# w_FC4_A — Control-policy decision (nine-step procedure)

## Step 1 — Specify the decision
Pick exactly one admission policy for a program facing applicants of unobservable risk type (low vs. high), where high-risk applicants are the most eager to apply (entry is self-selected and skewed toward the worst-for-us type). Two candidates:
- **A**: a menu of terms engineered so low- and high-risk applicants find different options optimal — type reveals itself through choice (an option only worthwhile to low-risk, or a requirement cheap for low-risk and costly for high-risk).
- **B**: a single uniform, stricter bar applied to everyone equally.

Success criteria (BOTH must hold): (i) the admitted pool must not be dominated by undisclosed high-risk applicants; (ii) low-risk applicants must not be needlessly turned away. There is also a stated *preference* (not a criterion) that a uniform bar is cleaner/easier to defend in a public report.

## Step 2 — Identify operative primes (search_prime / search_by_facets)
Semantic + facet retrieval surfaced a tight neighborhood:
- `adverse_selection` — the *problem*: hidden type + uniform terms + voluntary entry ⇒ the worst types self-select in, pool degrades, possible unraveling.
- `screening` — the *response*: an uninformed designer offers a menu whose incentive-compatibility + individual-rationality constraints make each type pick its intended option, revealing type without direct verification.
- `signaling` — the sender-side mirror (not the lever here; we are the uninformed receiver).
- `incentive_compatibility` — the property a good menu must satisfy: self-interested choice ⇒ the choice we wanted, no enforcement needed.
- `type_i_type_ii_errors` — every gate trades false rejection (turn away a good type) against false admission (let in a bad type); directly indexes both success criteria.

## Step 3 — Salience-rank
1. `adverse_selection` (the situation IS this: hidden type, eager bad types, self-selection).
2. `screening` (Approach A literally instantiates this; it is the canonical receiver-side fix).
3. `type_i_type_ii_errors` (the two success criteria are exactly the two error types).
4. `incentive_compatibility` (whether A's menu actually separates rather than letting high-risk mimic low-risk).
5. `signaling` (lower — informed-party action, not our lever).

## Step 4 — Prune
Drop `signaling` (wrong side of the asymmetry — we design, we don't emit). Drop crowded broad hits (`scarcity`, `selection_bias`, `herding`, `social_identity`) as off-target. Keep the four: adverse_selection (frame), screening (lever A), type_i_type_ii_errors (scorer), incentive_compatibility (validity check on A).

## Step 5 — Typed relational model
- Uninformed designer (the program) — objective: admitted pool not dominated by high-risk AND low-risk not needlessly excluded.
- Informed agents — heterogeneous hidden type {low-risk, high-risk}; high-risk most eager (selection pressure toward the bad pool).
- Lever space: {menu inducing self-separation (A); single uniform threshold (B)}.
- Constraints A must meet: incentive-compatibility (each type prefers its intended option; high-risk cannot profitably mimic low-risk) + individual-rationality (low-risk still prefers entering to the outside option).
- Outcome variable: pool composition + the two error rates (false reject of low-risk = criterion ii; false admit of high-risk = criterion i).

## Step 6 — Domain-stripped meta-model
"An uninformed allocator must commit to heterogeneous agents whose payoff-relevant type is private, where voluntary entry is biased toward the type the allocator least wants. One lever sorts on a *single shared dimension* applied identically to all (a uniform cutoff); the other offers a *type-differentiated menu* whose options have single-crossing costs, so each type self-selects its intended option and reveals type through choice. Evaluate each lever on a two-error objective: minimize wrongful exclusion of the wanted type AND wrongful inclusion of the unwanted type, given that the two types differ on the hidden dimension but a uniform cutoff can only sort on a *correlated observable*, not on type itself."

## Step 7 — Query archetypes whose source primes match (find_archetypes_for_prime / get_archetype)
`find_archetypes_for_prime(screening)` returned, in the `asymmetric_information_design` family, two source-prime matches squarely on point:
- **hidden_type_screening** — source primes {screening, adverse_selection, set_and_membership}. Logic: design an elicitation channel that reveals a hidden attribute before commitment; route on validated results; manage Type I/II error, gaming, fairness.
- **adverse_selection_filtering** — source primes {adverse_selection, screening, set_and_membership}. Logic: when voluntary entry under hidden type degrades a *pool*, filter/segment/adjust terms so the pool does not unravel; evaluate success at the *pool* level, not just per-applicant.

## Step 8 — Apply each candidate archetype's logic to BOTH approaches; reconcile

**adverse_selection_filtering applied:**
- A (menu / self-selection): a type-differentiated menu changes *who enters which option* and what exposure they bring. Because options have single-crossing costs (cheap for low-risk, costly for high-risk), high-risk applicants either decline the low-risk-only option or sort into a separating option — protecting pool composition while keeping the low-risk-only option attractive to low-risk (individual rationality holds). Directly satisfies "pool not dominated by high-risk" *and* "low-risk not needlessly excluded," because the option that is cheap for low-risk lets them in without paying the high-risk-targeted cost.
- B (uniform stricter bar): a single threshold can only sort on a *correlated observable*, not on hidden type. To keep high-risk out it must be raised, which mechanically raises the false-rejection of low-risk (criterion ii violated); to spare low-risk it must be lowered, which admits more high-risk (criterion i violated). A uniform bar cannot decouple the two errors when type is hidden — it slides them together. The archetype's explicit warning: a single pooled/uniform term offered to materially different hidden types attracts the worse type and/or repels the better one.

**hidden_type_screening applied:**
- A: an elicitation channel (the costly-for-high-risk requirement / the low-risk-only option) that turns hidden type into a *choice*, with incentive-compatibility making truthful self-sorting the agent's own best response — exactly the archetype's core move. Caveat to honor: validity (the cost must really be single-crossing, i.e., genuinely cheaper for low-risk) and anti-gaming (high-risk must not be able to cheaply mimic the low-risk choice). These are design obligations, not reasons to reject A.
- B: a uniform bar measures everyone on one axis and does not generate type-revealing evidence; the archetype treats a blunt uniform cutoff that cannot separate hidden types as the weak/absent-screen baseline against which screening is the improvement.

**Reconcile:** Both source-prime archetypes converge on the same verdict. The defining feature of the situation — hidden type with entry biased toward the bad type — is precisely the condition under which a uniform term sorts only on a correlated proxy and is forced to trade criterion (i) against criterion (ii). A type-differentiated, incentive-compatible menu is the canonical instrument that *decouples* those two errors by making type reveal itself, which is the only way to satisfy both criteria simultaneously. The committee's "cleaner public report" point is a presentation preference, not a success criterion, and cannot override a lever that fails the stated objective.

## Step 9 — Evaluate fit against failure conditions; pick

Walk each against the two success criteria and the situation's failure mode (high-risk eager, type hidden):

- **B fails on construction.** With type unobservable, the uniform bar acts on a proxy. Set it strict enough to suppress the eager high-risk inflow and it wrongly rejects low-risk applicants who score near the same proxy (violates ii). Relax it to spare low-risk and the eager high-risk pool floods in (violates i). It cannot satisfy both at once; its only virtue is reporting optics, which is not a criterion.
- **A satisfies both when its incentive-compatibility holds.** The low-risk-only option / low-cost-for-low-risk requirement keeps low-risk in (criterion ii) while the same option is unattractive or prohibitively costly to high-risk, so high-risk self-sort out or into a separating track (criterion i). A's residual risk is a *design* risk (the separation must be genuine and hard to game), which the screening archetype tells us to validate and monitor — not a structural impossibility like B's.

A dominates on the binding objective; B's advantage is confined to a non-criterion (defensibility of a uniform rule). **Choose A.**

===DECISION_BEGIN===
DECISIVE_FACTOR: Because the risk type is hidden and the riskiest applicants are the most eager, a single uniform cutoff can only sort on a proxy and is forced to trade off wrongly excluding good applicants against wrongly admitting bad ones, whereas a self-sorting menu lets type reveal itself and so can satisfy both goals at once.
CHOICE: A
JUSTIFICATION: You cannot see who is risky, and the riskiest applicants are the keenest to apply, so one strict bar for everyone either keeps the bad ones out only by also rejecting many good ones, or admits the good ones only by letting the bad ones flood in. A set of options designed so that a choice is cheap for safe applicants but costly for risky ones gets people to reveal their own type through what they pick. That lets safe applicants in while the risky ones either opt out or land on separate terms, which is the only way to keep the pool clean without needlessly turning good applicants away. A uniform bar's sole edge is being easier to explain in a report, which is not one of the goals we must meet.
===DECISION_END===
