Foray 245 · Essai 3 · 23 October 2026 · Synthetic construction
When agreement
outlives the frame
Everyone can agree on where to send help while the grouping they share hides where help is useful.
The enquiry. Find useful abstraction layers, notice when they lose the distinctions needed for action, and derive a replacement. Essai 2 exposed a hidden distinction. This attempt searches all 15 pairings of six queues and checks whether a structurally better grouping also improves a separate dispatch decision.
The limits. This is an invented system with known dynamics and an explicit objective. The results concern these assumptions. Shared categories can help or harm in the source literature; this example is not an empirical claim about teams.
Try the failure, then the repair
- Start with a surge at B after the links change. Read the old frame’s unanimous decision and its loss.
- Compare the grouping derived from the links. Its search never sees the surge or dispatch scores.
- Choose a surge at C and set the horizon to 0. Even a structurally good grouping can lose detail needed immediately.
- Set weak-link strength to 0.10. All pairings tie; the search must decline to nominate a replacement.
One system. Fixed evidence and options. Different frames.
Six service queues A–F pass work to each other. A dispatch reaches the whole load in one queue at the decision time; benefit is the true load reached minus a fixed travel cost. All three reviewers receive the same full initial readings, transition matrix and six dispatch options. Their frame controls the averaging they use, not what evidence is available.
Changes are immediate and stay only in this page. No record or file is saved, no information is sent, and reload restores the starting case.
1. Which relations deserve a boundary?
Each queue retains 0.50 of its load, sends 0.50 − 4ε to its partner, and ε to each other queue. All rows sum to 1. Lines show known model relations, not correlations inferred from field data.
All 15 candidate pairings and their cut weight
Minimise the sum of the 12 undirected transition weights that cross group boundaries. Self-loops are excluded. The search sees only the relation matrix.
2. What does each frame preserve?
Old and derived frames replace every pair’s two readings with their mean, then repeat transition → averaging for the chosen horizon. The full-detail reference never averages. Group totals survive; the within-pair contrast disappears.
Tables scroll sideways on narrow screens.
Show the complete transition matrix
3. Agreement is a different question from quality
Every reviewer ranks the same six options by predicted load minus travel cost: A 0.0, B 0.1, C 0.2, D 0.3, E 0.4, F 0.5. Sharing both a frame and this rule makes agreement automatic here. It is not evidence that sharing causes better decisions.
| Team’s frames | First choices | Agreement | Stable winner | Lost benefit | Largest forecast error |
|---|
Agreement: fraction of reviewer pairs with the same first-choice set. Stable winner: one option strictly beats every other in pairwise majority votes. Lost benefit: best attainable true benefit minus winner’s true benefit; lower is better. A tie or cycle gives no chosen action and no quality score. These quantities are not interchangeable.
4. Does the repair travel beyond this one surge?
The same matrix and grouping are checked on six single-queue surges, a B+D surge and a broad load. None is used to choose the grouping. This is a fixed synthetic audit, not a statistical sample or a field trial.
| Team’s frames | Mean agreement | Stable / cases | Optimal / cases | Mean lost benefit | Worst lost benefit |
|---|
Source → concept → construction → limitation
- Simon (1962), The Architecture of Complexity
- Paper · pp. 473–478 connect strong internal / weak external interactions, different time scales and economical descriptions. Here, the relation matrix supplies a search criterion. Simon did not supply this pairing search, dispatch rule or expiry test.
- Gibbons, LiCalzi & Warglien (2021), What Situation Is This? Shared Frames and Collective Performance
- Paper · §§2–6 model categories of games, frame-dependent behavior, improved or worsened payoffs, and frame change. They motivate separating common perception from performance. This experiment is not their game: it has a common dispatch objective, no strategic defection, and an explicit conscious frame comparison.
- Richards, McKay & Richards (2002), The Probability of Collective Choice with Shared Knowledge Structures
- Paper · pp. 339–347 connect graph-constrained preferences with the existence of a pairwise winner. Their graph represents alternatives and distance from ideal points. Ours represents queues’ dynamics. Only the distinction between collective stability and other criteria transfers: we do not import their probabilities or tree theorem into this model.
What this attempt contributes
A replacement is derived from changed relations without consulting the decision outcome. The old pairing remains perfectly shareable and can give a stable, unanimous answer even when it loses benefit. The counterexample is constructive; it does not establish how often real organisations have this problem.
The proposed operational heuristic is: keep an abstraction only for a stated action and horizon; monitor the relations its boundaries cut; when those change, search candidate boundaries independently of the favored decision, then test the new frame against the details it suppresses. If the structural objective ties, say that it cannot choose. If the decision is too immediate, retain finer detail.
Full method, arithmetic and limitations · Reading and run record · Recorded calculation · Model source · Essai 2: When may we forget the detail? · Essai 1: A proposed heuristic kit