Self-Selection Menu¶

Mechanism-design protocol — instantiates Hidden-Type Screening

Offers a menu of options priced so that different hidden types find different options attractive, letting candidates reveal their type by which one they choose.

A Self-Selection Menu screens without administering a test at all. Instead of measuring a candidate, it designs a set of options whose terms — price, effort, obligation, risk-sharing — are arranged so that a candidate's best choice differs by type. The low-risk type prefers option A; the high-risk type prefers option B; each reveals itself simply by picking the option that serves it best. What makes this the distinctive mechanism among its siblings is that the informed party does the work: the screen is the shape of the offer, not an interrogation of the chooser. Its correctness depends entirely on getting the menu geometry right, so that the incentive to choose "as yourself" beats the incentive to imitate the other type.

Example¶

An auto insurer cannot see which drivers are low-risk, and asking "are you careful?" is worthless. So it offers a menu instead of a single policy: Plan A carries a high deductible and a low premium; Plan B carries a low deductible and a high premium. A driver who privately knows they rarely file claims finds the high-deductible plan cheaper in expectation and picks A. A driver who expects to file finds the low-deductible plan worth its higher premium and picks B. Neither is asked to disclose anything — yet the choice itself sorts the pool into risk classes the insurer could not observe directly.

The design only works if the two plans are separated far enough that a high-risk driver cannot profitably masquerade as low-risk by taking Plan A. Set the deductible gap too small and both types crowd onto the cheaper premium, the menu collapses to a single pool, and it reveals nothing. The insurer tunes the gap until the choices separate.

How it works¶

Name the hidden attribute the choice will reveal. Decide what type distinction the menu must expose — risk level, willingness to pay, patience, commitment — and design toward that separation.
Build options that trade off along that attribute. Each option pairs a benefit with a cost the two types value differently, so their preference orderings diverge.
Enforce the incentive-compatibility gap. Space the terms so each type strictly prefers its intended option and gains nothing by imitating — this is the whole ballgame.
Read the choice as the signal. Which option a candidate selects, not what they claim, is the screen's output.

Tuning parameters¶

Separation gap — how far apart the options' terms sit. Wider guarantees clean sorting but pushes worse terms onto everyone; too narrow and the types pool.
Number of tiers — two options or a finely graded ladder. More tiers extract finer type information but add choice friction and design fragility.
Which attribute anchors the trade-off — deductible, effort, lock-in, or delay. The dimension must be one the types genuinely rank differently, or the menu sorts on nothing.
Default option — what a non-chooser gets. A poorly chosen default silently pools the passive majority and defeats the sort.

When it helps, and when it misleads¶

The menu is powerful precisely when direct testing is impossible, intrusive, or easy to lie through: it turns private information into a public choice at almost no measurement cost, and it feels fair because candidates opt in. Its failure mode is a menu that is not incentive-compatible — if a type can do better by choosing the "wrong" option, the separation silently collapses and the operator keeps trusting a sort that no longer exists.^[1] It can also be regressive: a menu that sorts on willingness to bear cost may reveal wealth rather than the intended type, so the option that "reveals low risk" is really the one only the well-off can shoulder. The classic misuse is designing the menu to nudge everyone toward the house-favorable option and then calling the resulting distribution "self-selection." The discipline is to check that each type's best response is the intended one, and to verify the choices actually predict the attribute rather than merely tracking budget.

How it implements the components¶

self_selection_menu — it is the menu: the designed option set whose geometry does the sorting.
candidate_pool_boundary — defining who is offered the menu determines whose private information is being elicited and bounds the sort to the intended set.
hidden_attribute_hypothesis — the menu is built around one explicit claim about which hidden type each option will attract; without that hypothesis it is just a price list.

It implements no measurement, verification, or scoring — a Self-Selection Menu never inspects a candidate. Producing an observed signal is Diagnostic Test and Work Sample or Audition; scoring and routing what is revealed is Risk Scoring Model.

Instantiates: Hidden-Type Screening — the screen-by-design variant, where the offer's shape substitutes for a test.
Sibling mechanisms: Diagnostic Test · Underwriting Assessment · Risk Scoring Model · Challenge or Proof-of-Work · Structured Application · Probationary Period · Pilot Project · Background Check · Credential Verification · Reference Check · Structured Interview · Work Sample or Audition

References¶

[1] In screening theory a menu that induces each type to choose a distinct option is a separating outcome; one where the types choose identically is a pooling outcome. A menu screens only in the separating case — the design task is to keep the terms incentive-compatible so imitation never pays. ↩