Pith. sign in

REVIEW 3 major objections 9 minor 66 references

Audits Under Resource, Data, and Access Constraints: Scaling Laws For Less Discriminatory Alternatives

T0 review · 3 major / 9 minor · reviewed 2026-08-15 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read This paper derives a closed-form upper bound on the loss–fairness Pareto frontier that claimants can fit with small models and extrapolate to a large contested model.

desk verdict A genuinely novel idea for low-resource LDA audits, but the main theorem as written has a load-bearing proof gap that needs fixing before this is citable. read the letter →

arxiv 2509.05627 v1 pith:536N5NJN submitted 2025-09-06 cs.CY cs.LGstat.ML

Sarah H. Cen , Salil Goyal , Zaynah Javed , Ananya Karthik , Percy Liang , Daniel E. Ho This is my paper · ORCID
classification cs.CYcs.LGstat.ML
keywords lessdiscriminatoryalternativeParetofrontierscalinglawdemographicparitybinarycross-entropylossAIauditresource-informationasymmetryfairness-performancetrade-off
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper tackles the burden of proof in "less discriminatory alternative" (LDA) claims, where a plaintiff must show that a less discriminatory model with comparable performance exists. It reframes that question as locating the loss–fairness Pareto frontier: if the contested model sits far from the frontier, such an alternative exists. The main result is a closed-form upper bound on the frontier as a function of the fairness gap, with constants that depend on model class, data size, and test distribution. The central move is to read the bound as a scaling law, so a claimant can fit it by training as few as seven small models on a small data subsample and extrapolate the frontier for the contested large model. A sympathetic reader would care because this gives a low-resource, low-information route to evidence in disputes where the model and training data are shielded as trade secrets.

What carries the argument

The machine is Lemma 4.1, the tilted-loss decomposition: $L(p,\hat f)=(L(q,\hat f)-L(q,q^{\mathrm{Bayes}}))+\mathbb{E}_{p}[\mathrm{KL}(p_{Y|X,A}\Vert q_{Y|X,A})]+L(p,p^{\mathrm{Bayes}})$, valid when the expected log-likelihood ratio $\mathbb{E}_p[S]$ equals $\mathbb{E}_q[S]$. Assumption 4.2 converts the first term into a constant $c_1(F,D)$ and imposes a group-symmetric offset, so a Pareto-optimal classifier can be treated as the Bayes estimator of an artificial distribution $q_\zeta$; then Chebyshev's association inequality makes the KL term an upper bound instead of an exact expression. The remaining constants $c,c',c''$ depend only on the test distribution, which is what permits the frontier to be fitted at small scale and extrapolated in model size and data.

What would settle it

Train a large model on a real dataset where the sensitive attribute correlates with features, trace the empirical Pareto frontier with linear scalarization, fit the seven constants using only small models and a data subsample, and check whether any empirically found Pareto-optimal point of the large model lies above the extrapolated curve; if it does, the claimed upper bound is violated.

Watch

Extended reading notes

Core claim

Under the data generating process $A\sim\mathrm{Ber}(\pi)$, $X\perp A$, and $Y|X,A\sim\mathrm{Ber}(\sigma(g(X)-\zeta A))$, with demographic parity as the fairness measure and binary cross-entropy as the loss, every Pareto-optimal classifier satisfies the upper bound $L(p,\hat f)\le B(F,D)-c c'\log(1-c''+\Delta)-c(1-c')\log(c''-\Delta)$ plus a variance-correction term and an $\varepsilon$ remainder. The paper derives the bound by decomposing the loss with an artificial tilted distribution $q_\zeta$, using a symmetry assumption on misspecification loss to replace each Pareto-optimal classifier by the Bayes-optimal classifier of the tilted distribution, and letting a non-negative covariance produce the inequality. Because only $B(F,D)$ depends on the model class and dataset size, and because established neural scaling laws give $B(F,D)\sim C_1+C_2/N^{C_3}+C_2/D^{C_4}$, the claimant can fit the constants on small models and extrapolate to the contested model without training it. The synthetic experiments relax the independence assumption and still find the fitted curves track empirical Pareto frontiers, which the paper reads as stress-testing support for the scaling law.

Load-bearing premise

The bound collapses if a Pareto-optimal classifier does not have the same expected log-likelihood distance to every tilted Bayes-optimal distribution used along the frontier, because the proof requires $\mathbb{E}_p[S]=\mathbb{E}_q[S]$ and Assumption 4.2 only states constant misspecification loss and a group-offset equality.

Editorial extensions

If this is right

  • A claimant can estimate the Pareto frontier for a large contested model using a small subsample of training data, test data, an estimate of the model's parameter count, and an estimate of its training-data size, without training any large model.
  • If the contested model's point lies at least $\delta$ above the extrapolated frontier, an LDA that preserves loss and shrinks the fairness gap by at least $\delta$ is feasible, turning the legal LDA step into a quantitative computation.
  • The same formula can be inverted to report the parameter count and data size the defendant would need to reach a given loss-fairness pair, so the claimant can argue that the alternative was within the defendant's reasonable reach.
  • The estimate is conservative by construction: empirical frontiers use only observed models and Theorem 4.3 is an upper bound, so a claim of $\delta$-feasibility is a lower bound on the true distance from the frontier.
  • The procedure is plug-and-play: any improvement in algorithms that trace Pareto-optimal models directly sharpens the fitted frontier and strengthens the claimant's evidence.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The split between scale-dependent $B(F,D)$ and shape constants $c,c',c''$ suggests the shape of the loss-fairness frontier may transfer across similar tasks; if that holds, fitting the shape once and adjusting only the scale could cut audit costs further.
  • The derivation's core is the Lemma 4.1 decomposition, so a parallel treatment of other fairness metrics or loss functions is a plausible extension even though the paper only proves the demographic-parity, binary-cross-entropy case.
  • The experiments violate the theorem's independence condition yet still fit, hinting that the operative assumption is the constant-misspecification symmetry on Pareto-optimal models rather than $X\perp A$; this is testable by comparing fits under manipulated covariate-group correlations.
  • A direct untested extension would apply the scaling law when train and test distributions differ, since the paper's experiments keep them identical; the behaviour of the bounds under distribution shift would decide how broadly the procedure works in practice.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 9 minor

Summary. The manuscript addresses the resource-information asymmetry confronting claimants who must prove the existence of a less discriminatory alternative (LDA) in US anti-discrimination litigation. The authors recast the LDA inquiry as locating the performance-fairness Pareto frontier (PF) and contribute a closed-form upper bound (Theorem 4.3, Eq. (4)) for the binary cross-entropy loss of Pareto-optimal classifiers as a function of the demographic-parity gap, under a specific data-generating process (A~Ber(pi), X independent of A, Y|X,A ~ Ber(sigma(g(X)-zeta A))) and a model-misspecification-symmetry assumption (Assumption 4.2). They propose using this bound as a scaling law: fit the constants c, c', c'' (claimed to depend only on the test distribution) and B(F,D) on small models, then extrapolate the PF to the contested large model using B(F,D) = C1 + C2/(N^-)^C3 + C2/(D^-)^C4, a form borrowed from language-model scaling laws. Synthetic experiments (Section 6.2, Figures 6 and 10-13) fit the closed form to empirical frontiers of MLPs of four sizes and report that the scaling law holds even when X perpendicular to A is relaxed. The paper is clearly written and unusually candid about its limitations. The central question is whether Theorem 4.3 is proven from the stated assumptions; on reading Appendix D together with Lemma 4.1, I find that the stress-test concern is real: the lemma's condition E_p[S] = E_q[S] is not implied by Assumption 4.2, so Eq. (4) does not follow as written.

Significance. If Theorem 4.3 could be established under a defensible assumption, the contribution would be significant: it would provide, to the best of my knowledge, the first closed-form performance-fairness Pareto frontier for the BCE/demographic-parity setting, and the claim that the shape constants c, c', c'' are independent of model class and dataset size is a sharp, falsifiable prediction that the experiments are designed to test. The legal framing is careful, the idea of replacing 'train an LDA' with 'locate the PF via a scaling law' is genuinely useful, and Section 8's limitations list is honest about the borrowed B-form, the synthetic-only experiments, and the upper-bound nature of the result. These strengths are real. However, the proof gap in Theorem 4.3 and the uncontrolled Taylor remainder in Lemma B.3 mean the central claim is not established as written, and the experiment section as currently reported does not convincingly demonstrate the extrapolation protocol because the fitted constants are not identifiable. Because all three problems are local and fixable within the manuscript's scope, the appropriate recommendation is major revision.

major comments (3)
  1. [§4.2 / Appendix D; Assumption 4.2; §4.1] Theorem 4.3 invokes Lemma 4.1 in Step 1 of its proof, but the lemma's statement requires E_{pX,A,Y}[S] = E_{qX,A,Y}[S] for the specific classifier fhat under evaluation, and this condition is not implied by Assumption 4.2 as printed. The first clause of Assumption 4.2, L(q, fhat) - L(q, q_Bayes) = c1(F,D), is equivalent to E_q[S] = c1(F,D) for the classifier that minimizes L(q,·) for that q; applied with q = p it gives E_p[S] = c1(F,D) for the classifier trained on p, which is generally a different model from the Pareto-optimal classifier trained on the tilted distribution q_zeta. The second clause is a first-moment group-offset equality and does not constrain the p-weighted log-ratio S. Consequently E_p[S] = E_{q_zeta}[S] is neither stated nor proven; without it, the terms (5) and (7) in the proof of Lemma 4.1 need not cancel, so equation (4) does not follow from the stated assumptions. The sentence in Section 4.1 that Assumption 4.2 'implicitly asks that this condition hold' does not repair the gap, because the required equality must hold for the same model under two distributions, not merely be constant across the family of fitted models, and the synthetic experiments in Section 6.2 never check the equality for trained models. This is load-bearing, since the Section 5 extrapolation procedure uses exactly this bound.
  2. [Appendix B, Lemma B.3] The claimed remainder bound in Lemma B.3 is not justified. For f(z) = log(1-z), the third derivative f'''(z) = -2/(1-z)^3 is unbounded on (0,1), so the Lagrange remainder (Z-mu)^3/(3(1-xi)^3), with xi between mu and Z, cannot be bounded by a constant times (Z-mu)^3 uniformly; the analogous statement for E[log Z] fails near z = 0. The claimed O(E[(Z-E[Z])^3]) therefore requires an additional assumption such as Z bounded away from 0 and 1. In the DGP of Theorem 4.3, the role of Z is played by q_zeta(1|x,1) = sigma(g(x)-zeta), which is not bounded away from 1 unless g is bounded above, a condition the paper does not impose. As a result, the epsilon term in equation (4) is not established as stated.
  3. [§6.2, Figures 6, 10-13; §5] The experiments do not demonstrate the small-to-large extrapolation protocol claimed in Section 5. Figures 6, 10, and 12 fit the constants to the empirical frontiers of all four model sizes jointly, which checks whether one set of shape constants explains every size but is not the proposed extrapolation; only Figures 11 and 13 fit to the small-model curve and extrapolate, and they do so qualitatively. The paper itself states that 'there were many possible fits,' and for the same (pi = 0.2, zeta = 0.5) data the reported constants differ materially (Figure 10: C2 = 55, C3 = 0.7, c = 0.16; Figure 11: C2 = 150, C3 = 0.8, c = 0.12; Figure 6: c = 0.0176). This non-identifiability is load-bearing: if the low-resource fits do not pin down the constants, the extrapolated PF at (N+, D+) is not well determined. In addition, the abstract's claim that 'as few as 7 (small) models' suffice to fit the scaling law is not tested anywhere, since the experiments train 300 models per model size.
minor comments (9)
  1. [Abstract] The abstract contains 'need totraina less discriminatory yet high-performing model'; 'totraina' is missing a space.
  2. [§4.1] 'Kullback-Liebler' should be 'Kullback-Leibler'.
  3. [Throughout] Assumption 4.2 is repeatedly referred to as 'Theorem 4.2' (Theorem 4.3 statement, Appendix D Step 1, Section 6.2, and the paragraph immediately after the assumption); the numbering should be made consistent.
  4. [§5, Step 3] The scaling-law formula uses C2 for both the N^{-C3} and D^{-C4} terms, whereas the preceding text justifies the form Theta(1/N^alpha + 1/D^beta), which requires independent coefficients; if the shared coefficient is intentional, it should be justified.
  5. [Appendices C and D] Items from Appendix B are called 'Theorem B.1' through 'Theorem B.4' in the proofs of Lemma 4.1 and Theorem 4.3, but they are stated as lemmas.
  6. [Appendix C] The proof of Lemma 4.1 uses H to denote the BCE loss, while the rest of the paper uses L; the notation should be unified.
  7. [Figure 7 caption] The caption appears garbled: 'for fixed values of c'' = C7 = 0.9 and c'' = 0.8 while varying c' repeats c'' twice; the captions of Figures 7-9 should be checked.
  8. [§6.2] The empirical PF is traced with linear scalarization L_BCE + lambda * L_DP, while the theory is built on tilting the distribution q_zeta; the correspondence between lambda and zeta is never established, so the connection between the experimental points and the theorem's assumptions remains indirect.
  9. [§4.1, 'Understanding the condition on fhat'] The discussion states that Assumption 4.2 implies E_q[S] is constant, but the lemma's condition is E_p[S] = E_q[S] for the same classifier; the text should address the stronger condition explicitly (related to major comment 1).

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity; the paper's derivation and extrapolation procedure are self-contained or explicitly assume their inputs.

full rationale

I walked the derivation chain and found no step that reduces to its own inputs. Theorem 4.3 is derived from Lemma 4.1, a telescoping loss decomposition, together with the stated data-generating process and Assumption 4.2; the proof does not presuppose the closed-form bound it claims. Lemma 4.1 explicitly states its required condition E_p[S]=E_q[S], and the paper's comment that Assumption 4.2 'implicitly asks that this condition hold' (Section 4.1) is a claim about the assumption's coverage, not a hidden use of the theorem's conclusion. Even if one doubts whether Assumption 4.2 as written formally implies that condition, that is a proof-formality or correctness concern, not circularity: the condition is not the quantity being predicted. The scaling-law application in Section 5 fits C1 through C7 to the empirical frontier of small models and then extrapolates to N+ and D+; the contested large-model frontier is not used to fit the constants, so the extrapolation is a genuine prediction conditional on the functional form. The form of B is explicitly borrowed from external scaling-law literature rather than derived in the paper, and the paper itself flags this in Limitation 6 ('the form of B that we adopt is borrowed from the literature on large language models'); an imported empirical ansatz is an input, not a circular conclusion. The self-citations present, e.g., Cen and Alur [17] and Raji et al. [51], are background references on AI auditing and are not load-bearing for the mathematical claim. The paper also candidly reports multiple possible fits to the same empirical data, which weakens empirical confidence but does not make the derivation circular. Accordingly, no circular step meets the evidentiary bar of quoting an equation or construction that is equivalent to its inputs.

Assumptions & free parameters 7 free parameters · 6 assumptions · 0 invented entities

The paper does not introduce new physical entities. Its load-bearing assumptions are the misspecification-symmetry assumption, the implicit Lemma 4.1 condition, the logistic DGP, the tilting duality, and the borrowed scaling form for B(F,D). In the practical procedure, seven constants are fitted to empirical frontiers, and the paper reports non-unique fits.

free parameters (7)
  • C1 (additive loss offset) = -0.285 in Figure 6; -1.205 in Figure 11
    Fitted to the empirical Pareto frontier; the paper reports different values for different equally good fits.
  • C2 (scaling-law scale) = 55 in Figure 6; 150 in Figure 11
    Fitted scale for the N and D scaling terms in B(F,D); not derived from first principles.
  • C3 (exponent on N) = 0.7 in Figure 6; 0.8 in Figure 11
    Set by fitting or by the common 0.5 default; the paper says C3 and C4 are often set to 0.5, but experiments use other values.
  • C4 (exponent on D) = 0.5
    Set to 0.5 by default in the paper's examples.
  • C5, c (distribution-dependent shape constant) = 0.0176 in Figure 6; 0.12 in Figure 11
    Fitted to the empirical frontier; the paper explicitly says there are many possible fits.
  • C6, c' (distribution-dependent shape constant) = 0.92 in Figure 6; 0.11 in Figure 10
    Fitted shape constant; varies across reported fits.
  • C7, c'' (distribution-dependent shape constant) = 0.1424 in Figure 6; 0.92 in Figure 10
    Fitted shape constant; varies across reported fits.
assumptions (6)
  • ad hoc to paper Assumption 4.2, model misspecification symmetry: L(q,fhat) - L(q,q_Bayes) is a constant c1(F,D) independent of q, and the group offsets E[fhat|A=0]-E[q_Bayes|A=0] and E[fhat|A=1]-E[q_Bayes|A=1] are equal.
    This is the main model-class assumption that lets the proof treat misspecification loss as a constant; it is not a standard theorem and is asserted for the paper's setting.
  • ad hoc to paper Lemma 4.1 condition: E_p[S] = E_q[S] for the log-likelihood-ratio statistic S and every artificial distribution q used in Theorem 4.3.
    This condition is required by Lemma 4.1 and is invoked in the proof of Theorem 4.3, but it is not stated in Assumption 4.2 and is not derived from it.
  • domain assumption Data generating process: A ~ Ber(pi), X independent of A, and Y|X,A ~ Ber(sigma(g(X) - zeta A)) for zeta >= 0; the test distribution p is q_{zeta_p} for fixed zeta_p.
    The closed-form bound is derived only for this logistic, additive DGP. The independence of X and A is relaxed in experiments but not in the theorem.
  • ad hoc to paper Constrained fairness minimization can be represented as unconstrained loss minimization under a tilted artificial distribution q_zeta.
    This duality is the key proof technique described in Section 4.2; it is tested empirically but not proven in the paper.
  • domain assumption B(F,D), the constant frontier offset, scales as C1 + C2/N^C3 + C2/D^C4 with constants borrowed from large-language-model scaling laws.
    The paper adopts the form from prior empirical scaling-law work rather than deriving it for the fairness frontier. The exponents are fitted or set by hand.
  • standard math Chebyshev's association inequality and Taylor expansions of log(1-Z) with third-order remainder terms.
    Used in Lemmas B.2 and B.3; the Taylor remainder is treated as O(...) without uniform control of its sign.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Audits Under Resource, Data, and Access Constraints: Scaling Laws For Less Discriminatory Alternatives." pith.science (2026). https://pith.science/paper/536N5NJN

@misc{pith2026250905627,
  author       = {Pith},
  title        = {Pith review of: Audits Under Resource, Data, and Access Constraints: Scaling Laws For Less Discriminatory Alternatives},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/536N5NJN}},
  note         = {Machine review of arXiv:2509.05627}
}
read the original abstract

AI audits play a critical role in AI accountability and safety. One branch of the law for which AI audits are particularly salient is anti-discrimination law. Several areas of anti-discrimination law implicate the "less discriminatory alternative" (LDA) requirement, in which a protocol (e.g., model) is defensible if no less discriminatory protocol that achieves comparable performance can be found with a reasonable amount of effort. Notably, the burden of proving an LDA exists typically falls on the claimant (the party alleging discrimination). This creates a significant hurdle in AI cases, as the claimant would seemingly need to train a less discriminatory yet high-performing model, a task requiring resources and expertise beyond most litigants. Moreover, developers often shield information about and access to their model and training data as trade secrets, making it difficult to reproduce a similar model from scratch. In this work, we present a procedure enabling claimants to determine if an LDA exists, even when they have limited compute, data, information, and model access. We focus on the setting in which fairness is given by demographic parity and performance by binary cross-entropy loss. As our main result, we provide a novel closed-form upper bound for the loss-fairness Pareto frontier (PF). We show how the claimant can use it to fit a PF in the "low-resource regime," then extrapolate the PF that applies to the (large) model being contested, all without training a single large model. The expression thus serves as a scaling law for loss-fairness PFs. To use this scaling law, the claimant would require a small subsample of the train/test data. Then, the claimant can fit the context-specific PF by training as few as 7 (small) models. We stress test our main result in simulations, finding that our scaling law holds even when the exact conditions of our theory do not.

Figures

Figures reproduced from arXiv: 2509.05627 by the authors.

Figure 1
Figure 1. (a) Consider the contested AI model, as given by the “X” on the loss vs. fairness gap plane. As described in Section 2, there are two steps in a disparate impact case before the less discriminatory alternatives (LDA) step. In the first step, the claimant establishes that there is disparate impact, typically by pointing to a statistical measure of discrimination (the fairness gap). Thus, the first step identifies the… view at source ↗
Figure 2
Figure 2. An illustration of the proposed method on the left and how it addresses the resource-information asymmetry on the right, as explained in Section 2. 4. Finally, the plaintiff considers establishing the existence of an LDA by characterizing the range of possible classifiers, in the same spirit as analyses in [24, 40], but discovers these approaches work well on finite-dimensional, categorical inputs but not on unstruc… view at source ↗
Figure 3
Figure 3. Simulations showing the shape of the closed-form expression for the Pareto frontier given in Theorem 4.3 for fixed values of c ′ = 0.5 and c ′′ = 0.8 while varying c. The left plot shows the precise closed-form, which is the lowest achievable loss among classifiers that have exactly the fairness gap value on the x-axis. The right plot shows lowest achievable loss among classifiers that satisfy the fairness gap budge… view at source ↗
Figures from the paper (10 more)
Figure 4
Figure 4. Figure 4: Simulations showing the shape of the closed-form expression for the Pareto frontier given in Theorem 4.3 for fixed values of c = 0.2 and c ′′ = 0.8 while varying c ′ . The left plot shows the precise closed-form, which is the lowest achievable loss among classifiers th…
Figure 5
Figure 5. Figure 5: Simulations showing the shape of the closed-form expression for the Pareto frontier given in Theorem 4.3 for fixed values of c = 0.2 and c ′ = 0.8 while varying c ′′. The left plot shows the precise closed-form, which is the lowest achievable loss among classifiers tha…
Figure 6
Figure 6. Figure 6: Pareto frontier for different model sizes under (π = 0.2) and bias strength ζ = 0.5. Each point corresponds to a trained model with a different fairness regularization weight λ. The dashed lines show the empirical Pareto frontier, created by finding the lower convex hu…
Figure 7
Figure 7. Figure 7: Simulations showing the shape of the closed-form expression for the Pareto frontier given in Theorem 4.3 for fixed values of c ′′ = C7 = 0.9 and c ′′ = 0.8 while varying c. The left plot shows the precise closed-form, which is the lowest achievable loss among classifie…
Figure 8
Figure 8. Figure 8: Simulations showing the shape of the closed-form expression for the Pareto frontier given in Theorem 4.3 for fixed values of c = 0.2 and c ′′ = 0.6 while varying c ′ . The left plot shows the precise closed-form, which is the lowest achievable loss among classifiers th…
Figure 9
Figure 9. Figure 9: Simulations showing the shape of the closed-form expression for the Pareto frontier given in Theorem 4.3 for fixed values of c = 0.2 and c ′′ = C7 = 0.5 while varying c ′′. The left plot shows the precise closed-form, which is the lowest achievable loss among classifie…
Figure 10
Figure 10. Figure 10: Pareto frontier for different model sizes under (π = 0.2) and bias strength ζ = 0.5. Each point corresponds to a trained model with a different fairness regularization weight λ. The dashed lines show the empirical Pareto frontier, created by finding the lower convex h…
Figure 11
Figure 11. Figure 11: Pareto frontier for different model sizes under (π = 0.2) and bias strength ζ = 0.5. Each point corresponds to a trained model with a different fairness regularization weight λ. The dashed lines show the empirical Pareto frontier, created by finding the lower convex h…
Figure 12
Figure 12. Figure 12: Pareto frontier for different model sizes under (π = 0.4) and bias strength ζ = 2. Each point corresponds to a trained model with a different fairness regularization weight λ. The dashed lines show the empirical Pareto frontier, created by finding the lower convex hul…
Figure 13
Figure 13. Figure 13: Pareto frontier for different model sizes under (π = 0.4) and bias strength ζ = 2. Each point corresponds to a trained model with a different fairness regularization weight λ. The dashed lines show the empirical Pareto frontier, created by finding the lower convex hul…

Review history (2 revisions) →

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

66 extracted references · 48 canonical work pages

  1. [1]

    URL http://www.jstor.org/ stable/1341935

    The Civil Rights Act of 1991 and Less Discriminatory Alternatives in Disparate Impact Lit- igation.Harvard Law Review, 106(7):1621–1638, 1993. URL http://www.jstor.org/ stable/1341935

    work page arXiv 1991

  2. [2]

    Loomis: Wisconsin Supreme Court Requires Warning Before Use of Al- gorithmic Risk Assessments in Sentencing.Harvard Law Review, 130(5):1530–1537, Mar

    Note, State v. Loomis: Wisconsin Supreme Court Requires Warning Before Use of Al- gorithmic Risk Assessments in Sentencing.Harvard Law Review, 130(5):1530–1537, Mar. 2017. URL https://harvardlawreview.org/wp-content/uploads/2017/03/ 1530-1537_online.pdf

    work page 2017

  3. [3]

    SAS Analytics Inc., January 2019

    Cahoo v. SAS Analytics Inc., January 2019

    work page 2019

  4. [4]

    Unemployment Insurance Agency, July 2022

    Bauserman v. Unemployment Insurance Agency, July 2022

    work page 2022

  5. [5]

    Complaint and Request for Investigation, Injunction, and Other Relief Submitted by the Elec- tronic Privacy Information Center (EPIC), January 2024

    work page 2024

  6. [6]

    Agarwal, A

    A. Agarwal, A. Beygelzimer, M. Dudík, J. Langford, and H. Wallach. A reductions approach to fair classification. InInternational conference on machine learning, pages 60–69. PMLR, 2018. 18

    work page 2018

  7. [7]

    Bahri, E

    Y . Bahri, E. Dyer, J. Kaplan, J. Lee, and U. Sharma. Explaining neural scaling laws.Proceedings of the National Academy of Sciences, 121(27):e2311878121, 2024

    work page 2024

  8. [8]

    Barocas and A

    S. Barocas and A. D. Selbst. Big Data’s Disparate Impact.California Law Review, 104(3): 671–732, 2016. doi: 10.15779/Z38BG31. URL https://www.cs.yale.edu/homes/jf/ BarocasSelbst.pdf

    doi:10.15779/z38bg31 2016

Show all 66 references
  1. [9]

    Bastress, Robert M

    J. Bastress, Robert M. The Less Restrictive Alternative in Constitutional Adjudication: An Analysis, a Justification, and Some Criteria.Vanderbilt Law Review, 27(5):971–1006, 1974. URLhttps://scholarship.law.vanderbilt.edu/vlr/vol27/iss5/3

    1974

  2. [10]

    Bertsimas, V

    D. Bertsimas, V . F. Farias, and N. Trichakis. The price of fairness.Operations research, 59(1): 17–31, 2011

    2011

  3. [11]

    Black, L

    E. Black, L. Koepke, P. Kim, S. Barocas, and M. Hsu. The Legal Duty to Search for Less Discriminatory Algorithms.arXiv preprint arXiv:2406.06817, 2024

    2024 arXiv

  4. [12]

    A. W. Blumrosen. Strangers in Paradise: Griggs v. Duke Power Co. and the Concept of Employment Discrimination.Michigan Law Review, 71(1):59–110, 1972

    1972

  5. [13]

    Boucheron, G

    S. Boucheron, G. Lugosi, and P. Massart. Basic Inequalities. InConcentration Inequalities: A Nonasymptotic Theory of Independence. Oxford University Press, online edition edition,

  6. [14]

    Brown, J

    S. Brown, J. Davidovic, and A. Hasan. The algorithm audit: Scoring the algorithms that score us.Big Data & Society, 8(1):2053951720983865, 2021

    2021

  7. [15]

    F. P. Calmon, D. Wei, B. Vinzamuri, K. N. Ramamurthy, and K. R. Varshney. Optimized pre- processing for discrimination prevention. InProceedings of the 31st International Conference on Neural Information Processing Systems, NIPS’17, pages 3995–4004, Red Hook, NY , USA,

  8. [16]

    Casper, C

    S. Casper, C. Ezell, C. Siegmann, N. Kolt, T. L. Curtis, B. Bucknall, A. Haupt, K. Wei, J. Scheurer, M. Hobbhahn, et al. Black-box access is insufficient for rigorous ai audits. In Proceedings of the 2024 ACM Conference on Fairness, Accountability, and Transparency, pages 2254...

    2024

  9. [17]

    S. H. Cen and R. Alur. From Transparency to Accountability and Back: A Discussion of Access and Evidence in AI Auditing. InProceedings of the 4th ACM Conference on Equity and Access in Algorithms, Mechanisms, and Optimization, pages 1–14, 2024

    2024

  10. [18]

    Chouldechova

    A. Chouldechova. Fair prediction with disparate impact: A study of bias in recidivism prediction instruments.Big data, 5(2):153–163, 2017

    2017

  11. [19]

    Chzhen and N

    E. Chzhen and N. Schreuder. A minimax framework for quantifying risk-fairness trade-off in regression.The Annals of Statistics, 50(4):2416–2442, 2022

    2022

  12. [20]

    Costanza-Chock, I

    S. Costanza-Chock, I. D. Raji, and J. Buolamwini. Who Audits the Auditors? Recommendations from a field scan of the algorithmic auditing ecosystem. InProceedings of the 2022 ACM Conference on Fairness, Accountability, and Transparency, pages 1571–1583, 2022

    2022

  13. [21]

    Feldman, S

    M. Feldman, S. A. Friedler, J. Moeller, C. Scheidegger, and S. Venkatasubramanian. Certifying and Removing Disparate Impact. InProceedings of the 21th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, KDD ’15, pages 259–268, New York, NY , USA, 2015. ...

    2015

  14. [22]

    Franzese, A

    O. Franzese, A. S. Shamsabadi, and H. Haddadi. OATH: Efficient and Flexible Zero-Knowledge Proofs of End-to-End ML Fairness.arXiv preprint arXiv:2410.02777, 2024. 19

    2024

  15. [23]

    Friedler, S

    S. Friedler, S. Choudhary, C. Scheidegger, E. Hamilton, S. Venkatasubramanian, and D. Roth. A comparative study of fairness-enhancing interventions in machine learning. InFAT* 2019 - Proceedings of the 2019 Conference on Fairness, Accountability, and Transparency, FAT* 2019 - ...

    2019

  16. [24]

    T. B. Gillis, V . Meursault, and B. Ustun. Operationalizing the search for less discriminatory alter- natives in fair lending. InProceedings of the 2024 ACM Conference on Fairness, Accountability, and Transparency, pages 377–387, 2024

    2024

  17. [25]

    E. P. Goodman and J. Trehu. Algorithmic auditing: Chasing AI accountability.Santa Clara High Tech. LJ, 39:289, 2022

    2022

  18. [26]

    S. S. Grover. The Business Necessity Defense in Disparate Impact Discrimination Cases. Georgia Law Review, 30(2):387–430, 1996

    1996

  19. [27]

    Hardt, E

    M. Hardt, E. Price, and N. Srebro. Equality of opportunity in supervised learning. InProceedings of the 30th International Conference on Neural Information Processing Systems, NIPS’16, pages 3323–3331, Red Hook, NY , USA, 2016. Curran Associates Inc. ISBN 9781510838819

    2016

  20. [28]

    C. I. Harris and K. West-Faulcon. Reading Ricci: Whitening Discrimination, Racing Test Fairness.UCLA Law Review, 58:73–150, 2009

    2009

  21. [29]

    Built-in Headwinds

    M. Hart. From Wards Cove to Ricci: Struggling Against the “Built-in Headwinds” of a Skeptical Court.Wake Forest Law Review, 46:261–278, 2011

    2011

  22. [30]

    D. Harwell. A face-scanning algorithm increasingly decides whether you deserve the job.The Washington Post, November 2019. URL https://www.washingtonpost.com/technology/2019/10/22/ ai-hiring-face-scanning-algorithm-increasingly-decides-whether-you-deserve-job/

    2019

  23. [31]

    Hestness, S

    J. Hestness, S. Narang, N. Ardalani, G. Diamos, H. Jun, H. Kianinejad, M. M. A. Patwary, Y . Yang, and Y . Zhou. Deep learning scaling is predictable, empirically.arXiv preprint arXiv:1712.00409, 2017

    2017 arXiv

  24. [32]

    Hoffmann, S

    J. Hoffmann, S. Borgeaud, A. Mensch, E. Buchatskaya, T. Cai, E. Rutherford, D. d. L. Casas, L. A. Hendricks, J. Welbl, A. Clark, et al. Training compute-optimal large language models. arXiv preprint arXiv:2203.15556, 2022

    2022 arXiv

  25. [33]

    C. C. Jones. Systematizing Discrimination: AI Vendors & Title VII Enforcement.University of Pennsylvania Law Review, 171(1):235–265, 2022. URL https://scholarship.law.upenn. edu/penn_law_review/vol171/iss1/6/

    2022

  26. [34]

    M. M. Kamani, R. Forsati, J. Z. Wang, and M. Mahdavi. Pareto Efficient Fairness in Supervised Learning: From Extraction to Tracing.arXiv preprint arXiv:2104.01634, 2021. URL https: //arxiv.org/abs/2104.01634

    2021 arXiv

  27. [35]

    Kamiran and T

    F. Kamiran and T. Calders. Data preprocessing techniques for classification without dis- crimination.Knowl. Inf. Syst., 33(1):1–33, Oct. 2012. ISSN 0219-1377. doi: 10.1007/ s10115-011-0463-8. URLhttps://doi.org/10.1007/s10115-011-0463-8

    2012 doi

  28. [36]

    Kaplan, S

    J. Kaplan, S. McCandlish, T. Henighan, T. B. Brown, B. Chess, R. Child, S. Gray, A. Rad- ford, J. Wu, and D. Amodei. Scaling laws for neural language models.arXiv preprint arXiv:2001.08361, 2020

    2001 arXiv

  29. [37]

    J. S. Kim, J. Chen, and A. Talwalkar. FACT: A diagnostic for group fairness trade-offs. In International Conference on Machine Learning, pages 5264–5274. PMLR, 2020

    2020

  30. [38]

    M. S. Lam, A. Pandit, C. H. Kalicki, R. Gupta, P. Sahoo, and D. Metaxa. Sociotechnical audits: Broadening the algorithm auditing lens to investigate targeted advertising.Proceedings of the ACM on Human-Computer Interaction, 7(CSCW2):1–37, 2023. 20

    2023

  31. [39]

    J. C. Lamber. Alternatives to Challenged Employee Selection Criteria: The Significance of Nonstatistical Evidence in Disparate Impact Cases Under Title VII.Wisconsin Law Review, pages 1–58, 1985

    1985

  32. [40]

    Laufer, M

    B. Laufer, M. Raghavan, and S. Barocas. Fundamental Limits in the Search for Less Discrimi- natory Algorithms–and How to Avoid Them.arXiv preprint arXiv:2412.18138, 2024

    2024 arXiv

  33. [41]

    Liu and L

    S. Liu and L. N. Vicente. Accuracy and fairness trade-offs in machine learning: a stochastic multi-objective approach.Computational Management Science, 19(3):513–537, 2022. doi: 10.1007/s10287-022-00425-z. URL https://link.springer.com/article/10.1007/ s10287-022-00425-z

    2022 doi

  34. [42]

    Longpre, S

    S. Longpre, S. Kapoor, K. Klyman, A. Ramaswami, R. Bommasani, B. Blili-Hamelin, Y . Huang, A. Skowron, Z.-X. Yong, S. Kotha, et al. A safe harbor for AI evaluation and red teaming.arXiv preprint arXiv:2403.04893, 2024

    2024 arXiv

  35. [43]

    A. K. Menon and R. C. Williamson. The cost of fairness in binary classification. In S. A. Friedler and C. Wilson, editors,Proceedings of the 1st Conference on Fairness, Accountability and Transparency, volume 81 ofProceedings of Machine Learning Research, pages 107–118. PMLR, ...

    2018

  36. [44]

    Metaxa, J

    D. Metaxa, J. S. Park, R. E. Robertson, K. Karahalios, C. Wilson, J. Hancock, C. Sandvig, et al. Auditing algorithms: Understanding algorithmic systems from the outside in.Foundations and Trends® in Human–Computer Interaction, 14(4):272–344, 2021

    2021

  37. [45]

    Insurance topics: Big data

    National Association of Insurance Commissioners. Insurance topics: Big data. https:// content.naic.org/insurance-topics/big-data

  38. [46]

    2023 Life Artificial Intelli- gence/Machine Learning Survey Report, December 2023

    National Association of Insurance Commissioners (NAIC). 2023 Life Artificial Intelli- gence/Machine Learning Survey Report, December 2023

    2023

  39. [47]

    Navon, A

    A. Navon, A. Shamsian, G. Chechik, and E. Fetaya. Learning the pareto front with hypernet- works.arXiv preprint arXiv:2010.04104, 2020

    2010 arXiv

  40. [48]

    Ojewale, R

    V . Ojewale, R. Steed, B. Vecchione, A. Birhane, and I. D. Raji. Towards AI accountability infrastructure: Gaps and opportunities in AI audit tooling. InProceedings of the 2025 CHI Conference on Human Factors in Computing Systems, pages 1–29, 2025

    2025

  41. [49]

    D. Ozkul. Automating Immigration and Asylum: The Uses of New Technolo- gies in Migration and Asylum Governance in Europe. Research report (algo- rithmic fairness for asylum seekers and refugees project), Refugee Studies Centre, University of Oxford, 2023. URL https://www.rsc.o...

    2023

  42. [50]

    I. D. Raji, A. Smart, R. N. White, M. Mitchell, T. Gebru, B. Hutchinson, J. Smith-Loud, D. Theron, and P. Barnes. Closing the AI accountability gap: Defining an end-to-end frame- work for internal algorithmic auditing. InProceedings of the 2020 conference on fairness, accounta...

    2020

  43. [51]

    I. D. Raji, P. Xu, C. Honigsberg, and D. Ho. Outsider oversight: Designing a third party audit ecosystem for ai governance. InProceedings of the 2022 AAAI/ACM Conference on AI, Ethics, and Society, pages 557–571, 2022

    2022

  44. [52]

    G. N. Rothblum and G. Yona. Consider the Alternatives: Navigating Fairness-Accuracy Tradeoffs via Disqualification.arXiv preprint arXiv:2110.00813, 2021

    2021 arXiv

  45. [53]

    Ruchte and J

    M. Ruchte and J. Grabocka. Scalable pareto front approximation for deep multi-objective learning. In2021 IEEE international conference on data mining (ICDM), pages 1306–1311. IEEE, 2021

    2021

  46. [54]

    Rutherglen

    G. Rutherglen. Disparate Impact, Discrimination, and the Essentially Contested Concept of Equality.Fordham Law Review, 74(4):2313–2338, 2006

    2006

  47. [55]

    M. Selmi. Was the Disparate Impact Theory a Mistake?UCLA Law Review, 53:701–782, 2006. 21

    2006

  48. [56]

    Singh, S

    G. Singh, S. Gupta, M. Lease, and C. Dawson. A Hybrid 2-stage Neural Optimization for Pareto Front Extraction.arXiv preprint arXiv:2101.11684, 2021

    2021 arXiv

  49. [57]

    Solaiman

    I. Solaiman. The gradient of generative AI release: Methods and considerations. InProceedings of the 2023 ACM conference on fairness, accountability, and transparency, pages 111–122, 2023

    2023

  50. [58]

    G. Tang, W. Tan, and M. Cai. Privacy-preserving and trustless verifiable fairness audit of ma- chine learning models.International Journal of Advanced Computer Science and Applications, 14(2), 2023

    2023

  51. [59]

    Terzis, M

    P. Terzis, M. Veale, and N. Gaumann. Law and the Emerging Political Economy of Algorith- mic Audits. InProceedings of the 2024 ACM Conference on Fairness, Accountability, and Transparency, pages 1255–1267, 2024

    2024

  52. [60]

    Waiwitlikhit, I

    S. Waiwitlikhit, I. Stoica, Y . Sun, T. Hashimoto, and D. Kang. Trustless audits without revealing data or models.arXiv preprint arXiv:2404.04500, 2024

    2024 arXiv

  53. [61]

    M. B. Zafar, I. Valera, M. G. Rogriguez, and K. P. Gummadi. Fairness constraints: Mechanisms for fair classification. InArtificial intelligence and statistics, pages 962–970. PMLR, 2017

    2017

  54. [62]

    X. Zeng, G. Cheng, and E. Dobriban. Bayes-optimal fair classification with linear disparity constraints via pre-, in-, and post-processing.arXiv preprint arXiv:2402.02817, 2024

    2024 arXiv

  55. [63]

    less ___ alternative

    I. Zliobaite. A survey on measuring indirect discrimination in machine learning.CoRR, abs/1511.00148, 2015. URLhttp://arxiv.org/abs/1511.00148. 22 A LDAs Beyond Employment Law The “less ___ alternative” requirement expands beyond employment to areas including housing, lend- in...

    2015 arXiv

  56. [338]

    Association for Computing Machinery, Inc, Jan. 2019. doi: 10.1145/3287560.3287589. Publisher Copyright: © 2019 Copyright held by the owner/author(s).; 2019 ACM Conference on Fairness, Accountability, and Transparency, FAT* 2019 ; Conference date: 29-01-2019 Through 31-01-2019

    2019

  57. [2013]

    URL https://doi.org/10.1093/ acprof:oso/9780199535255.003.0002

    doi: 10.1093/acprof:oso/9780199535255.003.0002. URL https://doi.org/10.1093/ acprof:oso/9780199535255.003.0002. Accessed: 2025-05-11

    2025

  58. [2017]

    ISBN 9781510860964

    Curran Associates Inc. ISBN 9781510860964

Pith tools

Reviewed August 15, 2026 · model on record in the stance chip above.