{"id":"21758414-e37c-4d4a-9e48-f557a35ec29f","arxiv_id":"2411.18122","paper_version":4,"verdict":"REJECT","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"high","formal_verification":"none","parameter_count":2,"one_line_summary":"A method that uses models trained on human decisions, after threshold recalibration to equalize a recall-precision ratio, to estimate group disparities in human true positive rates from a small disjoint gold-standard set.","lead":"This paper proposes a machine learning pipeline that estimates bias in human decisions, such as hiring or medical judgments, when only a small set of correct answers is available. It trains a separate model on each decision maker's history, adjusts those models to share a common error ratio, and then measures the adjusted models' error gaps across groups as a proxy for human bias.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"","rationale":"","tokens_in":25218,"tokens_out":4514,"duration_ms":40838,"concrete_test":"","verdict_should_be":"UNCHANGED","load_bearing_attack":"","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes MDBA, a machine-learning framework for estimating human decision bias (defined as group disparities in true positive rates) when gold standard labels are scarce and possibly disjoint from the instances labeled by the humans under evaluation. The method trains one predictive model per human on that human's historical decisions, post-processes each model by recalibrating group-specific thresholds to equalize a recall-versus-precision ratio (RPR) across models and groups, applies the recalibrated models to the gold-standard set, and then divides the resulting model bias gap by the common RPR constant c to recover the human bias. The manuscript claims theoretical guarantees (Lemma, Theorem 1, Theorem 2) and reports extensive simulation experiments on four public datasets showing that MDBA outperforms selection rates, a gold-standard-based model, and confident learning.","tokens_in":25132,"tokens_out":5702,"duration_ms":53248,"significance":"The problem is important and timely: measuring bias in human decisions without full gold-standard labels has broad applications in healthcare, hiring, and crowdsourcing. The proposed pipeline is intuitively appealing, and the authors provide a reproducible simulation framework and code, which is a strength. However, the central theoretical claim is not sustained: the proof of the Lemma rests on an assertion that correct functional form implies the trained model is a deterministic copy of the human decision, which is false, and this invalidates the derived equality in Theorem 2. The empirical evaluation is explicitly conducted under conditions that violate the theoretical assumptions, so the experiments do not validate the theorems and instead function as evidence for a heuristic. If the theoretical claims were corrected or appropriately weakened, the empirical framework could serve as a useful benchmark for future work, but as stated the paper's core contribution is not supported.","major_comments":[{"comment":"The proof asserts 'Given the correct functional form for fk : Xk -> Y'_k then Yhat_k = Y'_k + epsilon' and from this concludes Yhat_k ⊥ Y_k | Y'_k. Correct functional form means the chosen model class contains the true decision function; it does not imply that the estimated model is a deterministic copy of the human decision, nor that any noise is constant. In general Yhat is a function of X estimated from finite data, and Y' may contain human noise, so Yhat and Y can be dependent even conditional on Y'. This conditional independence is load-bearing: equations (13), (14), and (18) in the proof of Theorem 1, and consequently equation (20) in Theorem 2, all rely on it. Without a valid proof of the Lemma, the theoretical guarantee is not established.","section":"Appendix A, Theorem 1"},{"comment":"The proof assumes that there exists a single constant c such that for every human model and both protected groups the ratio TPR_{Yhat|Y',A}/PPV_{Yhat|Y',A} can be set to c by threshold recalibration. This existence is asserted, not proven. If no threshold yields a common c for all models and groups, Algorithm 1 cannot be executed. If multiple thresholds do, then different c values give different estimates of GAP_{Y'|Y,A} because the estimate is GAP_{Yhat|Y,A}/c; the suggestion to average over thresholds does not follow from the theorem, which guarantees equality only for the specific c satisfying equation (16), not for an average of several c's.","section":"Section 4.2, Theorem 2"},{"comment":"Dividing the model gap by c rescales by a quantity that is the model's own recall-precision ratio with respect to Y'. Since c is determined by the same thresholding procedure that the method uses to equalize RPR across groups, the claimed recovery of GAP_{Y'|Y,A} is essentially a rearrangement of the model's confusion w.r.t. Y' rather than an independent measurement. Equation (18) shows that c directly multiplies the human TPR terms; any error or arbitrariness in c scales the estimated human bias linearly. The paper provides no error analysis or sensitivity analysis for the choice of c, which is central to the method's output.","section":"Section 5, paragraph beginning 'It is crucial to highlight'"},{"comment":"The empirical evaluation is deliberately constructed to violate the theoretical assumptions ('we purposefully create all simulations such that the core assumption underlying the theoretical guarantees of our method is violated'). This is a strength for robustness, but it also means the reported MAE improvements cannot be used to support the theoretical claims in Section 4.2; the experiments test a different regime in which the Lemma is known to fail. The paper should either restrict its claims to an empirical heuristic or redesign the experiments to also validate the theory under settings where the assumptions hold.","section":"Section 5"}],"minor_comments":[{"comment":"The text 'PRP ratio = c' appears to be a typo for 'RPR ratio = c'.","section":"Appendix B"},{"comment":"The heading 'theoretical garantee removed' contains a typo: 'garantee' should be 'guarantee'.","section":""},{"comment":"The word 'advencing' in the final sentence should be 'advancing'.","section":""},{"comment":"The phrases 'methodoloigies' and 'decison makers' are typos and should be corrected.","section":""},{"comment":"'refereed as GS-based' should be 'referred to as GS-based'.","section":""},{"comment":"The text reports '95% confidence bound' while the body text in Section 6 reports '90% confidence bounds'; these should be reconciled.","section":""},{"comment":"The notation 'Yhat_kY_k|Y'_k' in the proof appears to be missing the independence symbol; it should be 'Yhat_k ⊥ Y_k | Y'_k'.","section":""}],"recommendation":"reject","confidential_remarks":"The stress-test concern about circularity lands: the Lemma's claim that correct functional form implies Yhat = Y' + epsilon is not a consequence of correct specification, and the conditional independence used throughout the proofs does not hold in general. The paper's own statement that the simulations violate the theoretical assumptions further confirms that the theorems are not exercised by the experiments. I would encourage the authors to resubmit a revised version that either supplies a substantially different theoretical foundation or reframes the contribution as an empirical method with appropriate hedging of the theoretical claims. The empirical framework, code, and benchmark comparisons are potentially useful to the community and could be the basis of a publishable paper."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The headline: the problem is real and the empirical work is solid, but the theoretical guarantee is not. The claim that correct functional form gives Yhat = Y' + epsilon is false, and the main theorem divides by the model's own ratio, making the result circular. Still, the paper is worth a serious referee because the problem—measuring group error-rate bias in human decisions from a small disjoint gold set—is under-served and the proposed heuristic is plausible.\n\nWhat is genuinely new: the formulation of estimating TPR gaps across groups when gold labels are scarce and non-overlapping, plus a pipeline that trains per-decision-maker models, post-processes thresholds to equalize a recall/precision ratio, and measures the gap on a small gold set. The empirical comparison against selection rates, a gold-standard-trained model, and confident learning is thorough; the simulation framework across four datasets is a useful contribution.\n\nThe soft spot is load-bearing. The Lemma's proof asserts that correct functional form implies Yhat = Y' + epsilon, which is false: correct specification means the model class contains the true function, not that the fitted model is a deterministic copy of the human. The conditional independence Yhat ⊥ Y | Y' does not follow, and Theorem 2 divides the model gap by c, the model's own recall-precision ratio, so the result is essentially read off from the assumption. The c parameter is also underspecified—the paper says there exists a c but doesn't say how to choose it in practice, and the ablation only compares to a no-threshold variant.\n\nThe simulations stack the deck. Human decisions are generated by thresholding ML predictions of Y, so the imitation models are near-perfect and effectively satisfy the flawed assumption. The paper claims the simulations violate the functional-form assumption, but that is only about the choice of XGBoost vs logistic for the gold labels; the actual Y' process is still deterministic given X, which is the assumption that matters. And the code, despite the text saying 'we provide code,' is anonymized and unavailable.\n\nSo the central theoretical guarantee is invalid, and the empirical evidence cannot rescue it because the design favors the method. That said, the problem is important and the heuristic may work under conditions worth stating explicitly—e.g., when humans are fairly consistent and models can approximate them well. The paper overclaims, but it is not nonsense; it is a promising idea with an unsupported proof.\n\nRecommendation: send to peer review. A good referee could push the authors to fix the theory or reframe the method as a heuristic with empirical support, and to tighten the simulation and c-selection discussion. The reading group would enjoy dissecting the proof.","headline":"Real problem, plausible heuristic, but the theoretical guarantee is circular and the simulations favor the method; still worth a serious referee.","tokens_in":25699,"tokens_out":2680,"would_cite":false,"duration_ms":25929,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"A framework that trains one model per human decision-maker claims to recover that person's decision-bias gap from a small, disjoint set of gold-standard labels by dividing the model's adjusted true-positive-rate gap by a common ratio $c$.","keywords":["human labels","label bias","bias assessment","crowdsourcing","machine learning","algorithmic fairness","true positive rate gap","gold standard scarcity"],"falsifier":"Fit a correctly specified model to each of several decision-makers whose decisions and gold outcomes are both fully known, then check whether $\\Pr(\\hat Y=1 \\mid Y'=1, A=a) = \\Pr(\\hat Y=1 \\mid Y'=1, A=a, Y=1)$ for each group. Wherever this equality fails by a measurable amount, the identity $\\mathrm{GAP}_{\\hat Y|Y,A}/c = \\mathrm{GAP}_{Y'|Y,A}$ will also fail, and the size of the failure shows how much of the method's estimate is model artifact rather than human bias.","tokens_in":24909,"feed_emoji":"⚖️","tokens_out":10932,"duration_ms":87221,"temperature":0.7,"pith_summary":"The paper proposes using machine bias as a measuring instrument for human bias. It trains a separate model on each decision-maker's past decisions, recalibrates the models so they share a common recall-versus-precision ratio $c$, and applies them to a small set of gold-standard labels that the decision-makers never saw. The central theoretical claim is that this yields the true gap in error rates across groups for each human. The method matters because current practice either compares selection rates, which confound base-rate differences with bias, or requires gold-standard labels for every assessed decision.","feed_headline":"Divide a model's bias gap by c to recover human bias","feed_subtitle":"Equalize a recall-precision ratio across models and the adjusted TPR gap is the human's bias.","key_machinery":"The load-bearing object is the recall-versus-precision ratio $c=\\mathrm{TPR}_{\\hat Y|Y',A}/\\mathrm{PPV}_{\\hat Y|Y',A}$, which is also equal to the ratio of the number of positive predictions to the number of positive human decisions within each group. MDBA trains one base model per human, then adjusts group-specific classification thresholds until every model shares the same $c$; this post-processing step is designed to remove bias introduced during model training. The adjusted models are applied to the small gold-standard set to obtain $\\mathrm{GAP}_{\\hat Y|Y,A}$, and dividing by $c$ gives the human bias estimate. The lemma $\\hat Y \\perp Y \\mid Y'$ is the algebraic hinge that turns this ratio identity into an exact equality.","core_discovery":"The central result, Theorem 2, states that when the functional form of a human's decision model is correct, there is a ratio $c=\\mathrm{TPR}_{\\hat Y|Y',A}/\\mathrm{PPV}_{\\hat Y|Y',A}$ such that $\\mathrm{GAP}_{\\hat Y|Y,A}/c = \\mathrm{GAP}_{Y'|Y,A}$. In words, the disparity in true positive rates that the model exhibits between groups, divided by the model's over-prediction ratio, recovers the disparity the human decision-maker would exhibit if gold labels were available for every instance. The proof relies on a lemma that correct specification makes the model's prediction conditionally independent of the gold label given the human's decision. The experiments simulate biased decisions with and without correct internal ordering of candidates, on four datasets, and report that the proposed method has lower mean absolute error than the alternative benchmarks in most settings.","pith_inferences":["The authors do not spell this out, but the same ratio-adjustment identity should transfer to other disparity metrics such as false-positive-rate gaps, since the proof only uses the group-conditional true positive rate and positive predictive value of the model relative to the human.","If the method works in practice, the fixed cost of a small expert panel becomes a reusable audit instrument, shifting the economics of bias measurement from per-decision labeling to one-time gold-standard collection.","A diagnostic the authors do not propose: the spread of $c$ values across fitted models is itself a warning signal, since a wide spread indicates that equalizing the ratio is forcing the models away from their natural behavior and the conditional-independence premise is likely violated.","The simulations intentionally violate the correct-functional-form assumption by generating gold labels with one model family and fitting human-decision models with another, so the natural next test is real human decisions with true gold labels, where the noise process is not generated by any known model."],"forward_implications":["Organizations could audit physicians, recruiters, or crowd workers using a few hundred gold-standard labels drawn from a disjoint sample, rather than labeling every decision.","Decision-makers who evaluated completely different instances can be compared, because each model is trained on that individual's own historical decisions and the gold-standard set only needs to come from the same distribution.","The estimate can be computed before and after an intervention, allowing organizations to measure whether a bias-mitigation policy actually changed the error-rate gap.","Because the method produces an estimate of bias in the human labels themselves, it can identify training sets that would propagate societal bias into downstream machine learning models.","The simulations show estimation error falling substantially as the gold-standard pool grows from 100 to 400 instances per group, so small investments in expert labels can yield large gains in measurement accuracy."],"supporting_citations":[{"why":"Establishes that machine learning models absorb and reproduce biases present in training labels, the premise the method exploits.","marker":"[12]"},{"why":"Supplies the algorithmic-bias measurement perspective and the focus on error-rate disparities that the paper adapts to human decisions.","marker":"[16]"},{"why":"Provides the post-processing fairness technique used to equalize the recall-versus-precision ratio across models in the method's second step.","marker":"[17]"},{"why":"Confident learning is the noisy-label benchmark the proposed method is compared against.","marker":"[65]"},{"why":"Logistic regression is the functional form used to simulate gold-standard labels in the experiments.","marker":"[78]"},{"why":"XGBoost is the base modeling tool used to implement the proposed method and the model-based benchmarks.","marker":"[79]"}],"fun_headline_variants":["Model bias gap split by c reveals human bias","Divide model disparity to recover human bias","One ratio converts model bias to human bias","Machine bias measurement exposes human bias","The c-ratio: from model bias to human bias"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The theory assumes that a correctly specified model of a person's decisions reproduces those decisions so faithfully that, knowing the person's decision, the gold-standard outcome adds no extra information about what the model would predict.","fun_headline_variants_meta":{"raw":{"variants":["Model bias gap split by c reveals human bias","Divide model disparity to recover human bias","One ratio converts model bias to human bias","Machine bias measurement exposes human bias","The c-ratio: from model bias to human bias"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000181,"raw_usage":{"total_tokens":1274,"prompt_tokens":878,"completion_tokens":396,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":494,"completion_tokens_details":{"reasoning_tokens":329}},"tokens_in":494,"tokens_out":396,"duration_ms":3903,"temperature":1.0,"reasoning_tokens":329,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-12T11:30:02.062139+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Fit a correctly specified model to each of several decision-makers whose decisions and gold outcomes are both fully known, then check whether $\\Pr(\\hat Y=1 \\mid Y'=1, A=a) = \\Pr(\\hat Y=1 \\mid Y'=1, A=a, Y=1)$ for each group. Wherever this equality fails by a measurable amount, the identity $\\mathrm{GAP}_{\\hat Y|Y,A}/c = \\mathrm{GAP}_{Y'|Y,A}$ will also fail, and the size of the failure shows how much of the method's estimate is model artifact rather than human bias.","supporting_citations":[{"cited_title":"Algorithmic fairness in business analytics: Directions for research and practice","cited_arxiv_id":null,"evidence_quote":"Supplies the algorithmic-bias measurement perspective and the focus on error-rate disparities that the paper adapts to human decisions."},{"cited_title":"Equality of opportunity in supervised learning","cited_arxiv_id":null,"evidence_quote":"Provides the post-processing fairness technique used to equalize the recall-versus-precision ratio across models in the method's second step."},{"cited_title":"Confident learning: Estimating uncertainty in dataset labels","cited_arxiv_id":null,"evidence_quote":"Confident learning is the noisy-label benchmark the proposed method is compared against."},{"cited_title":"Logistic regression","cited_arxiv_id":null,"evidence_quote":"Logistic regression is the functional form used to simulate gold-standard labels in the experiments."}],"review_version":1}