Fairness in Prediction Sets: Beyond Equal Coverage

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Author: Denis Avetisyan

New research reveals that prioritizing equal-sized prediction sets-rather than uniform coverage-significantly improves fairness when using conformal prediction in real-world decision-making.

Label-Clustered Conformal Prediction addresses disparities in set size to enhance substantive fairness and mitigate bias.

While conformal prediction (CP) provides valuable uncertainty quantification, its impact on equitable downstream decision-making remains largely unexamined. This work, ‘Beyond Procedure: Substantive Fairness in Conformal Prediction’, shifts the focus from procedural fairness to substantive fairness-the equity of outcomes-and demonstrates that equalizing prediction set sizes, rather than simply ensuring coverage, strongly correlates with improved fairness. Through theoretical analysis and an LLM-in-the-loop evaluation framework, we identify how label-clustered CP can mitigate unfairness stemming from method design. Can these findings pave the way for more reliable and equitable machine learning systems in sensitive applications?

The Emergence of Inequality in Prediction

Prediction sets, a relatively new approach to machine learning, are gaining traction as tools for reliable decision-making across various fields, from medical diagnoses to loan applications. However, a growing body of research reveals these sets frequently exhibit disparities in both coverage and size when applied to different demographic groups. Coverage refers to the proportion of times the correct answer falls within the predicted set; unequal coverage means certain groups are less likely to have accurate predictions. Simultaneously, variations in set size – the number of possible predictions offered – can also disadvantage specific populations; larger sets, while potentially more accurate, can be impractical or costly to act upon, while smaller sets risk increased error rates. These discrepancies aren’t simply statistical curiosities; they represent a critical challenge to the equitable deployment of predictive systems, demanding careful consideration of fairness metrics beyond overall accuracy.

While much algorithmic fairness research centers on achieving equitable outcomes – ensuring predictions are equally accurate across groups – a growing body of work highlights the critical importance of procedural fairness. This perspective shifts the focus from simply what a model predicts to how it arrives at those predictions, arguing that the integrity of the prediction process itself is paramount for building trustworthy systems. Simply achieving equal error rates does not address concerns if the method for generating predictions is systematically biased or unreliable for certain groups; a system can appear fair on the surface while still perpetuating inequity through its underlying mechanics. Consequently, researchers are increasingly exploring metrics and techniques that assess the robustness and consistency of prediction sets, ensuring that all groups are afforded the same level of reliability and confidence in the generated predictions, irrespective of the final outcome.

Prediction sets, while designed to quantify uncertainty and improve decision-making, are susceptible to a phenomenon termed ‘Set Size Disparity’, where the average size of these sets differs significantly across demographic groups. This isn’t merely an aesthetic concern; larger sets, while offering greater coverage – the probability of the true value being included – simultaneously dilute the precision of the prediction. Consequently, a group consistently receiving larger prediction sets may experience a lower overall error rate, but at the cost of diminished usefulness for fine-grained decisions. Conversely, consistently smaller sets, while appearing more precise, heighten the risk of excluding the correct answer, leading to disproportionately higher error rates for that group. This imbalance erodes the perceived reliability and trustworthiness of the predictive system, particularly for those consistently subjected to less informative, or more risk-laden, predictions – a critical impediment to the equitable deployment of machine learning in sensitive applications.

Defining Equitable Processes Through Metrics

Equalized Coverage and Equalized Set Size are procedural fairness metrics designed to evaluate the equity of prediction processes, specifically focusing on confidence and prediction breadth across different demographic groups. Equalized Coverage seeks to ensure that the proportion of individuals receiving a positive prediction is consistent across groups, regardless of base rates. Equalized Set Size, conversely, aims for similar sizes of the predicted positive sets for each group; this means that, for any given threshold, the number of individuals flagged as positive should be comparable, irrespective of group membership. Both metrics are calculated based on the predicted scores and group labels, and represent a shift from evaluating overall prediction accuracy to assessing the distribution of predictions and associated confidence levels across potentially sensitive attributes.

Traditional machine learning evaluation often prioritizes overall accuracy, potentially overlooking disparities in performance across different demographic groups. Procedural fairness metrics, such as Equalized Coverage and Equalized Set Size, shift the focus to the process of prediction rather than solely the outcome. This approach acknowledges that equitable treatment requires similar levels of consideration – quantified by confidence and prediction breadth – for all groups, even if achieving identical accuracy rates is not feasible or desirable. By explicitly measuring these procedural aspects, these metrics provide a mechanism for identifying and mitigating biases embedded within predictive systems, moving beyond a singular emphasis on aggregate performance and towards a more nuanced assessment of fairness.

Analysis of model performance revealed a positive correlation between Equalized Set Size and substantive fairness outcomes. Specifically, interventions designed to equalize the size of predicted sets across demographic groups consistently improved fairness metrics. Conversely, optimizing for Equalized Coverage – ensuring equal prediction rates – demonstrated a negative correlation with fairness, as evidenced by increases in metrics such as maxROR (maximum relative opportunity ratio). This indicates that while Equalized Coverage aims for equitable rates of prediction, it does not necessarily guarantee equitable outcomes and may, in some cases, exacerbate disparities.

Evaluating Fairness Beyond Aggregate Statistics

Traditional statistical methods for evaluating fairness often rely on group-level comparisons of predetermined metrics, which can fail to identify disparities arising from complex interactions between multiple sensitive attributes and contextual factors. Substantive fairness, however, necessitates evaluating whether outcomes are equitable given the specific circumstances of each case, requiring consideration of nuanced details that are difficult to quantify and incorporate into standard statistical models. These complexities include variations in individual circumstances, differing levels of risk, and the potential for disparate impact arising from seemingly neutral criteria, all of which necessitate a more holistic and context-aware approach than is typically provided by aggregate statistical analyses.

An LLM-in-the-loop evaluator employs large language models (LLMs) to assess fairness by simulating human judgment in outcome determination. This approach moves beyond simple statistical parity by enabling the LLM to consider contextual factors and nuanced reasoning when evaluating whether a given outcome is equitable. The LLM is presented with case data and tasked with assessing the appropriateness of the result, effectively functioning as a proxy for human review. This allows for the evaluation of complex scenarios where traditional fairness metrics are insufficient, and provides a more granular understanding of potential biases within a system’s decision-making process.

Generalized Estimating Equations (GEE) are employed within this fairness evaluation framework to address potential correlations present in the data, which violate the independence assumptions of standard regression models. Specifically, GEE models account for within-subject or within-group dependencies that may arise from repeated measures or clustered data structures, preventing underestimates of standard errors and ensuring the validity of statistical inference. The approach utilizes a correlation structure, typically specified as independent, exchangeable, autoregressive, or unstructured, to model these dependencies. By appropriately handling correlated data, GEE provides more robust and reliable estimates of fairness metrics and their associated statistical significance, leading to more defensible conclusions regarding the equitable performance of the evaluated models.

Mitigating Disparities Through Adaptive Prediction

Conventional conformal prediction, while statistically rigorous in guaranteeing coverage, can inadvertently amplify existing biases within datasets, leading to what is known as ‘Set Size Disparity’. This phenomenon arises because the method’s prediction sets – the range of plausible outcomes – aren’t uniform across different subgroups of the population. Consequently, minority or disadvantaged groups often receive larger, less informative prediction sets, effectively increasing their risk exposure when decisions are made based on these predictions. The disparity isn’t a failure of coverage – the method still guarantees a certain level of accuracy – but rather a disproportionate allocation of uncertainty, leading to systematically unfair outcomes where some groups are subjected to more conservative, and potentially restrictive, decision-making processes than others. This highlights a crucial limitation of standard conformal prediction when deployed in sensitive applications requiring equitable treatment.

Label-Clustered Conformal Prediction addresses a critical limitation of standard conformal prediction methods: the potential for unfair outcomes stemming from ‘Set Size Disparity’. This innovative technique operates by grouping similar labels into clusters before generating prediction sets, thereby mitigating the tendency for certain groups to receive disproportionately large – and thus less useful – prediction sets. Crucially, this clustering process doesn’t compromise the foundational guarantee of conformal prediction – valid coverage. By strategically reducing set size disparities, Label-Clustered CP ensures that all individuals or data points are afforded similarly sized and informative predictions, fostering greater fairness without sacrificing statistical rigor. The method effectively balances prediction set size across different groups, leading to more equitable downstream decision-making.

Evaluations demonstrate that Label-Clustered Conformal Prediction significantly minimizes disparities in predictive outcomes when compared to conventional conformal prediction techniques. Across multiple datasets, this approach consistently achieved the lowest maximum risk of rejection ratio (maxROR), indicating a more equitable distribution of prediction set sizes. Notably, analysis revealed a V-shaped relationship between the number of label clusters – denoted as ‘K’ – and the resulting gap in prediction set sizes between different groups; the most effective disparity reduction occurred when utilizing just two clusters (K=2). This finding suggests a sweet spot in balancing coverage guarantees with fairness, offering a practical strategy for deploying reliable and equitable machine learning models.

The study illuminates how localized adjustments to prediction set sizes demonstrably impact downstream fairness-a principle echoing Thomas Hobbes’ observation that “the only way to make a man help is to make it more painful to not help.” While Hobbes focused on social contracts, this research suggests a parallel: minimizing disparity in prediction set sizes-effectively reducing the ‘pain’ of unequal prediction quality-correlates with improved substantive fairness. By focusing on equalizing set sizes, rather than simply coverage, the proposed Label-Clustered Conformal Prediction fosters a system where prediction quality is more evenly distributed, subtly guiding outcomes towards a more equitable distribution, akin to influencing rather than controlling the system.

What’s Next?

The pursuit of fairness, predictably, reveals itself less as a problem of procedure and more as an emergent property of the system. This work highlights a critical distinction: equalizing prediction set sizes, rather than striving for uniform coverage, appears to correlate strongly with downstream fairness. Robustness emerges, it’s never engineered. The implications are clear: attempts to control fairness through calibration metrics are likely chasing shadows. The focus should shift toward understanding the landscape of label distributions and how conformal prediction interacts with inherent clustering within data.

Future work needn’t fixate on optimizing for a single, elusive fairness definition. Instead, investigation should embrace the observation that small interactions create monumental shifts. How do different label clustering strategies within conformal prediction influence not just fairness, but also the utility of the predictions in diverse decision-making contexts? The field needs to move beyond assessing fairness after prediction and consider how the prediction process itself can be shaped by an awareness of underlying data structure.

Ultimately, the question isn’t whether conformal prediction can be fair, but how its inherent properties – its reliance on local rules and neighborhood structure – can be leveraged to produce systems where fairness isn’t a goal, but a consequence. Order doesn’t need architects; it emerges. The true challenge lies in mapping the conditions under which this emergence is most likely to occur.

Original article: https://arxiv.org/pdf/2602.16794.pdf

Contact the author: https://www.linkedin.com/in/avetisyan/

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2026-02-23 00:51