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. The boundary is also not fixed, and a single reading of it is incomplete. A new head of procurement arrives; within two quarters the observed threshold drifts to $52,000, still under the same unrevised $50,000 rule, with no document anyone updated. Or: at fiscal year-end, the same rule's real boundary tightens to $41,000 as budget owners hedge against overrun, then eases back once the new year opens. The threshold is conditional on facts the written rule never names — who is deciding, and where the institution sits in its own cycle — and a system that encodes $48,000 as a fixed constant is correct only until either condition changes^[1], at which point it is silently wrong in a way nothing will flag. The strongest objection is that a single number is false precision. Officers weigh supplier history, urgency, and budget alongside the amount; fitting one threshold to that behaviour invents a rule nobody follows. Partly right, and the framework already answers half of it: a boundary is reported with its dispersion, so a soft, wide transition is shown as soft and wide rather than as a sharp line^[2]. The other half is a real warning. A boundary found on one field may belong to another. If expensive orders also tend to come from new suppliers, the line at $48,000 may be a line on supplier tenure seen through the amount. Separating those readings is the work of Lecture 3.4. The records also have a limit of their own. They contain only the orders that were raised. If officers have learned to split a $60,000 purchase into two of $30,000 — a familiar procurement pattern — the decisions near the threshold are not a clean sample of demand; they have been shaped by the threshold itself. Economists who study thresholds look for exactly this signature: an excess of cases bunched just below the line and a gap just above it^[3]. A reconstructed boundary should be checked for bunching before it is read as a policy, because a bunched distribution records how people respond to the rule, not where the institution draws it.

• 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?
• What evidence would tell you a boundary has genuinely moved, rather than drifted temporarily?
• If cases bunch just below a threshold, is the threshold working, or being gamed — and how would you tell?

No responses yet. Be the first to answer one of the questions above.

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.
6. 06Plot the number of cases just below and just above the threshold, and check for bunching.