datasets are larger.
- Mechanisms under comparison: The Geneva data exhibit a large discrepancy between relevance and geometric-model attention distributions across the top-10 positions.The geometric model uses p = 0.5, with weights based on empirical position-bias observations.
4.6 Performance on synthetic data
Synthetic-data experiments show that amortization can periodically eliminate unfairness, but attainable fairness depends on relevance ties, quality constraints, and the attention model.
- Uniform relevance: Amortization methods periodically reduce unfairness to 0 every n iterations for uniform relevance, with each subject occupying the top position once per cycle.Here, n is the number of subjects in the dataset.
- Linear relevance: With no relevance-score ties in the Linear dataset, fairness cannot improve without quality loss; ILP with θ < 0.8 nevertheless remains less unfair than the Relevance baseline.Methods with θ > 0 have higher unfairness than the Objective baseline.
- Exponential relevance: For exponentially decreasing relevance, the ILP cannot satisfy the quality constraint for any θ >= 0.5, making those rerankings equivalent to the Relevance heuristic.The quality constraint therefore prevents these settings from producing distinct ILP rerankings.
- Geometric attention model: Under the general geometric attention model, increasing the attention cut-off k smooths position weights and reduces the pronounced periodicity of unfairness.At k = 1, the model is equivalent to Singular.
- Geometric attention model: When relevance and attention distributions are nearly identical, the ILP reorders only occasionally, after lower-ranked subjects accumulate enough deserved attention.In the reported case, subjects below position 5 in the original ranking trigger reordering after accumulating deserved attention.
4.7 Performance on Airbnb data
On Airbnb data, amortizing methods generally reduce unfairness over repeated rankings, especially when relevance distributions vary or contain top ties, while quality loss remains bounded by the ILP threshold.
- Single-query, singular attention: The Relevance baseline’s unfairness increases linearly, whereas relaxing the quality constraint allows lower unfairness in corresponding iterations.
- Single-query, singular attention: The unconstrained Objective heuristic and ILP with θ = 0 amortize fairness without significant unfairness growth over time.
- Single-query, singular attention: Candidate prefiltering can cause unfairness to grow linearly when no filtered subject can move to the top without violating the quality constraint.
- Multi-query, singular attention: Multi-query Airbnb datasets achieve lower unfairness because varying relevance and ordering smooth deserved-attention distributions across iterations.More uniform rating attributes and top ties also let conservative constraints, including θ = 1, perform well.
- Geometric attention: Geometric attention improves performance partly because its distribution is closer to Airbnb relevance distributions and quality is constrained at a higher rank.
- Actual ranking quality: Actual NDCG-quality loss is often below the ILP threshold, with quality periodically returning to 1 when top-relevant subjects regain priority.
4.8 Performance on StackExchange data
On StackExchange, the method follows the same relative performance trends but needs a longer amortization timeframe because each subject appears in relatively few rankings.
- The StackExchange results preserve the method’s relative performance trends observed on the other datasets.
- A longer amortization timeframe is necessary because each subject occurs in relatively few rankings.Subjects need repeated appearances before the model can reposition them to distribute attention fairly.
5 RELATED WORK
Prior fairness-ranking work mainly addresses static group fairness, while this paper’s related context also draws on position-bias research and individual fairness formulations from adjacent settings.
- Fairness research in machine learning studies bias, discrimination, and unfair decisions, with much prior work centered on group fairness.
- Individual fairness requires similar individuals to receive the same prediction outcomes with high probability, primarily in classification and selection settings.
- Fair-ranking proposals diversify group representation or equalize exposure while preserving ranking quality, but prior approaches focus on groups and static rankings.
- Position bias research finds that top-ranked answers are more likely to be viewed or clicked, even when rank assignments are randomly permuted.
6 CONCLUSION
The paper proposes equity of attention, amortized over consecutive rankings through constrained optimization, and finds substantial attention discrepancies in real-world data while retaining ranking quality. It identifies calibration and fairness-aware relevance labeling as future directions.
- Equity of attention requires ranked subjects’ accumulated attention to remain proportional to their relevance across consecutive rankings.Because a single ranking cannot satisfy this condition, the paper amortizes fairness over time by reordering rankings through constrained optimization.
- Real-world experiments find substantial discrepancies between received and deserved attention, while suggesting equity can often improve without sacrificing much ranking quality.
- Future work includes calibrating ranker scores and training judges to provide relevance labels with fairness in mind.