What a Fairness Audit Must Report When Demographic Labels Are Missing: Assumption-Free Disparity Intervals, a Determinacy Rule, and a Disclosure Checklist

In the paper's words

Fairness audits of machine-learning systems publish group-level rates such as selection rates, but the protected labels those rates depend on are frequently missing for a substantial fraction of the audited population, and no settled rule says what the audit must disclose in that case. The gap is practical: an oversight reader who sees a rate computed only on labeled records cannot tell from the published numbers alone whether the rate would survive, shrink, or reverse if the unlabeled records were labeled. We close the gap with an assumption-free worst-case analysis.

The abstract, verbatim, and its opening sentence is the claim. Every line below is quoted from the text.

Numbers it reports

1. We derive a determinacy rule — certification of a threshold $\delta_{\min}$ is impossible exactly when the shifted threshold $\delta_{\min} + p_B$ lies inside the interval $[p_{\min,A},\, p_{\max,A}]$, while $m \lt \delta_{\min}$ guarantees that some certification is possible whatever the point estimate — and instantiate it: with $m = 0.2$, an observed rate of $0.30$ against a fully labeled comparison rate of $0.35$ gives a four-fifths ratio interval $[0.686,\ 1.257]$, so compliance cannot be certified even though the point estimate $0.857$ suggests it, and $134$ labels must be recovered to change that.

   from Abstract

2. A determinacy rule — certification of a threshold $\delta_{\min}$ is impossible exactly when $\delta_{\min} + p_B$ lies inside the interval $[p_{\min,A},\, p_{\max,A}]$, with $m \lt \delta_{\min}$ sufficient for some certification whatever the point estimate, and a reported positive gap surviving scrutiny if $\hat{g} \gt m_1 + m_2$ — derived in Section 4.3, together with the exact necessary-and-sufficient condition and a counter-example showing the shortcut is not necessary (Section 4.4).

   from 1. Introduction

3. A worked numerical audit in the mixed-completeness case: for $n = 1000$, $k = 800$, $\hat{p}_A = 0.30$ against a fully labeled comparison rate of $0.35$, the rate interval is $[0.24,\ 0.44]$, the four-fifths ratio interval is $[0.686,\ 1.257]$, the verdict is indeterminate, and the label-recovery target is $134$ labels (Section 4.5).

   from 1. Introduction

4. Under our framework, an audit with incomplete labels publishes, for each group rate: the point estimate $\hat{r}_g$ on labeled records, the missing-label fraction ($m_g$ in the known-group-size regime, $m$ in the pooled regime), the worst-case interval $[r_{\min,g},\ r_{\max,g}]$ derived in Section 4.1, a determinacy verdict for each disparity threshold $\delta_{\min}$ of interest (Section 4.3), and the minimum number of labels to recover, $\Delta k$, that would make the verdict determinate (Section 4.5).

   from 3.3 What the audit publishes

5. We use a ratio threshold of $0.8$ (the four-fifths threshold) as a stated example threshold; the derivations hold for any threshold $\rho_{\min}$, and the difference-form determinacy rule of Section 4.3 holds for any policy-set threshold $\delta_{\min}$.

   from 3.4 Comparison baselines and the four-fifths rule

6. For the Section 4.2 example, $\hat{g} = 0.10$ against $m_1 + m_2 = 1.10$: the shortcut condition fails by a factor of $11$, matching the exact finding that the claim does not survive.

   from 4.3 The determinacy rule

How it is done

1. For any published rate we derive the exact interval $[\hat{p}(1-m),\ \hat{p}(1-m)+m]$ containing the full-population rate under any pattern of missingness, where $\hat{p}$ is the labeled-subset rate and $m$ the missing-label fraction; the interval width equals $m$ exactly.

   from Abstract

2. Instead we compute worst-case bounds over all assignments of the unlabeled records; the bounds depend on only two numbers the audit already has, the labeled fraction and the observed rate among labeled records.

   from 1. Introduction

3. The starting point for this paper is [1], which asks what a fairness audit must disclose when the protected labels it depends on are incomplete, and focuses on the rates an audit publishes and on what an oversight reader needs beside them; its approach pairs every published rate with a matched baseline drawn from the same audit.

   from 2. Background and Related Work

4. We assume nothing about which records are unlabeled or why.

   from 3.2 The worst-case missingness model

What would falsify it

1. This section states the limitations, the failure modes, and what would falsify the results.

   from 6. Discussion

2. What would falsify the main result.

   from 6. Discussion

3. A single counter-example would falsify it: any assignment of unlabeled records, admissible under the framework's own definition of admissibility (Section 3.2), whose true disparity falls outside $[\hat{r}_1(1-m_1) - \hat{r}_2(1-m_2) - m_2,\ \hat{r}_1(1-m_1) + m_1 - \hat{r}_2(1-m_2)]$.

   from 6. Discussion

Where the claim stops

1. The framework's strength is that its intervals are exact and its inputs are two numbers every audit already has; its weakness is that exactness is bought with width, and the interpretation of the width depends on assumptions the framework itself does not supply.

   from 6. Discussion

2. An oversight reader handed only these intervals at high missingness learns almost nothing except that the audit cannot certify anything — which is itself the correct answer, but a reader expecting a verdict may read the width as methodological failure rather than as an honest measurement of the audit's evidence.

   from 6. Discussion

3. Third, the additive combination of sampling and missingness uncertainty in Section 4.6 is conservative and approximate; a reader who treats $0.09422177$ as an exact confidence statement over-reads it.

   from 6. Discussion

Where to read

1. Abstract273 words · 1 min
2. 1. Introduction767 words · 3 min
3. 2. Background and Related Work1,039 words · 5 min
4. 3. Methods641 words · 3 min
5. 4. Analysis2,037 words · 9 min
6. 5. Results519 words · 2 min
7. 6. Discussion895 words · 4 min
8. 7. Practical Implications and Engineering Pathways819 words · 4 min
9. 8. Conclusion263 words · 1 min
10. Provenance and AI Involvement197 words · 1 min