Fairness Is More Than Algorithms: Racial Disparities in Time-to-Recidivism

Devavrat Shah; Jessy Xinyi Han; Kristjan Greenewald

REVIEW 3 major objections 6 minor 35 references

Fairness Is More Than Algorithms: Racial Disparities in Time-to-Recidivism

T0 review · 3 major / 6 minor · reviewed 2026-08-16 · deepseek-v4-flash

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Pith's one-line read Racial differences in time-to-recidivism appear within identical COMPAS risk groups after roughly seven months.

desk verdict A clean conditional-independence core and a useful temporal angle, but the headline causal claim is undermined by a censoring assumption that fails under the paper's own alternative. read the letter →

arxiv 2504.18629 v1 pith:LSFAOFDI submitted 2025-04-25 cs.CY stat.AP

Jessy Xinyi Han , Kristjan Greenewald , Devavrat Shah This is my paper · ORCID

classification cs.CYstat.AP MSC 62N0162D2062P25

keywords recidivismracialdisparitysurvivalanalysiscausalinferencealgorithmicfairnessCOMPAStime-to-eventcounterfactual

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

Most fairness audits treat recidivism as a yes/no event measured over a fixed window. This paper argues that when to look matters: it develops a causal framework for time-to-recidivism and a formal test for whether racial groups with the same algorithmic risk score follow the same survival curve. The test says that if those curves differ, the algorithm alone cannot explain the difference, because the score is already held fixed; unobserved contextual factors must be influencing recidivism timing. Applied to the COMPAS dataset, the test finds no racial gap in the first seven months, but significant divergence afterward for low-risk defendants, with African-American defendants recidivating sooner. The paper's conclusion is that structural conditions outside the algorithm—housing, employment, social support—accumulate over time and deserve policy attention.

What carries the argument

The carrying object is the race-and-score-conditioned survival curve $S_d(t\mid m)=P[\tau>t \mid D=d, M=m]$, i.e., the probability that a defendant of race $d$ in COMPAS score group $m$ has not been rearrested by time $t$. Theorem 1 shows that under the null of no direct context effect, the counterfactual survival curve after an intervention on race equals this observational curve and hence is identical across races; Lemma 1 turns the contrapositive into a decision rule. The test itself is the non-parametric log-rank test applied to the observed time $T=\min\{\tau,\tau'\}$, with return to custody for non-criminal violations treated as independent right-censoring. The machinery gives a temporal answer: it identifies not only whether disparities exist but when they begin.

What would settle it

Re-analyze the COMPAS cohort with direct measures of post-release context, such as verified housing, employment, and social-support enrollment. If the post-seven-month survival curves for African-American and Caucasian low-risk defendants become indistinguishable after adjusting for those measures, the paper's contextual explanation passes; if they remain different, the claim that context drives the divergence would need revising. A second check is to re-estimate the model treating return to custody as a competing risk rather than independent censoring: if the racial divergence shrinks or disappears, the result hinges on that censoring assumption.

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Extended reading notes

Core claim

The central claim is that within identical COMPAS risk-score groups, time-to-recidivism is racially different once follow-up extends past about seven months, and this difference signals a direct effect of non-algorithmic context on recidivism. The authors define counterfactual racial parity as equality of the survival curves $P^{\mathrm{do}(D=d)}[\tau > t \mid M=m]$ across races, and prove (Theorem 1) that under their causal DAG this counterfactual quantity collapses to the observable quantity $P[\tau>t \mid D=d, M=m]$ whenever context $U$ has no direct edge to $\tau$ or $\tau'$. Therefore a statistically significant difference between races in the same score group, assessed with a log-rank test on censored data, rejects the null that context plays no direct role. The COMPAS analysis finds exactly such a rejection for low-risk defendants after roughly seven months: African-American defendants show a faster drop in no-recidivism probability than Caucasian defendants with the same score. Medium- and high-risk groups show no significant divergence.

Load-bearing premise

The argument holds together only if the COMPAS score is a fully informative proxy for all individual characteristics relevant to recidivism, and race itself has no direct effect on recidivism or return-to-custody timing once score and context are fixed; if the score omits race-correlated traits, the observed divergence could appear even with no unobserved contextual factor at work.

Editorial extensions

If this is right

Binary two-year recidivism audits can miss disparities that appear only after longer follow-up, so evaluation windows should be reported and varied.
Fixing the risk algorithm will not remove all racial gaps in recidivism, since the gaps arise within groups receiving the same score.
Low-risk minority defendants, who might otherwise seem least in need of intervention, are the group where long-term divergence is detected.
Housing, employment, and social support become plausible intervention targets implied by the contextual account, rather than algorithmic tuning.
The same survival test can be carried to other settings where a score and a censored time-to-event outcome coexist, such as loan repayment versus default.

Reading between the lines

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

The seven-month threshold may track the typical duration of post-release supervision or the point at which short-term support programs end; a direct test would compare divergence times across jurisdictions with different supervision lengths.
The analysis treats return to custody as independent censoring, but if return to custody is more frequent for one race, the log-rank comparison can be distorted; a competing-risk analysis is a natural robustness check the paper does not report.
If datasets with direct measures of housing, employment, and social support were linked to COMPAS records, the socioeconomic mechanism could be tested head-on rather than inferred from the timing of divergence.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

Start with what you should know: the paper's theoretical core is basically correct, but the empirical test doesn't deliver what it promises. The authors show that under their DAG, if context has no direct effect on recidivism or return-to-custody, then within a risk-score group, race and true recidivism time are independent. That's just d-separation, and they prove it cleanly. The nice move is looking at time-to-recidivism rather than binary outcomes, and the descriptive finding that low-risk defendants show no racial difference for about seven months then diverge is genuinely new and worth taking seriously as a pattern. The problems start when they bridge from that clean null to the log-rank test on observed times. Their independent-censoring assumption is tau independent of tau' given M, and they state it freely. But the alternative they want to detect—context affects both recidivism and return-to-custody—creates dependence between tau and tau' through U. So under the very alternative they're testing for, independent censoring fails, and the log-rank statistic on T = min(tau, tau') is no longer a valid test of the latent survival curves. A race-correlated pattern in non-criminal returns to custody can produce exactly the kind of late divergence they report. That's not a small caveat; it undercuts the causal headline. Compounding that, the analysis has the usual selection problems: log-rank tests are run repeatedly across time points and risk groups without multiple-comparison control, the 'approximately seven months' threshold looks post hoc, and the appendix shows the effect is concentrated in risk scores 3 and 4. Those facts don't disprove the finding, but they strip away the confidence the abstract implies. What's genuinely good: the paper is transparent about its assumptions, the framework is stated with enough precision to see where it breaks, and the short-term parity result is a solid descriptive contribution. The authors also don't oversell causality in the conclusion—they note they can't directly verify socioeconomic factors. Who's it for: people working on fair-ML and criminal justice will find the temporal angle worth engaging, but the paper shouldn't be cited as evidence that structural factors cause the divergence until the censoring issue is addressed with bounds or a sensitivity analysis. I'd send it to a serious referee rather than desk reject—the question matters and the core framework is salvageable—but as it stands the central claim is not supported.

Referee Report

3 major / 6 minor

Summary. The paper proposes a multi-stage causal framework, represented by a DAG, for studying racial disparities in time-to-recidivism. It introduces a counterfactual notion of racial parity and shows that, under a null hypothesis in which unobserved context U does not directly affect time-to-recidivism or time-to-return-to-custody, the no-recidivism survival curves within a COMPAS risk-score group should be equal across races. The paper then uses a log-rank test on the observed time to rearrest or return to custody as an empirical test of this null. Applying the test to the COMPAS data, the authors find no significant racial differences for medium- and high-risk groups, but report that for low-risk defendants a significant divergence appears after roughly seven months, with African-American defendants showing faster declines in no-recidivism probability. The paper interprets this as evidence that non-algorithmic, potentially socioeconomic, factors affect recidivism trajectories.

Significance. If valid, the framework would be a useful contribution: it moves the algorithmic-fairness debate from binary recidivism outcomes to time-to-event data, explicitly incorporates censoring, and formalizes a contrapositive test for the presence of contextual effects. The paper is clearly written and its empirical strategy is transparent enough to be scrutinized. However, the central inferential claim is compromised by a load-bearing problem: the log-rank test is applied to the observed composite time T = min(tau, tau'), and the independent-censoring assumption under which T identifies the latent recidivism survival curves fails precisely under the alternative the test is designed to detect. In addition, the empirical headline rests on repeated testing without multiple-comparison correction and on a post hoc seven-month threshold. These issues prevent the paper from supporting its strongest conclusion that contextual factors affect recidivism timing, as opposed to affecting the joint recidivism/return-to-custody process.

major comments (3)

[§3.4 and §4.2] The independent-censoring assumption stated in §3.4, tau independent of tau' given M=m, fails exactly under the alternative H1 that the test is designed to detect. Under H1, U directly affects both tau and tau', so tau and tau' share U as a common cause and are dependent conditional on M. Consequently, the observed time T=min(tau,tau') does not identify S_d(t|m)=P(tau>t|D=d,M=m), and a significant log-rank statistic on T can arise from a race-dependent difference in the return-to-custody process even when the true time-to-recidivism curves are identical. The abstract and §4.2 therefore overstate the finding: the empirical test only supports a difference in the joint recidivism/return-to-custody process, not 'recidivism patterns' or the claim that factors beyond the algorithmic risk assessment significantly influence recidivism patterns. Lemma 1 is stated in terms of P(tau>t|D,M), but Empirical Test 1 replaces this with a test on T; the replacement is valid only under an assumption that is false on the alternative of interest.
[§4.2 and Appendix A] The significance claim is based on repeated log-rank tests computed over follow-up time without any multiple-comparison correction, and the 'approximately seven months' threshold is selected post hoc. Appendix A further narrows the significant effect to individual COMPAS scores 3 and 4, which multiplies the number of strata tested. Because no adjusted p-values are reported, the reader cannot assess whether the finding survives correction for the number of time points and risk-score strata. The analysis should either pre-specify the follow-up horizon and testing procedure or report family-wise error-rate-adjusted p-values, and it should report stratum-specific sample sizes and event counts. The appendix's caveat that the lack of effect for other scores 'might also be due to limited data' should be stated in the main text alongside the headline result.
[§3.1 and §3.3] The causal interpretation relies on the structural assumption that race has no direct edge to tau or tau', together with the associated DAG specification. If perceived race directly shapes supervision intensity, charging decisions, or return-to-custody practices beyond the algorithmic score, then a within-M log-rank difference could reflect racial discrimination in the justice process rather than the effect of socioeconomic context U. The paper presents these assumptions without sensitivity analysis, and the data cannot distinguish between the two explanations. Given that the policy conclusion in §4.3 and §5 is specifically about structural socioeconomic factors, the paper should at least discuss how robust the claimed interpretation is to violations of the no-direct-race-edge assumption.

minor comments (6)

[Figures 2-5] The captions describe subplots (a) survival curves for Caucasian defendants, (b) survival curves for African-American defendants, and (c) p-values, but each panel appears to contain one survival curve plot and one p-value plot per risk group; the captions and figures should be aligned.
[Additional Key Words and Section 1] The 'Additional Key Words and Phrases' field contains a placeholder string ('Do, Not, Us, This, Code, Put, the, Correct, Terms, for, Your, Paper') and the ACM reference block still says 2018; these should be corrected before submission.
[§3.4] The 'proportional hazards' bullet is stated as equality of derivatives of log survival curves, which is actually the condition of equal hazard rates; moreover, the log-rank test is a valid test of equality of hazard functions without requiring proportional hazards. The text should be corrected.
[Figures 4-5] The x-axis is labeled 'Time (months)' but reaches values around 1000, which appear to be days; the units should be unified and clearly stated.
[§3.4] The notation for observed and expected events is inconsistent: the text defines O_d,m,t and E_d,m,t but later refers to O_d,m and E_m,t without clearly connecting the aggregated quantities.
[§3.3 and Hypothesis 1] Lemma 1 describes H0 as 'context U does not directly affect time-to-recidivism tau', while Hypothesis 1 defines H0 as no direct effect on both tau and tau'; these statements should be aligned to avoid ambiguity about what is being rejected.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the causal test is a contrapositive of a conditional-independence implication, and no fitted parameter is relabeled as a prediction.

full rationale

The derivation chain is self-contained. Theorem 1 derives the observable equality P[tau>t|D=d,M=m] = P[tau>t|M=m] from the DAG's no-direct-edge assumption plus H0 (removal of U->tau and U->tau'), using d-separation and do-calculus; Lemma 1 is the valid contrapositive of that implication, and Empirical Test 1 implements Lemma 1 with a standard log-rank test under explicitly stated assumptions. No parameters are fitted and then 'predicted': the seven-month divergence is a direct log-rank rejection of equality of survival curves, not the output of a model fitted to that same quantity. The only self-citation ([16], cited for 911-call disparities) is background and not load-bearing. A genuine caveat, but not a circularity, is that the independent-censoring assumption tau perpendicular tau' | M=m holds under H0 but can fail under H1; a rejection could in principle be driven by U affecting return-to-custody timing rather than recidivism timing. The paper's Section 5 limitation ('we do not have the privilege of directly verifying if the socioeconomic factors are indeed the additional sources of bias') appropriately concedes this. Because the test statistic is not defined in terms of the causal conclusion and the causal claim rests on stated structural assumptions rather than on a self-referential fit, the circularity score is 0.

Assumptions & free parameters 1 free parameters · 5 assumptions · 0 invented entities

No new physical or mathematical entities are introduced. The latent context U is a standard unobserved-variable construct. The only ad hoc quantity is the post hoc seven-month divergence threshold. The main load-bearing axioms are the fully informative M assumption, the no-direct-race-edge assumption, and independent censoring, none of which are tested.

free parameters (1)

Follow-up divergence threshold = ~7 months
The paper reports that disparities begin 'approximately seven months' after release (Section 4.2). This cutoff is read off the time-varying p-value plot after the fact, not pre-specified, and it is central to the headline claim.

assumptions (5)

domain assumption Causal DAG: context U affects race D and decision M and, under H0, has no edge to tau or tau'; D has no direct edge to tau or tau'.
Figure 1 and Section 3.1 encode that race affects recidivism only through M. This is the premise that makes a rejection of D independence from tau given M attributable to context rather than to direct discrimination or alternate pathways.
domain assumption M, the COMPAS risk category, is a fully informative proxy for all observable characteristics relevant to recidivism.
Section 3.1 states the risk scores are 'fully informative (but likely biased) characterization' of demographic and contextual information. This is needed to rule out omitted-observable explanations for a rejection.
domain assumption Independent censoring: tau is independent of tau' given M=m.
Section 3.4 lists this as an assumption of the log-rank test. If returning to custody for non-criminal violations depends on race through context, the test on observed T does not test the survival curves of tau directly.
domain assumption The COMPAS dataset's recorded outcomes align with the framework definitions: rearrest is the recidivism event, return to custody for non-criminal violations is censoring, and follow-up extends to roughly 36 months.
Section 4.1 asserts this correspondence, but the paper does not validate the exact definitions against raw fields, such as how the typical two-year binary recidivism flag is converted into event times and censoring indicators.
standard math Standard log-rank conditions: independent recidivism events across individuals and correct event-time recording.
Section 3.4 requires independence of recidivism events; violations, such as neighborhood-level correlation, could inflate significance.

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Pith. "Pith review of Fairness Is More Than Algorithms: Racial Disparities in Time-to-Recidivism." pith.science (2026). https://pith.science/paper/LSFAOFDI

@misc{pith2026250418629,
  author       = {Pith},
  title        = {Pith review of: Fairness Is More Than Algorithms: Racial Disparities in Time-to-Recidivism},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/LSFAOFDI}},
  note         = {Machine review of arXiv:2504.18629}
}

read the original abstract

Racial disparities in recidivism remain a persistent challenge within the criminal justice system, increasingly exacerbated by the adoption of algorithmic risk assessment tools. Past works have primarily focused on bias induced by these tools, treating recidivism as a binary outcome. Limited attention has been given to non-algorithmic factors (including socioeconomic ones) in driving racial disparities from a systemic perspective. To that end, this work presents a multi-stage causal framework to investigate the advent and extent of disparities by considering time-to-recidivism rather than a simple binary outcome. The framework captures interactions among races, the algorithm, and contextual factors. This work introduces the notion of counterfactual racial disparity and offers a formal test using survival analysis that can be conducted with observational data to assess if differences in recidivism arise from algorithmic bias, contextual factors, or their interplay. In particular, it is formally established that if sufficient statistical evidence for differences across racial groups is observed, it would support rejecting the null hypothesis that non-algorithmic factors (including socioeconomic ones) do not affect recidivism. An empirical study applying this framework to the COMPAS dataset reveals that short-term recidivism patterns do not exhibit racial disparities when controlling for risk scores. However, statistically significant disparities emerge with longer follow-up periods, particularly for low-risk groups. This suggests that factors beyond algorithmic scores, possibly structural disparities in housing, employment, and social support, may accumulate and exacerbate recidivism risks over time. This underscores the need for policy interventions extending beyond algorithmic improvements to address broader influences on recidivism trajectories.

Figures

Figures reproduced from arXiv: 2504.18629 by the authors.

**Figure 2.** Survival analysis of recidivism patterns across racial groups and COMPAS recidivism risk groups. The subplots display survival [PITH_FULL_IMAGE:figures/full_fig_p011_2.png] view at source ↗

**Figure 3.** Survival analysis of recidivism patterns across racial groups and COMPAS [PITH_FULL_IMAGE:figures/full_fig_p017_3.png] view at source ↗

Figures from the paper (2 more)

**Figure 4.** Figure 4: Survival analysis of recidivism patterns across racial scores and COMPAS recidivism risk groups. The subplots display survival [PITH_FULL_IMAGE:figures/full_fig_p018_4.png]

**Figure 5.** Figure 5: Survival analysis of recidivism patterns across racial scores and COMPAS [PITH_FULL_IMAGE:figures/full_fig_p019_5.png]

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Reviewed August 16, 2026 · model on record in the stance chip above.

[1] [1]

Julia Angwin, Jeff Larson, Surya Mattu, and Lauren Kirchner. 2016. Machine Bias. https://www.propublica.org/article/machine-bias-risk-assessments- in-criminal-sentencing

work page 2016

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Michelle Bao, Angela Zhou, Samantha Zottola, Brian Brubach, Sarah Desmarais, Aaron Horowitz, Kristian Lum, and Suresh Venkatasubramanian

work page

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Chelsea Barabas, Madars Virza, Karthik Dinakar, Joichi Ito, and Jonathan Zittrain. 2018. Interventions over Predictions: Reframing the Ethical Debate for Actuarial Risk Assessment. In Proceedings of the 1st Conference on Fairness, Accountability and Transparency (Proceedings of Machine Learning Research, Vol. 81). PMLR, 62–76. https://proceedings.mlr.pres...

work page 2018

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Richard Berk, Hoda Heidari, Shahin Jabbari, Michael Kearns, and Aaron Roth. 2021. Fairness in Criminal Justice Risk Assessments: The State of the Art. Sociological Methods & Research 50, 1 (2021), 3–44. https://doi.org/10.1177/0049124118782533

doi:10.1177/0049124118782533 2021

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Marco Castillo, Sera Linardi, and Ragan Petrie. 2024. Recidivism and Barriers to Reintegration: A Field Experiment Encouraging Use of Reentry Support. https://ssrn.com/abstract=4891486 Manuscript submitted to ACM 14 Jessy Xinyi Han, Kristjan Greenewald, and Devavrat Shah

work page 2024

[6] [6]

Alexandra Chouldechova. 2016. Fair prediction with disparate impact: A study of bias in recidivism prediction instruments. arXiv:1610.07524 [stat.AP] https://arxiv.org/abs/1610.07524

arXiv 2016

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Sam Corbett-Davies, Emma Pierson, Avi Feller, Sharad Goel, and Aziz Huq. 2017. Algorithmic Decision Making and the Cost of Fairness. In Proceedings of the 23rd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (Halifax, NS, Canada) (KDD ’17). Association for Computing Machinery, New York, NY, USA, 797–806. https://doi.org/10.1145/...

arXiv 2017

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Kennedy, and Alexandra Chouldechova

Amanda Coston, Alan Mishler, Edward H. Kennedy, and Alexandra Chouldechova. 2020. Counterfactual Risk Assessments, Evaluation, and Fairness. In Proceedings of the 2020 Conference on Fairness, Accountability, and Transparency (Barcelona Spain). ACM, New York, NY, USA, 582–593. https://doi.org/10.1145/3351095.3372851

arXiv 2020