research30 min studyLesson 909 in Engineering

Human disagreement is evidence to investigate, not a truth label to erase

Design blinded independent review, calculate agreement and chance-adjusted summaries, and adjudicate with task evidence while preserving rubric changes and uncertainty.

On this page

What you’ll understand

  • Separate agreement, accuracy, adjudication, and rubric clarity.
  • Calculate binary observed agreement and Cohen's kappa from a labeled table.
  • Preserve independent labels, decisive evidence, and cohort uncertainty rather than hiding ambiguous cases.

Some agent outcomes require human interpretation because goals admit several valid solutions, traces are incomplete, or quality cannot be reduced to one exact state check. Human review adds judgment rather than an automatic oracle. Two reviewers can agree on a mistaken rubric or disagree because the evidence is genuinely ambiguous. Record independent decisions and reasons, then adjudicate against the task contract. Agreement statistics help describe the process, but they do not establish that the final labels are true or that the evaluated agent is reliable in every setting.

Make the rubric and evidence boundary explicit before review

Define outcome criteria, allowed alternatives, process constraints, severity categories, and treatment of incomplete evidence. Provide reviewers the artifacts needed to assess those criteria, including authoritative effects where relevant, while avoiding unnecessary identity cues about the system being compared. Blinding can reduce some expectations or preferences, but removing all trace context may make the task unjudgeable. Randomize presentation order where order should not matter and record the actual review interface. An attractive explanation or longer answer should not substitute for evidence of the requested state change.

Collect independent initial labels before showing another reviewer's decision. Preserve uncertainty or an unresolved category when the protocol permits it instead of forcing false precision. The judge-evaluation research of Zheng and colleagues examines how assessment systems can respond to presentation and other biases; a human review workflow also needs its own direct audit rather than assuming that a named bias correction eliminates every error. Sample difficult and apparently easy cases, and inspect whether disagreements cluster by task family, language, evidence quality, or ambiguous rubric wording.

Po=n+++n−−NP_o=\frac{n_{++}+n_{--}}{N}
For N positive-size, fully binary paired reviews, n++ counts both-pass labels and n-- both-fail labels. P_o is dimensionless observed agreement. Unresolved categories require an explicitly extended analysis or separate reporting, and agreement does not establish accuracy against an independent target.↔ Scroll wide equations horizontally.

Chance adjustment describes a baseline, not correctness

Cohen's kappa compares observed agreement with the agreement expected from the two reviewers' marginal label proportions under its chance baseline. A large majority class can produce high raw agreement, and changing prevalence can change kappa even with a similar number of disagreements. Report the underlying table and marginal rates rather than treating one threshold as a universal approval rule. A high kappa can coexist with a shared misconception or missing evidence because both reviewers can make the same mistake. The statistic is a description of labels under a protocol, not a certificate of truth.

Review sampling also determines what the statistic represents. A deliberately oversampled set of disputed or high-risk cases does not automatically estimate agreement across all ordinary tasks without appropriate weighting. Repeated traces from one task can cluster, and uncertainty analysis should respect that unit. Keep independent review labels separate from the later adjudicated reference labels. Once reviewers discuss a case, the resulting consensus can be useful but no longer measures their original independent agreement. Record which evidence resolved the issue rather than simply replacing both earlier labels with the final answer.

Pe=ab+(1−a)(1−b),κ=Po−Pe1−PeP_e=ab+(1-a)(1-b),\qquad \kappa=\frac{P_o-P_e}{1-P_e}
a and b are the two reviewers' marginal pass fractions on the same binary cohort. P_e is the chance-baseline agreement and kappa is defined when P_e≠1. All quantities are dimensionless. The baseline does not assert that actual reviewers are random, independent truth oracles or free of shared error.↔ Scroll wide equations horizontally.

Adjudicate against evidence and version any rubric change

Use a documented adjudication process for disagreements, such as another reviewer examining the task contract and decisive state evidence. Majority vote can be a rule, but it is not automatically ground truth. Distinguish an annotation mistake from a legitimate alternative interpretation, grader bug, or incomplete task specification. If adjudication changes the rubric, version it and reconsider affected earlier cases rather than applying the new interpretation only where it benefits one system. Preserve original labels, reasons, final labels, and unresolved cases with appropriate access control for sensitive trace contents.

The probability lab models only a stipulated independent disagreement count. Reset, explicitly set BOTH p=0.2 and n=20, predict four disagreements on average, then Play or Step. Reset and re-set BOTH p=0.1 and n=20; predict two. Edits retain t; playback highlights exact binomial outcomes. The toy has no reviewers, rubric, marginal table, kappa calculation, or adjudication. It cannot determine whether disagreements reveal reviewer error or task ambiguity; those interpretations require the evidence and review process defined above.

Compute agreement without calling it accuracy

Two independent binary reviewers label one hundred cases. Both pass forty and both fail forty; reviewer A alone passes fifteen and reviewer B alone passes five. Under a stated later protocol, adjudication marks ten of the twenty disputed cases pass and ten fail.

  1. Observed independent agreement is (40+40)/100=0.8. A's pass fraction is (40+15)/100=0.55 and B's is (40+5)/100=0.45.

  2. Chance-baseline agreement is 0.55×0.45+0.45×0.55=0.495. Kappa is (0.8−0.495)/(1−0.495)≈0.604, with no automatic accuracy interpretation.

  3. The later adjudicated labels contain 40+10=50 passes and 40+10=50 failures. Preserve the original twenty disagreements and their evidence; replacing them before computing agreement would erase the independent-review measurement.

The result

Agreement, marginal prevalence, and adjudicated outcomes are separate records that support different claims.

Explore the model

Interactive lab

Interactive lab · probability

A disagreement-count model does not resolve the disagreement

For EACH run Reset, set BOTH p and n, predict, then Play or Step. At n=20, assumed disagreement p=0.2 gives mean 4 and p=0.1 gives mean 2. Edits retain t. This exact iid model has no reviewers, label marginals, kappa, rubric, evidence audit, or adjudication process.

A disagreement-count model does not resolve the disagreementThese are exact binomial probabilities for independent trials with one fixed success probability. Playback tours the distribution; it does not resample outcomes. Current readings: Mean · np: 5; Variance · np(1−p): 2.5; Total probability: 1. All parameters are adjustable with the labeled controls below.03581000.070.150.220.3Successes kP(X = k)k = 0 · P = 9.77e-4
Exact probabilityHighlighted outcomeMean np
Mean · np
5
Variance · np(1−p)
2.5
Total probability
1
t = 0 s

These are exact binomial probabilities for independent trials with one fixed success probability. Playback tours the distribution; it does not resample outcomes. Parameter changes pause playback and recompute the model at the current elapsed time. Reset restores both parameters and returns time to zero. Playback starts paused. Adjust either parameter, then choose Play or Step.

Look forMeasure agreement and inspect its causes; a count or consensus alone does not establish truthful outcome labels.

Check your understanding

Why does high agreement between two human graders not establish that their labels are accurate?

Try it yourself

A hundred binary reviews have thirty both-pass, fifty both-fail, ten A-only pass, and ten B-only pass labels. Calculate raw agreement, each pass fraction, chance-baseline agreement, and kappa. Does the result settle the disputed labels?

Take a moment to make a prediction or work it out on paper. Open a hint when you need one.

Give me a hint

Both marginal pass fractions are 0.4; keep agreement separate from adjudication.

Compare with the solution

Raw agreement is 0.8 and both pass fractions are 0.4. P_e=0.4²+0.6²=0.52, so kappa=(0.8−0.52)/(1−0.52)=7/12≈0.5833. Neither statistic settles the twenty disputes or proves the agreed labels correct; adjudication still needs the rubric and task evidence.

Take it with you

  • Independent review needs a clear rubric and the right outcome evidence.
  • Observed agreement and kappa describe label consistency rather than truth.
  • Adjudication should preserve original labels, uncertainty, and versioned rubric changes.

Read further

Original sources and deeper explanations to follow at your own pace.

Optional progress, saved in this browser when available. Revisit any lesson at any time.

Lesson not marked complete.