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arxiv: 2606.26200 · v1 · pith:QXCVIAVSnew · submitted 2026-06-24 · 💻 cs.LG · cs.AI· stat.ML

Statistical and Structural Approaches to Algorithmic Fairness

Antonio Ferrara This is my paper

Pith reviewed 2026-06-26 01:38 UTC · model grok-4.3

classification 💻 cs.LG cs.AIstat.ML
keywords algorithmic fairnesspoint estimatesstructural contextsocio-technical systemsfairness auditingmachine learningstatistical approachesfairness paradigms
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The pith

Algorithmic fairness requires moving beyond deterministic point estimates and isolated individual views to include structural context.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

Modern machine learning systems function as socio-technical architectures that shape access to opportunities and carry forward existing inequalities. The thesis identifies two central limitations in current fairness work: reliance on deterministic point estimates when auditing models and the treatment of individuals as standalone entities without their relational and environmental contexts. It proposes statistical and structural approaches as replacements. A sympathetic reader would care because these simplifications have constrained how effectively fairness methods can operate in complex real-world settings where algorithms decide economic and social access.

Core claim

Early fairness mitigation strategies rested on fragile simplifications that limited effectiveness in complex socio-technical environments. This thesis identifies and addresses two fundamental limitations of contemporary fairness paradigms: the reliance on deterministic point estimates for auditing and the treatment of individuals as isolated entities devoid of structural context.

What carries the argument

Statistical and structural approaches that replace point estimates with uncertainty-aware auditing and embed individuals within relational and environmental contexts.

If this is right

  • Fairness auditing will shift from single deterministic values to methods that incorporate statistical variability and uncertainty.
  • Assessments will treat individuals as embedded in structural positions rather than as isolated data points.
  • Mitigation strategies will become more robust when applied inside complex socio-technical systems.
  • Models will more directly confront how environmental inequalities propagate through algorithmic decisions.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Deployed systems affecting opportunities could face requirements to document structural context in addition to standard fairness metrics.
  • Data collection practices might need to capture relational information such as network position or community membership to enable the new approaches.
  • Toolkits for practitioners could incorporate graph or embedding layers that represent structural context when computing fairness scores.
  • Longitudinal studies could test whether the proposed methods produce sustained reductions in disparate outcomes across multiple deployment cycles.

Load-bearing premise

The two listed limitations of point estimates and isolated individuals are the central problems whose removal will materially improve fairness outcomes in socio-technical systems.

What would settle it

A controlled deployment comparison in which fairness metrics and outcomes using distributional estimates plus structural context show no material reduction in disadvantage relative to standard point-estimate group fairness methods.

Figures

Figures reproduced from arXiv: 2606.26200 by Antonio Ferrara.

Figure 1
Figure 1. Figure 1: Resolution limits for Statistical Parity violations under varying global negative rates [PITH_FULL_IMAGE:figures/full_fig_p045_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Point-wise estimation versus confidence intervals, COMPAS dataset. [PITH_FULL_IMAGE:figures/full_fig_p047_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Point-wise estimation versus confidence intervals, Adult dataset. [PITH_FULL_IMAGE:figures/full_fig_p048_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: (COMPAS on the left, Adult on the right) shows that no single threshold (horizontal line) on γSP can cleanly separate true violations from non-violations. These plots further support the need for a size-adaptive hypothesis-testing approach. 10 0 10 1 10 2 10 3 Size of Protected Group (ns) 10 4 10 3 10 2 10 1 |S P(S)| (x S( )) COMPAS dataset Fairness violation detected NO Fairness violation detected 10 0 10… view at source ↗
Figure 5
Figure 5. Figure 5: Resolution limits for Statistical Parity violations under varying global negative rates [PITH_FULL_IMAGE:figures/full_fig_p056_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Point-wise estimation versus confidence intervals, Adult dataset. [PITH_FULL_IMAGE:figures/full_fig_p057_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Point-wise estimation versus confidence intervals, Adult dataset (continued). [PITH_FULL_IMAGE:figures/full_fig_p058_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Point-wise estimation versus confidence intervals, COMPAS dataset. [PITH_FULL_IMAGE:figures/full_fig_p059_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Point-wise estimation versus confidence intervals, COMPAS dataset (continued). [PITH_FULL_IMAGE:figures/full_fig_p060_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Point-wise estimation versus confidence intervals, German dataset [PITH_FULL_IMAGE:figures/full_fig_p061_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Point-wise estimation versus confidence intervals, Student dataset [PITH_FULL_IMAGE:figures/full_fig_p062_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Protected groups size, [PITH_FULL_IMAGE:figures/full_fig_p063_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: Comparison of Bayesian credible intervals (blue) and asymptotic normal confidence [PITH_FULL_IMAGE:figures/full_fig_p063_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: Point-wise estimation versus confidence intervals for Equal Opportunity, Adult dataset. [PITH_FULL_IMAGE:figures/full_fig_p066_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: Point-wise estimation versus confidence intervals for Equal Opportunity, Adult dataset [PITH_FULL_IMAGE:figures/full_fig_p067_15.png] view at source ↗
Figure 17
Figure 17. Figure 17: Point-wise estimation versus confidence intervals for Equal Opportunity, COMPAS dataset [PITH_FULL_IMAGE:figures/full_fig_p069_17.png] view at source ↗
Figure 1
Figure 1. Figure 1: Condor Pipeline and Causal Diagnostic Framework. (Left) We observe a dataset of 𝑛 individuals with protected attributes 𝑍 and task-relevant features 𝑋, alongside an opaque ranking 𝑅 (§3). (Center) Condor audits this black box by projecting 𝑅 and 𝑍 into a Reproducing Kernel Hilbert Space (RKHS) to residualize (“regress out”) the legitimate influence of 𝑋. Distance correlation on these residuals yields the P… view at source ↗
Figure 2
Figure 2. Figure 2: Heatmap of 𝑝-values on synthetic data (𝑛=1000, 𝑘𝑥=𝑘𝑡=5). Top four heatmaps: 𝑑𝑜=5, 𝑑𝑝=2. Bottom four heatmaps: 𝑑𝑜=10, 𝑑𝑝=5. Each panel corresponds to one scor￾ing rule; axes report the influence of 𝑋 on 𝑍 (𝛾) and of 𝑍 on the ranking (𝛽), and the red/white/blue scale marks respec￾tively strong evidence against, the 𝛼 = 0.05 boundary, and little evidence against 𝐻0 : 𝑅 ⊥⊥ 𝑍 | 𝑋. RQ4: How does Condor work as a… view at source ↗
Figure 3
Figure 3. Figure 3: Compas and Adult datasets. Heatmap of 𝑝-values on Compas and Adult rankings. Each row corresponds to one dataset and each heatmap to a specific composition of the protected features 𝑍. For each heatmap, the scoring rule is reported on the row and on the columns the influence of 𝑍 on the ranking (𝛽), and the red/white/blue scale marks respectively strong evidence against, the 𝛼 = 0.05 boundary, and little e… view at source ↗
Figure 6
Figure 6. Figure 6: Runtime (in seconds) of each method as a function [PITH_FULL_IMAGE:figures/full_fig_p080_6.png] view at source ↗
Figure 1
Figure 1. Figure 1: Equal Treatment Inspector workflow. The model [PITH_FULL_IMAGE:figures/full_fig_p090_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: In the “Indirect case” (left): good unfairness detection methods should follow a increasing [PITH_FULL_IMAGE:figures/full_fig_p094_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: In the left figure, a comparison of ET and DP measures on the US Income data. The AUC [PITH_FULL_IMAGE:figures/full_fig_p094_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Left: AUC of the inspector for ET and DP, over the district of California 2014 for the ACS [PITH_FULL_IMAGE:figures/full_fig_p105_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Left: AUC of the inspector for ET and DP, over the district of California 2014 for the ACS [PITH_FULL_IMAGE:figures/full_fig_p106_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Left: AUC of the inspector for ET and DP, over the district of California 2014 for the ACS [PITH_FULL_IMAGE:figures/full_fig_p106_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Comparing the power of C2ST based on Accuracy vs AUC. [PITH_FULL_IMAGE:figures/full_fig_p107_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: AUC of the inspector for ET, over the district of CA14 for the US Income dataset. [PITH_FULL_IMAGE:figures/full_fig_p108_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Coefficient of gψ over γ for synthetic datasets in two experimental scenarios. E.5 Statistical Comparison of Demographic Parity versus Equal Treatment So far, we measured ET and DP fairness usingthe AUC of an inspector, gψ and gv respectively (see Section 5). For DP, however, other probability density distance metrics can be considered, including the p-value of the Kolmogorov–Smirnov (KS) test and the Wass… view at source ↗
Figure 10
Figure 10. Figure 10: AUC of the ET inspect using SHAP vs using LIME. [PITH_FULL_IMAGE:figures/full_fig_p111_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Elapsed time for generating explanation distributions using SHAP and LIME with different [PITH_FULL_IMAGE:figures/full_fig_p112_11.png] view at source ↗
Figure 1
Figure 1. Figure 1: (a) Toy example: in red, a forward path that is not the shortest path (blue). Moving from the source A to D reduces the distance to the destination C from 8 to 5, sat￾isfying the definition of forward path. In black, a path that is not forward: moving from A to E increases the distance to C from 8 to 8.5. (b) Drivable street network of Piedmont (California). For a random pair of source-destination nodes, t… view at source ↗
Figure 2
Figure 2. Figure 2: (a) A portion of the Florence city-center road network. The input to our problem, along with the map, is a source [PITH_FULL_IMAGE:figures/full_fig_p117_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: A portion of the DAG from [PITH_FULL_IMAGE:figures/full_fig_p122_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Visualization of the paths (in red) produced by differ [PITH_FULL_IMAGE:figures/full_fig_p124_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: (Left) and (Center) Generalized Lorenz curve for a source-destination random pair of the Essaouira dataset. The [PITH_FULL_IMAGE:figures/full_fig_p126_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: (Left) Average runtime over 100 random source-target pairs for each component of our method, as well as their total sum, across datasets of varying sizes. (Center) Runtime for each component of our method for the Kyoto dataset. Each point corresponds to a source-target pair, with the number of nodes in the corresponding DAG reported on the horizontal axis. The sub-linear growth in the semi-log plot of MMFP… view at source ↗
Figure 1
Figure 1. Figure 1: The recommendation cycle: A network-based rec [PITH_FULL_IMAGE:figures/full_fig_p130_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Recommendation algorithms: Given the network in Figure 1, here we explain the recommendation suggested to node [PITH_FULL_IMAGE:figures/full_fig_p131_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: The evolution of network structure for different recommendation algorithms and different values of homophily [PITH_FULL_IMAGE:figures/full_fig_p133_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Changes in the visibility of minorities for different [PITH_FULL_IMAGE:figures/full_fig_p134_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Visibility of the minority group as a function of homophily. Heatmaps show the visibility of the minority group [PITH_FULL_IMAGE:figures/full_fig_p135_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Changes in the visibility of minorities as a function of the minority size. The y-axis shows the change in visibility for [PITH_FULL_IMAGE:figures/full_fig_p136_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: The evolution of the in-group links within majority nodes (blue) and within minority nodes (orange) for different [PITH_FULL_IMAGE:figures/full_fig_p137_7.png] view at source ↗
Figure 1
Figure 1. Figure 1: Schematic overview of the Spatial-GNN framework. [PITH_FULL_IMAGE:figures/full_fig_p143_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Socioeconomic consistency in user trajectories. The [PITH_FULL_IMAGE:figures/full_fig_p145_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Model Performance as Recall@20 over the dataset [PITH_FULL_IMAGE:figures/full_fig_p147_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Test ROC-AUC on classification (high vs low) so [PITH_FULL_IMAGE:figures/full_fig_p147_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Example maps of the super-resolution regression on the "Median Income", Philadelphia metropolitan area. Darker [PITH_FULL_IMAGE:figures/full_fig_p148_5.png] view at source ↗
Figure 7
Figure 7. Figure 7: Second K-Means clustering on the two business [PITH_FULL_IMAGE:figures/full_fig_p150_7.png] view at source ↗
Figure 6
Figure 6. Figure 6: (Left) Prevalence of cluster B across the business of [PITH_FULL_IMAGE:figures/full_fig_p150_6.png] view at source ↗
Figure 1
Figure 1. Figure 1: Research Setup. We investigate the effect of sam [PITH_FULL_IMAGE:figures/full_fig_p180_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: We consider the standard We’re All Equal world [PITH_FULL_IMAGE:figures/full_fig_p182_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Correlations of Skill Score (higher is better) and [PITH_FULL_IMAGE:figures/full_fig_p184_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Results of Simulated Pairwise Comparisons, by Sampling Approach (rows) and Ranking Recovery Method (colors). [PITH_FULL_IMAGE:figures/full_fig_p185_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Post-Processed Results the FA*IR algorithm [ [PITH_FULL_IMAGE:figures/full_fig_p186_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Ranking Recovery Results from the IMDB-WIKI-SbS dataset [ [PITH_FULL_IMAGE:figures/full_fig_p187_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Parameters for the Oversampling Method: Rela [PITH_FULL_IMAGE:figures/full_fig_p189_7.png] view at source ↗
Figure 1
Figure 1. Figure 1: Toy example for our proposed approach for the node v in the graph. 3 FairMC Markov Chain methods allow interpreting the search of the consensus ranking in terms of transition probabilities among nodes of a graph and the graph-structured representa￾tion has advantages in terms of computational complexity and interpretability. However, as for the other rank aggregation methods, Markov Chain rank aggregation … view at source ↗
Figure 2
Figure 2. Figure 2: Violin plots of summary statistics of performance. 4.1 Performance Evaluation Figure 2a and 2b show the violin plots of fairness@k of the consensus rankings of the top 10% and 50% of the full ranking. At each level, the non-fair approaches, Markov Chain approaches, and the competing fair rank aggregation approaches tend to obtain 1 best rank aggregated, Borda aggregation, exponential enhanced Borda, expone… view at source ↗
Figure 1
Figure 1. Figure 1: Illustration of the role of the abstainer in a ranking process. A standard ranker produces a [PITH_FULL_IMAGE:figures/full_fig_p201_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Accuracy Acc on the selected pairs (mean ± std over five folds) for the BT model (top line) and the TM model (bottom line). For smaller target coverages c (i.e., more abstention), the accuracy increases for BALToR, remains stable for the random abstainer, has erratic performance for the entropy-based abstainer. (a) (b) (c) [PITH_FULL_IMAGE:figures/full_fig_p206_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Actual (empirical) coverage Cov on the test set (mean ± std over five folds) for the BT model . The actual coverage remains very close to the target coverage c. OHSUMED [Hersh et al., 1994] is a MEDLINE database subset containing 106 queries with 16,140 query-documents pairs. Each query-document pair has a 25-dimensional feature vector that contains popular information-retrieval features, such as tf-idf an… view at source ↗
Figure 4
Figure 4. Figure 4: Distribution of classes SelRate on the selected pairs (mean ± std over five folds) for the BT model . While the target coverage c varies, BALToR maintains stable the proportions of the classes in Y = {−1, 0, 1}. predicted probabilities rather than the conditional risk (the higher the entropy, the more uncertain the ranker); (ii) a random abstainer, namely a selection function that selects a fraction c of p… view at source ↗
Figure 5
Figure 5. Figure 5: Estimated density functions over MQ2007 Fold 1 calibration set for BT (Figure 5a) and TM (Figure 5b) when using an XGBRanker. The shapes of the density functions differ (are similar) when using BT (TM) model. (a) (b) (c) [PITH_FULL_IMAGE:figures/full_fig_p215_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Actual (empirical) coverage Cov on the test set (mean ± std over five folds) for the TM model . The actual coverage remains very close to the target coverage c. (a) (b) (c) [PITH_FULL_IMAGE:figures/full_fig_p215_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Distribution of classes SelRate on the selected pairs (mean ± std over five folds) for the TM model . While the target coverage c varies, BALToR maintains stable the proportions of the classes in Y = {−1, 0, 1}. (a) (b) (c) [PITH_FULL_IMAGE:figures/full_fig_p215_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Distribution of classes SelRate on the selected pairs (mean ± std over five folds) for the TM model . While the target coverage c varies, entropy maintains stable the proportions of the classes in Y = {−1, 0, 1}. 16 7.1 Bounded-Abstention Pairwise Learning to Rank 209 [PITH_FULL_IMAGE:figures/full_fig_p215_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Acc results (mean ± std over five folds) for the BT model (top line) and the TM model (bottom line) when using LightGBM. (a) (b) (c) (d) (e) (f) [PITH_FULL_IMAGE:figures/full_fig_p216_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Cov results (mean ± std over five folds) for the BT model (top line) and the TM model (bottom line) when using LightGBM. 17 7.1 Bounded-Abstention Pairwise Learning to Rank 210 [PITH_FULL_IMAGE:figures/full_fig_p216_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: SelRate results (mean ± std over five folds) for the BT model (top line) and the TM model (bottom line) when using LightGBM and BALToR. (a) (b) (c) (d) (e) (f) [PITH_FULL_IMAGE:figures/full_fig_p217_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: SelRate results (mean ± std over five folds) for the BT model (top line) and the TM model (bottom line) when using LightGBM and entropy. 18 7.1 Bounded-Abstention Pairwise Learning to Rank 211 [PITH_FULL_IMAGE:figures/full_fig_p217_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: Acc results (mean ± std over five folds) for the BT model (top line) and the TM model (bottom line) when using CatBoost. (a) (b) (c) (d) (e) (f) [PITH_FULL_IMAGE:figures/full_fig_p218_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: Cov results (mean ± std over five folds) for the BT model (top line) and the TM model (bottom line) when using CatBoost. 19 7.1 Bounded-Abstention Pairwise Learning to Rank 212 [PITH_FULL_IMAGE:figures/full_fig_p218_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: SelRate results (mean ± std over five folds) for the BT model (top line) and the TM model (bottom line) when using CatBoost and BALToR. (a) (b) (c) (d) (e) (f) [PITH_FULL_IMAGE:figures/full_fig_p219_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: SelRate results (mean ± std over five folds) for the BT model (top line) and the TM model (bottom line) when using CatBoost and entropy. 20 7.1 Bounded-Abstention Pairwise Learning to Rank 213 [PITH_FULL_IMAGE:figures/full_fig_p219_16.png] view at source ↗
read the original abstract

Modern machine learning systems have outgrown their origins as isolated predictive constructs, evolving into complex socio-technical architectures that actively mediate human opportunity. As algorithms increasingly determine access to economic and social opportunities, it has become widely recognized that these systems are deeply embedded with the structural inequalities and prejudices of their environments. The field of algorithmic fairness emerged in response to the growing recognition that models optimized for predictive accuracy can systematically disadvantage marginalized groups. Early mitigation strategies, however, rested on fragile simplifications that limited their effectiveness in complex socio-technical environments. This thesis identifies and addresses two fundamental limitations of contemporary fairness paradigms: the reliance on deterministic point estimates for auditing and the treatment of individuals as isolated entities devoid of structural context.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 0 minor

Summary. This thesis abstract claims that contemporary algorithmic fairness paradigms are limited by two fundamental issues: reliance on deterministic point estimates for auditing fairness and modeling individuals as isolated entities without structural context. It states that the thesis identifies and addresses these limitations in socio-technical ML systems.

Significance. If the thesis were to supply rigorous derivations, empirical demonstrations, or comparative analyses showing that interventions on these two axes produce larger fairness gains than alternatives, the work could meaningfully advance the field beyond current point-estimate and individual-level approaches. The abstract supplies none of this evidence, so the potential significance cannot be assessed from the provided material.

major comments (1)
  1. [Abstract] Abstract, paragraph 3: The assertion that reliance on deterministic point estimates and isolated-individual modeling are the two central, load-bearing limitations is presented without any comparative analysis, outcome deltas, or literature synthesis demonstrating that these dominate other documented problems such as training-data provenance, causal identifiability, or deployment feedback loops.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their review. We respond to the single major comment below, focusing on the justification for the two limitations highlighted in the abstract.

read point-by-point responses

  1. Referee: [Abstract] Abstract, paragraph 3: The assertion that reliance on deterministic point estimates and isolated-individual modeling are the two central, load-bearing limitations is presented without any comparative analysis, outcome deltas, or literature synthesis demonstrating that these dominate other documented problems such as training-data provenance, causal identifiability, or deployment feedback loops.

    Authors: The abstract is a concise summary; the full thesis contains the requested literature synthesis, comparative discussion of alternative limitations (including data provenance and causal issues), and empirical demonstrations of the relative impact of addressing point-estimate and structural-modeling shortcomings. We agree the abstract itself does not convey this supporting material and will revise it to include a brief clause referencing the comparative framework and outcome analyses developed in Chapters 3–5. revision: yes

Circularity Check

0 steps flagged

No circularity: identification claim with no derivation chain

full rationale

The abstract presents an identification of two limitations as fundamental but supplies no equations, derivations, fitted parameters, or self-citations. No load-bearing step reduces to its own inputs by construction, self-definition, or renaming. The central claim is a problem statement rather than a predictive or uniqueness derivation, so no circularity patterns apply. Full text reference yields the same absence of visible mathematical structure.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract supplies no technical content; ledger is empty by necessity.

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Reference graph

Works this paper leans on

79 extracted references · 2 canonical work pages

  1. [1]

    Technology and history: Kranzberg’s laws,

    M. Kranzberg, “Technology and history: Kranzberg’s laws,”Technology and culture, vol. 27, no. 3, pp. 544–560, 1986

    1986

  2. [2]

    Fairness through awareness,

    C. Dwork, M. Hardt, T. Pitassi, O. Reingold, and R. Zemel, “Fairness through awareness,” inProceedings of the 3rd innovations in theoretical computer science conference, 2012, pp. 214–226

    2012

  3. [3]

    Equality of opportunity in super- vised learning,

    M. Hardt, E. Price, and N. Srebro, “Equality of opportunity in super- vised learning,”Advances in neural information processing systems, vol. 29, 2016

    2016

  4. [4]

    An analysis of the eeocc “four-fifths

    I. Greenberg, “An analysis of the eeocc “four-fifths” rule,”Management Science, vol. 25, no. 8, pp. 762–769, 1979

    1979

  5. [5]

    Sch¨ olkopf and A

    B. Sch¨ olkopf and A. J. Smola,Learning with Kernels: Support Vector Ma- chines, Regularization, Optimization, and Beyond. MIT Press, 2002

    2002

  6. [6]

    Birds of a feather: Ho- mophily in social networks,

    M. McPherson, L. Smith-Lovin, and J. M. Cook, “Birds of a feather: Ho- mophily in social networks,”Annual review of sociology, vol. 27, no. 1, pp. 415–444, 2001

    2001

  7. [7]

    Emergence of scaling in random networks,

    A.-L. Barab´ asi and R. Albert, “Emergence of scaling in random networks,” science, vol. 286, no. 5439, pp. 509–512, 1999

    1999

  8. [8]

    Size-adaptive hypothesis testing for fairness,

    A. Ferrara, F. Cozzi, A. Perotti, A. Panisson, and F. Bonchi, “Size-adaptive hypothesis testing for fairness,”Advances in neural information processing systems, vol. 38, 2025

    2025

  9. [9]

    Auditing for demographic bias in opaque rankings,

    A. Ferrara, C. Abrate, F. Vitale, and F. Bonchi, “Auditing for demographic bias in opaque rankings,”Proceedings of the VLDB Endowment, vol. 19, 2026

    2026

  10. [10]

    Beyond shortest paths: Node fairness in route recommendation,

    A. Ferrara, D. Garc´ ıa-Soriano, and F. Bonchi, “Beyond shortest paths: Node fairness in route recommendation,”Proceedings of the VLDB En- dowment, vol. 18, no. 9, pp. 3230–3242, 2025

    2025

  11. [11]

    Bias-aware ranking from pairwise comparisons,

    A. Ferrara, F. Bonchi, F. Fabbri, F. Karimi, and C. Wagner, “Bias-aware ranking from pairwise comparisons,”Data Mining and Knowledge Discov- ery, vol. 38, no. 4, pp. 2062–2086, 2024

    2062

  12. [12]

    Link recommen- dations: Their impact on network structure and minorities,

    A. Ferrara, L. Esp´ ın-Noboa, F. Karimi, and C. Wagner, “Link recommen- dations: Their impact on network structure and minorities,” inProceedings of the 14th ACM Web Science Conference 2022, 2022, pp. 228–238. 245

    2022

  13. [13]

    Bounded-abstention pairwise learning to rank,

    A. Ferrara*, A. Pugnana*, F. Bonchi, and S. Ruggieri, “Bounded-abstention pairwise learning to rank,” inProceedings of the 32nd ACM SIGKDD Con- ference on Knowledge Discovery and Data Mining, 2026

    2026

  14. [14]

    Policy advice and best practices on bias and fairness in ai,

    J. M. Alvarez, A. B. Colmenarejo, A. Elobaid, S. Fabbrizzi, M. Fahimi, A. Ferrara, S. Ghodsi, C. Mougan, I. Papageorgiou, P. Reyero, et al., “Policy advice and best practices on bias and fairness in ai,”Ethics and Informa- tion Technology, vol. 26, no. 2, p. 31, 2024

    2024

  15. [15]

    Fairness-aware ranking recovery from pairwise comparisons,

    G. Ahnert, A. Ferrara, and C. Wagner, “Fairness-aware ranking recovery from pairwise comparisons,” inProceedings of the 18th ACM Web Science Conference 2026, 2026, pp. 289–298.doi:10.1145/3795766.3799744

    work page doi:10.1145/3795766.3799744 2026

  16. [16]

    Fairmc fair–markov chain rank aggregation methods,

    C. Balestra, A. Ferrara, and E. M¨ uller, “Fairmc fair–markov chain rank aggregation methods,” inInternational Conference on Big Data Analytics and Knowledge Discovery, Springer, 2024, pp. 315–321

    2024

  17. [17]

    Super-resolution of urban socioeconomic indicators via graph-based recommender systems,

    F. P. Nerini, C. Borile, A. Ferrara, and A. Panisson, “Super-resolution of urban socioeconomic indicators via graph-based recommender systems,” Web and the City, workshop at the WebConference, 2026

    2026

  18. [18]

    Beyond demo- graphic parity: Redefining equal treatment,

    C. Mougan, L. State, A. Ferrara, S. Ruggieri, and S. Staab, “Beyond demo- graphic parity: Redefining equal treatment,”arXiv preprint arXiv:2303.08040, 2023

    arXiv 2023

  19. [19]

    A multidisciplinary lens of bias in hate speech,

    P. Reyero Lobo, J. Kwarteng, M. Russo, M. Fahimi, K. Scott, A. Fer- rara, I. Sen, and M. Fernandez, “A multidisciplinary lens of bias in hate speech,” inProceedings of the International Conference on Advances in Social Networks Analysis and Mining, 2023, pp. 121–125

    2023

  20. [20]

    Kierkegaard,Soren Kierkegaard’s Journals and Papers, 1845-1855

    S. Kierkegaard,Soren Kierkegaard’s Journals and Papers, 1845-1855. In- diana University Press, 1967, vol. 6

    1967

  21. [21]

    C. J. Rowe, S. Broadie, et al.,Nicomachean ethics. Oxford University Press, 2002

    2002

  22. [22]

    Maxmin-fair ranking: Individual fair- ness under group-fairness constraints,

    D. Garc´ ıa-Soriano and F. Bonchi, “Maxmin-fair ranking: Individual fair- ness under group-fairness constraints,” inProceedings of the 27th ACM SIGKDD Conference on Knowledge Discovery & Data Mining, 2021, pp. 436– 446

    2021

  23. [23]

    Fair-by-design matching,

    D. Garc´ ıa-Soriano and F. Bonchi, “Fair-by-design matching,”Data Mining and Knowledge Discovery, vol. 34, no. 5, pp. 1291–1335, 2020

    2020

  24. [24]

    A theory of justice,

    J. Rawls, “A theory of justice,” inApplied ethics, Routledge, 2017, pp. 21– 29

    2017

  25. [25]

    Fairness definitions explained,

    S. Verma and J. Rubin, “Fairness definitions explained,” inProceedings of the international workshop on software fairness, 2018, pp. 1–7. 246

    2018

  26. [26]

    Inherent trade-offs in the fair determination of risk scores,

    J. Kleinberg, S. Mullainathan, and M. Raghavan, “Inherent trade-offs in the fair determination of risk scores,”arXiv preprint arXiv:1609.05807, 2016

    Pith/arXiv arXiv 2016

  27. [27]

    Fair prediction with disparate impact: A study of bias in recidivism prediction instruments,

    A. Chouldechova, “Fair prediction with disparate impact: A study of bias in recidivism prediction instruments,”Big data, vol. 5, no. 2, pp. 153–163, 2017

    2017

  28. [28]

    Counterfactual fairness,

    M. J. Kusner, J. Loftus, C. Russell, and R. Silva, “Counterfactual fairness,” Advances in neural information processing systems, vol. 30, 2017

    2017

  29. [29]

    Causal inference in statistics: An overview,

    J. Pearl, “Causal inference in statistics: An overview,”Statistics Surveys, vol. 3, pp. 96–146, 2009.doi:10 . 1214 / 09 - SS057[Online]. Available: https://projecteuclid.org/journals/statistics-surveys/volume- 3/issue-none/Causal-inference-in-statistics-An-overview/10.1 214/09-SS057.full

    2009

  30. [30]

    Can i trust my fairness metric? assessing fairness with unlabeled data and bayesian inference,

    D. Ji, P. Smyth, and M. Steyvers, “Can i trust my fairness metric? assessing fairness with unlabeled data and bayesian inference,”Advances in Neural Information Processing Systems, vol. 33, pp. 18 600–18 612, 2020

    2020

  31. [31]

    Statistical inference for fairness auditing,

    J. J. Cherian and E. J. Cand` es, “Statistical inference for fairness auditing,” Journal of machine learning research, vol. 25, no. 149, pp. 1–49, 2024

    2024

  32. [32]

    A survey of bias in machine learning through the prism of statistical parity,

    P. Besse, E. del Barrio, P. Gordaliza, J.-M. Loubes, and L. Risser, “A survey of bias in machine learning through the prism of statistical parity,” The American Statistician, vol. 76, no. 2, pp. 188–198, 2022

    2022

  33. [33]

    Fair- learn: Assessing and improving fairness of ai systems,

    H. Weerts, M. Dud´ ık, R. Edgar, A. Jalali, R. Lutz, and M. Madaio, “Fair- learn: Assessing and improving fairness of ai systems,”Journal of Machine Learning Research, vol. 24, no. 257, pp. 1–8, 2023

    2023

  34. [34]

    A central limit theorem for lp transportation cost on the real line with application to fairness as- sessment in machine learning,

    E. Del Barrio, P. Gordaliza, and J.-M. Loubes, “A central limit theorem for lp transportation cost on the real line with application to fairness as- sessment in machine learning,”Information and Inference: A Journal of the IMA, vol. 8, no. 4, pp. 817–849, 2019

    2019

  35. [35]

    Bringing practical statistical science to ai and predictive model fairness testing,

    V. S. Lo, S. Datta, and Y. Salami, “Bringing practical statistical science to ai and predictive model fairness testing,”AI and Ethics, vol. 5, no. 3, pp. 2149–2164, 2025

    2025

  36. [36]

    Disentangling influence: Using disentangled representations to audit model predictions,

    C. Marx, R. Phillips, S. Friedler, C. Scheidegger, and S. Venkatasubrama- nian, “Disentangling influence: Using disentangled representations to audit model predictions,”Advances in Neural Information Processing Systems, vol. 32, 2019. 247

    2019

  37. [37]

    Auditing black-box models for indi- rect influence,

    P. Adler, C. Falk, S. A. Friedler, T. Nix, G. Rybeck, C. Scheidegger, B. Smith, and S. Venkatasubramanian, “Auditing black-box models for indi- rect influence,”Knowledge and Information Systems, vol. 54, no. 1, pp. 95– 122, 2018

    2018

  38. [38]

    Kernel-based condi- tional independence test and application in causal discovery,

    K. Zhang, J. Peters, D. Janzing, and B. Sch¨ olkopf, “Kernel-based condi- tional independence test and application in causal discovery,” inProceed- ings of the 27th Conference on Uncertainty in Artificial Intelligence (UAI), Barcelona, Spain: AUAI Press, 2011, pp. 804–813

    2011

  39. [39]

    Partial distance correlation with methods for dissimilarities,

    G. J. Szekely and M. L. Rizzo, “Partial distance correlation with methods for dissimilarities,”Annals of Statistics, vol. 42, no. 6, pp. 2382–2412, 2014. doi:10.1214/14-AOS1255

    work page doi:10.1214/14-aos1255 2014

  40. [40]

    Interventional fairness: Causal database repair for algorithmic fairness,

    B. Salimi, L. Rodriguez, B. Howe, and D. Suciu, “Interventional fairness: Causal database repair for algorithmic fairness,” inProceedings of the 2019 international conference on management of data, 2019, pp. 793–810

    2019

  41. [41]

    Data preprocessing techniques for classifica- tion without discrimination,

    F. Kamiran and T. Calders, “Data preprocessing techniques for classifica- tion without discrimination,”Knowledge and information systems, vol. 33, no. 1, pp. 1–33, 2012

    2012

  42. [42]

    Certifying and removing disparate impact,

    M. Feldman, S. A. Friedler, J. Moeller, C. Scheidegger, and S. Venkatasub- ramanian, “Certifying and removing disparate impact,” inproceedings of the 21th ACM SIGKDD international conference on knowledge discovery and data mining, 2015, pp. 259–268

    2015

  43. [43]

    Centrality in social networks conceptual clarification,

    L. C. Freeman, “Centrality in social networks conceptual clarification,” Social networks, vol. 1, no. 3, pp. 215–239, 1978

    1978

  44. [44]

    The pagerank citation ranking: Bringing order to the web.,

    L. Page, S. Brin, R. Motwani, and T. Winograd, “The pagerank citation ranking: Bringing order to the web.,” Stanford infolab, Tech. Rep., 1999

    1999

  45. [45]

    Network inequality through preferential attachment, triadic clo- sure, and homophily,

    J. Bachmann, S. Martin-Gutierrez, L. Esp´ ın-Noboa, N. Cinardi, and F. Karimi, “Network inequality through preferential attachment, triadic clo- sure, and homophily,”Scientific Reports, 2026

    2026

  46. [46]

    Fairsna: Algorithmic fairness in social network analysis,

    A. Saxena, G. Fletcher, and M. Pechenizkiy, “Fairsna: Algorithmic fairness in social network analysis,”ACM Computing Surveys, vol. 56, no. 8, pp. 1– 45, 2024

    2024

  47. [47]

    Fairness in graph mining: A survey,

    Y. Dong, J. Ma, S. Wang, C. Chen, and J. Li, “Fairness in graph mining: A survey,”IEEE Transactions on Knowledge and Data Engineering, vol. 35, no. 10, pp. 10 583–10 602, 2023

    2023

  48. [48]

    Minorities in networks and algorithms,

    F. Karimi, M. Oliveira, and M. Strohmaier, “Minorities in networks and algorithms,” inHandbook of Computational Social Science, Edward Elgar Publishing Limited, 2025, pp. 438–451. 248

    2025

  49. [49]

    Compositional fairness constraints for graph embeddings,

    A. Bose and W. Hamilton, “Compositional fairness constraints for graph embeddings,” inInternational conference on machine learning, PMLR, 2019, pp. 715–724

    2019

  50. [50]

    Fairwalk: Towards fair graph embedding,

    T. Rahman, B. Surma, M. Backes, and Y. Zhang, “Fairwalk: Towards fair graph embedding,” 2019

    2019

  51. [51]

    Crosswalk: Fairness-enhanced node representation learning,

    A. Khajehnejad, M. Khajehnejad, M. Babaei, K. P. Gummadi, A. Weller, and B. Mirzasoleiman, “Crosswalk: Fairness-enhanced node representation learning,” inProceedings of the AAAI Conference on Artificial Intelligence, vol. 36, 2022, pp. 11 963–11 970

    2022

  52. [52]

    Learning fair graph neural networks with limited and private sensitive attribute information,

    E. Dai and S. Wang, “Learning fair graph neural networks with limited and private sensitive attribute information,”IEEE Transactions on Knowledge and Data Engineering, vol. 35, no. 7, pp. 7103–7117, 2022

    2022

  53. [53]

    Subgroup generalization and fairness of graph neural networks,

    J. Ma, J. Deng, and Q. Mei, “Subgroup generalization and fairness of graph neural networks,”Advances in Neural Information Processing Sys- tems, vol. 34, pp. 1048–1061, 2021

    2021

  54. [54]

    Fairness-aware pagerank,

    S. Tsioutsiouliklis, E. Pitoura, P. Tsaparas, I. Kleftakis, and N. Mamoulis, “Fairness-aware pagerank,” inProceedings of the Web Conference 2021, 2021, pp. 3815–3826

    2021

  55. [55]

    Applying fairness constraints on graph node ranks under personalization bias,

    E. Krasanakis, S. Papadopoulos, and I. Kompatsiaris, “Applying fairness constraints on graph node ranks under personalization bias,” inInterna- tional Conference on Complex Networks and Their Applications, Springer, 2020, pp. 610–622

    2020

  56. [56]

    Algorithmic glass ceiling in social networks: The effects of social recommendations on network di- versity,

    A.-A. Stoica, C. Riederer, and A. Chaintreau, “Algorithmic glass ceiling in social networks: The effects of social recommendations on network di- versity,” inProceedings of the 2018 World Wide Web Conference, 2018, pp. 923–932

    2018

  57. [57]

    Implicit social cognition: Attitudes, self-esteem, and stereotypes.,

    A. G. Greenwald and M. R. Banaji, “Implicit social cognition: Attitudes, self-esteem, and stereotypes.,”Psychological review, vol. 102, no. 1, p. 4, 1995

    1995

  58. [58]

    Are emily and greg more employable than lakisha and jamal? a field experiment on labor market discrimina- tion,

    M. Bertrand and S. Mullainathan, “Are emily and greg more employable than lakisha and jamal? a field experiment on labor market discrimina- tion,”American economic review, vol. 94, no. 4, pp. 991–1013, 2004

    2004

  59. [59]

    Rank analysis of incomplete block designs: I. the method of paired comparisons,

    R. A. Bradley and M. E. Terry, “Rank analysis of incomplete block designs: I. the method of paired comparisons,”Biometrika, vol. 39, no. 3/4, pp. 324– 345, 1952

    1952

  60. [60]

    R. D. Luce,Individual choice behavior: A theoretical analysis. New York: John Wiley and Sons, 1959. 249

    1959

  61. [61]

    Achieving budget-optimality with adaptive schemes in crowdsourcing,

    A. Khetan and S. Oh, “Achieving budget-optimality with adaptive schemes in crowdsourcing,” inAdvances in Neural Information Processing Systems, vol. 29, 2016

    2016

  62. [62]

    A permutation- based model for crowd labeling: Optimal estimation and robustness,

    N. B. Shah, S. Balakrishnan, and M. J. Wainwright, “A permutation- based model for crowd labeling: Optimal estimation and robustness,”arXiv preprint arXiv:1606.09632, 2016

    arXiv 2016

  63. [63]

    Estimation from pairwise comparisons: Sharp min- imax bounds with topology dependence,

    N. B. Shah, S. Balakrishnan, J. Bradley, A. Parekh, K. Ramchandran, and M. J. Wainwright, “Estimation from pairwise comparisons: Sharp min- imax bounds with topology dependence,”Journal of Machine Learning Research, vol. 17, no. 58, pp. 1–47, 2016

    2016

  64. [64]

    FA*IR: A fair top-k ranking algorithm,

    M. Zehlike, F. Bonchi, C. Castillo, S. Hajian, M. Megahed, and R. Baeza- Yates, “FA*IR: A fair top-k ranking algorithm,” inProceedings of the 26th ACM on International Conference on Information and Knowledge Man- agement, 2017, pp. 1569–1578

    2017

  65. [65]

    Fairness of exposure in rankings,

    A. Singh and T. Joachims, “Fairness of exposure in rankings,” inProceed- ings of the 24th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining, 2018, pp. 2219–2228

    2018

  66. [66]

    Equity of attention: Amor- tizing individual fairness in rankings,

    A. J. Biega, K. P. Gummadi, and G. Weikum, “Equity of attention: Amor- tizing individual fairness in rankings,” inThe 41st International ACM SIGIR Conference on Research & Development in Information Retrieval, 2018, pp. 405–414

    2018

  67. [67]

    M´ emoire sur les ´ elections au scrutin,

    J.-C. de Borda, “M´ emoire sur les ´ elections au scrutin,”Histoire de l’Acad´ emie Royale des Sciences, vol. 1, pp. 657–665, 1781

  68. [68]

    Rank aggregation methods for the web,

    C. Dwork, R. Kumar, M. Naor, and D. Sivakumar, “Rank aggregation methods for the web,” inProceedings of the 10th International Conference on World Wide Web, ACM, 2001, pp. 613–622

    2001

  69. [69]

    Schopenhauer,Parerga and paralipomena: Short philosophical essays

    A. Schopenhauer,Parerga and paralipomena: Short philosophical essays. Oxford University Press, 2000, vol. 1

    2000

  70. [70]

    Scaling personalized web search,

    G. Jeh and J. Widom, “Scaling personalized web search,” inProceedings of the 12th international conference on World Wide Web, 2003, pp. 271–279

    2003

  71. [71]

    Wtf: The who to follow service at twitter,

    P. Gupta, A. Goel, J. Lin, A. Sharma, D. Wang, and R. Zadeh, “Wtf: The who to follow service at twitter,” inProceedings of the 22nd international conference on World Wide Web, ACM, 2013, pp. 505–514

    2013

  72. [72]

    Node2vec: Scalable feature learning for net- works,

    A. Grover and J. Leskovec, “Node2vec: Scalable feature learning for net- works,” inProceedings of the 22nd ACM SIGKDD international conference on Knowledge discovery and data mining, 2016, pp. 855–864. 250

    2016

  73. [73]

    GP Putnam’s Sons, 1919

    Voltaire,Voltaire in His Letters: Being a Selection from His Correspon- dence. GP Putnam’s Sons, 1919

    1919

  74. [74]

    My first summer in the sierra,

    J. Muir, “My first summer in the sierra,” inBritish Politics and the Envi- ronment in the Long Nineteenth Century, Routledge, 2023, pp. 291–296

    2023

  75. [75]

    The archetypes of the collective uncon- scious,

    C. G. Jung and R. F. C. Hull, “The archetypes of the collective uncon- scious,” inCollected works of CG Jung, Routledge, 2023, v7 90–v7 113

    2023

  76. [76]

    de Saint-Exup´ ery,The Little Prince

    A. de Saint-Exup´ ery,The Little Prince. Reynal & Hitchcock, 1943

    1943

  77. [77]

    O. E. Butler,Parable of the Sower. Four Walls Eight Windows, 1993

    1993

  78. [78]

    Deep reinforcement learning from human preferences,

    P. F. Christiano, J. Leike, T. Brown, M. Martic, S. Legg, and D. Amodei, “Deep reinforcement learning from human preferences,”Advances in neural information processing systems, vol. 30, 2017

    2017

  79. [79]

    The rise and potential of large language model based agents: A survey,

    Z. Xi, W. Chen, X. Guo, W. He, Y. Ding, B. Hong, M. Zhang, J. Wang, S. Jin, E. Zhou, et al., “The rise and potential of large language model based agents: A survey,”Science China Information Sciences, vol. 68, no. 2, p. 121 101, 2025. 251

    2025