What does Dawid–Skene do when the two auditors share their errors?

What it found

Extending the two-auditor model, the second auditor copies the first with probability ρ (each stays 0.8 accurate). Dawid–Skene reads their agreement as correctness: the accuracy it assigns auditor 1 rises from 0.80 to 0.91 at ρ = 0.5 and 1.00 at ρ = 1. At label accuracy 0.9 its policy utility falls from 0.4066 (ρ = 0) to 0.4026 and 0.3992, where it equals taking one auditor as truth, and never goes below that in this model; an oracle told auditor 1’s accuracy is unaffected. Stylised: one shared-error model, uniform errors, round-number utilities; nothing measured on people.

A figure from its own output

Paper, code and results

• README and method
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More in Ambient AI assistant

• What if the two auditors only share errors on hard messages, and can a hardness-aware EM fix Dawid–Skene?What if the auditors only share errors on hard messages: Dawid-Skene's cost is much smaller than with copying (policy utility 0.4060 vs 0.4066 at 30% hard messages), reaching the naive estimator only in an extreme cell, and a hardness-aware EM recovers the classifier but cannot identify the hard share (stylised)
• Does a third auditor identify the hard-message share, and does it help plain Dawid–Skene?Does a third auditor identify the hard-message share: yes at the population level (P(hard) 0.300 from informed starts), only loosely at n=1000 (sd 0.07), and in the extreme cell plain Dawid-Skene with three auditors falls below the naive estimator (0.3912 vs 0.3992) while the hardness-aware EM does not (stylised)
• Does a likelihood-ranked multi-start make the hardness-aware EM robust to a poor start?Does a likelihood-ranked multi-start make hardness-aware Dawid-Skene robust to a poor start: at the population level yes (P(hard) 0.300, vs 0.500 and a lower likelihood from a poor single start), at finite n it matches one informed start, and where hardness is absent the hard share is not identified (stylised)
• How many starts does the likelihood-ranked multi-start need, and are grid starts better than random ones?How many starts does a likelihood-ranked multi-start need, and are grid starts better than random ones: one start is nearly enough with strong hardness or n = 1000, 4 starts reach the best optimum in most cells, more help only in the weak-hardness and null cells, and policy utility barely moves (stylised)
• Can a likelihood-ratio test tell “no hard messages” from “some”, and is the chi-square cutoff usable?Can a likelihood-ratio test tell no hard messages from some: chi-square cutoffs reject 35-72% of null data sets, a parametric bootstrap holds its level and detects h = 0.3 at n = 1000 but not h = 0.1 (stylised).
• Does the bootstrap likelihood-ratio test of “no hard messages” hold its level?Does the bootstrap likelihood-ratio test of no hard messages hold its level: 200 null draws per n give rejection 0.040-0.055 at nominal 0.05, all intervals containing 0.05 (stylised).

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Produced with AI assistance (Claude). Results are from the code in this repository and are simulated or stylised unless the abstract says otherwise; nothing here implies affiliation with or endorsement by any lab, researcher or company cited. MIT licensed.