Decision Boundaries

After this lesson, the reader should understand:

• 01Define a decision boundary and distinguish it from a rule.
• 02Explain why organisational behaviour is a distribution rather than a function.
• 03Identify the boundary implied by a body of past decisions.

The approval limit nobody set

A procurement team's records show near-universal approval below £48,000 and near-universal escalation above it. The written limit is £50,000. Where is the boundary?

At £48,000. The written figure states intent; the observed figure states practice, and the difference between them is recorded nowhere. The gap is not noise — it is stable across years and across officers, which is precisely what makes it a boundary rather than variance. Note carefully what the observation does not establish: whether £48,000 represents prudent caution or an unauthorised tightening that has been quietly denying suppliers a hearing. Locating a boundary and judging it are separate operations, and collapsing them is the most common error in this work.

• Can a boundary exist if no one in the institution can state it?
• What distinguishes a stable boundary from a run of coincidences?
• Should a boundary that has held for a decade be ratified, or corrected?
• What does a boundary look like for a decision with no numeric field?

Recover a boundary from records.

1. 01Choose a decision with a numeric input and a recorded outcome.
2. 02Plot outcomes against that input.
3. 03Identify the value at which the outcome flips.
4. 04State which side of it is the permissive region.
5. 05Compare it to the documented threshold and record the difference.

• Process mining — conformance checking against event logs (van der Aalst).
• Regression discontinuity — identifying thresholds from observational data.
• Decision theory — thresholds under uncertainty.
• Operational Logic, §5 — decision boundaries as the fundamental unit.