Independent competence compounds
Five independent jurors at 70% accuracy produce an 83.7% correct majority in the exact binomial model. Each vote carries some new information.
Independent evidence, under pressure
When does agreement earn trust?
Build a tribunal. Predict first. Then watch shared bias turn five voices into one repeated mistake.
Awaiting prediction
Observed verdict --
Quorum 3 of 5
What the court is measuring
Agreement is only evidence when the errors can disagree.
Shared bias repeats one draw
At 100% correlation, five unanimous voices still contain one effective observation. Panel accuracy falls back to the individual baseline.
Quorum buys caution with delay
A stricter gate can turn marginal decisions into escalation. Fewer wrong resolutions may mean fewer resolutions overall.
P(panel correct)
83.7%
n=5 · p=.70 · independent majority
Worked reasoning
The extra confidence is not free.
For a five-juror majority, add the probabilities of exactly three, four, or five correct independent votes. Correlation removes those independent chances and replaces them with a shared outcome.