Arrival rate of consequential decisions
Count state changes that bind someone, not every model output. A ranking that a person must act on is a different arrival rate from an automatic denial.
Capacity planning for consequential decisions
Compare the rate of decisions that bind someone with the rate at which reviewers can check them. See what an institution can change when reviews fall behind.
Two rates decide whether review keeps up: how fast decisions that bind someone arrive, and how fast reviewers can check them. The rule behind the comparison is an invariant: no system may accumulate consequential agency faster than the institution accumulates the capacity to inspect, challenge, revise, and survive its decisions. Treat it as a queue. Decisions that bind someone arrive at rate λ. Reviewers complete inspections at rate μ, counting each decision once whether or not its inspection passes the quality test.
The ratio Φ = λ / (μ × q) measures load. Fidelity, q, is the share of completed inspections whose records let a reviewer reconstruct the decision and explain what would have changed it. Multiply μ by q once to get the rate of valid verification. When Φ exceeds 1, decisions awaiting valid review accumulate unless the institution lets them through unchecked.
The answer is not always more reviewers. The four levers are scope, autonomy, volume, and verification. Narrow what the system decides, lower its authority, reduce the number of consequential decisions, or raise the rate and fidelity of verification. An institution that pulls none of them and adds paperwork has renamed the gap.
A hypothetical case. Worked example with invented numbers. A prior-authorization queue receives 1,200 decisions a day. Forty reviewers inspect thirty decisions each. Three quarters of completed inspections pass the quality test, giving 900 valid reviews a day and Φ = 1,200 / 900 ≈ 1.33. The institution narrows which decisions can be denied automatically, bringing arrivals to 800 a day. At the same inspection rate and a pass rate of 85%, it now has 1,020 valid reviews a day and Φ = 800 / 1,020 ≈ 0.78.
In practice
What to look for
Completed inspections per day
Count each decision whose inspection was completed, including inspections that fail the quality test. Record the pass rate separately.
Fidelity
Sample completed inspections. Record the share whose evidence lets a reviewer reconstruct the decision and identify what would have changed it.
Queue age
Report the age of the oldest uninspected consequential decision. A stable average can hide a tail that never gets reviewed.
Which lever moved
When Φ exceeds 1, record whether scope, autonomy, volume, or verification changed. If none did, the institution chose to run unaudited.
Where the standards use it:
- The reproduction of corrective power (theory). The essay that states the chain, the four levers, and the limits of the queue model.
- MEC-26 Effective corrective power (mechanism). The five conditions from detection to enforcement, and the escalation route.
- MEC-28 Reproductive conditions (mechanism). The capacity inventory, the correction window, and the transition record.
- MEC-29 Reconstructable delegation (mechanism). The record and counterfactual test behind the fidelity term.
- MEC-30 Active epistemic scaffolding (mechanism). The interface patterns that raise fidelity without adding passive friction.
Is this Little's Law?
Φ compares arrival and service rates. It does not estimate how long a case will wait. Even when Φ is below 1, a burst of arrivals or a batch of complex cases can delay review.
Does the invariant require linear hiring?
No. It requires capacity proportional to consequential agency. Scope, autonomy, and volume can restore the ratio without hiring, and verification can be raised by tooling as well as by staff.