Base-Rate-Adjusted Racial Error-Rate Disparities in Pretrial Risk Tools

What the evidence says

Arnold (2022) decomposes the release-rate gap between white and Black defendants using quasi-random assignment of defendants to bail judges, after adjusting for misconduct risk (the base rate). Of a 6.8 percentage point total disparity in release rates, 4.2 percentage points (62 percent) is attributable to the disparate impact of judges' release decisions, with the remaining share attributable to omitted variable bias (OVB) — factors correlated with race that the adjustment does not capture. This is a tier A quasi-experimental estimate and the study's own framing calls it "conservative."

The disparate impact is not concentrated in a small number of outlier judges. In the same dataset, 87 percent of individual bail judges make release decisions with nonzero disparate impact between white and Black defendants, by the study's most conservative estimate. That share is higher among judges who are more stringent overall, judges assigned a lower share of cases involving Black defendants, and judges not newly appointed within the sample period — three moderators the source states directly.

Arnold further separates a "statistical discrimination" channel from disparate impact using a structural model (hierarchical marginal treatment effects, simulated minimum distance). Two countervailing components make up this channel for Black defendants: a higher average level of misconduct risk, which exacerbates disparate impact, and less precise risk signals, which alleviates it. This estimate carries lower confidence (medium direction, low magnitude) because it depends on structural model assumptions rather than a design-based identification strategy.

Downstream of the release decision, Donnelly (2018) finds that cash-only bail and pretrial detention increase a defendant's likelihood of conviction, of pleading guilty, of being incarcerated, and of receiving a longer incarceration sentence, after controlling for case severity and criminal history. The source is causal in framing (observational with regression adjustment) but its abstract does not quantify the size of these increases. The same study estimates that bail and pretrial detention account for 30 to 47 percent of the explained Black-White disparity in criminal adjudications and court dispositions.

Taken together, the claims here describe disparities in judges' base-rate-adjusted release decisions and their downstream effects on case outcomes — not the error-rate properties (false positive/negative rates by race) of an algorithmic pretrial risk-assessment tool itself. No claim in this set measures a risk tool's predictive accuracy or error rate by race.

Where the evidence splits

No contradictions in the current sources.

Thresholds and dose-response

No threshold established in the current sources.

Open empirical questions

• Whether unmeasured misconduct potential systematically differs by race in ways the base-rate adjustment cannot capture — unresolved by the Arnold decomposition itself.
• The size of the increase in conviction, guilty-plea, incarceration, and sentence-length likelihood from cash bail and detention — Donnelly's abstract states direction but not magnitude.
• Whether judge-specific disparate-impact estimates are sensitive to sampling variation or judge case-load size.
• Whether the statistical-discrimination decomposition (risk level versus signal precision) holds outside NYC or under different structural model assumptions.