Reservation Value Table¶
Decision table — instantiates Sequential Stopping Boundary Design
A transparent, horizon-indexed schedule of minimum acceptable values that anyone can apply — the acceptance bar relaxes on a recorded rationale as the deadline nears.
A Reservation Value Table is a written schedule: for each point in the horizon it states the minimum value (or evidence level) that justifies stopping and accepting then. Its defining property is that the acceptance bar is not a single number but a curve — high while there is time and room to keep searching, deliberately lowered as the window closes and the option to keep looking runs out — and that the whole schedule is legible to non-experts and comes with a recorded reason for each step. It is the family's answer to the question "how should the threshold change as the deadline approaches?", turned into an operational artifact a committee, a caseworker, or a procurement officer can read off a page without re-deriving anything.
Example¶
A hiring committee has eight weeks to fill a role before the budget lapses, and interviews candidates as they come. Rather than argue "is this one good enough?" afresh each week, they build a table up front. Their current fallback is a competent internal stopgap worth, on their rubric, a score of 70. In weeks 1–2 the bar to stop searching and make an offer is set high — 88 — because there is ample time to see stronger candidates; in weeks 3–4 it steps down to 84; weeks 5–6, 80; and in the final fortnight it drops to 74, still comfortably above the 70 stopgap but low enough to avoid ending empty-handed. Beside each step sits a one-line rationale ("weeks 1–2 high: full pipeline still ahead; final fortnight low: re-advertising past the budget deadline is worse than a solid-not-stellar hire").
In week four a candidate scores 85. The table says the week 3–4 bar is 84, so the committee stops and makes the offer — and because the rule and its reasons were written before this particular candidate appeared, no one can later claim the bar was quietly moved to fit a favorite. Had the same 85 arrived in week one, the table would have said keep looking.
How it works¶
- Anchor on the fallback. Establish the value of the walk-away or stopgap; every threshold in the table must stay above it, or accepting would be worse than not accepting at all.
- Lay the threshold over the horizon. For each interval to the deadline, set a minimum acceptable value, starting strict and declining as remaining opportunities to keep searching dwindle.
- Record the reason per step. Each threshold carries a short written rationale, so the schedule is auditable and the drift is a deliberate, inspectable choice rather than an unrecorded slide.
- Read and act. At each decision point, look up the current threshold, compare the option in hand, and stop-and-accept or continue — no fresh argument required.
Tuning parameters¶
- Decline schedule shape — how fast the bar drops toward the deadline. A steep late drop guarantees a stop but risks accepting weak options; a flat schedule holds standards but courts an empty-handed finish.
- Interval granularity — how finely the horizon is sliced. Fine intervals track the closing window closely but multiply the numbers to maintain; coarse ones are simpler but jump more abruptly.
- Floor above fallback — how much headroom the lowest threshold keeps over the walk-away value. A thin floor accepts almost anything at the end; a thick one may still finish empty.
- Rationale depth — how much reasoning each step records. Richer notes make later audit and recalibration easier but cost effort to write and maintain.
When it helps, and when it misleads¶
Its strength is transparent, horizon-aware operability: it hands a repeatable, inspectable rule to people who are not decision theorists, encodes the correct intuition that a search threshold should fall as the horizon closes, and — because both the numbers and their reasons are written in advance — it defends against the after-the-fact standard-drift the archetype warns about. It is the search-theoretic reservation value made into a chart, one threshold per remaining slice of the window.[n1]
It misleads when the table is mistaken for the territory. A schedule set from a stale sense of the candidate pool can be miscalibrated — too strict and it finishes empty, too loose and it accepts early mediocrity — and because it is written down and official-looking, a bad table is obeyed more faithfully than a bad hunch would be. Its transparency is also exploitable: a schedule can be reverse-engineered so the declining bar happens to clear a pre-favored option exactly when that option arrives. The guarding discipline is to set the schedule before the sequence starts, keep the rationale honest enough that a reviewer could challenge it, and treat a table that repeatedly finishes empty or accepts too early as evidence to recalibrate — a job the Stop-Rule Postmortem exists to do.
How it implements the components¶
current_best_and_fallback_state— the walk-away value is the table's foundation stone; every threshold is set as headroom above it, keeping the schedule anchored to a real alternative.horizon_and_reversibility_window— the table's whole structure is horizon-indexed: the threshold is an explicit function of time-to-deadline, declining as the chance to keep searching runs out.decision_rationale_trace— each step carries a written reason, producing an auditable record of why the bar sits where it does, which is what makes drift a deliberate choice rather than a hidden slide.stopping_boundary— the schedule is the boundary in tabular form: look up the current interval, compare the option, and stop-and-accept or continue.
It is not a single fixed accept-and-commit price with a rehearsed close — that compressed cutoff plus post_stop_commitment_plan is its nearest twin, the Bid Acceptance Cutoff; nor does it run an exploration sampling_budget before committing, which is the Secretary-Problem Sampling Rule.
Related¶
- Instantiates: Sequential Stopping Boundary Design — the boundary rendered as a transparent, horizon-indexed lookup table.
- Sibling mechanisms: Bid Acceptance Cutoff · Secretary-Problem Sampling Rule · Bayesian Value-of-Information Update · Real-Option Exercise Boundary · Sequential Monitoring Stop Rule · Stop-Rule Postmortem
Editorial Notes¶
Form Classification¶
Form family: Rule, Policy & Commitment
Rationale: Reservation Value Table operates by sets time-indexed minimum acceptable values above the fallback and constrains future accept-or-walk decisions. That concrete deployed or enacted form is Rule, Policy & Commitment under the frozen taxonomy.
Nearest alternative: Representation, Specification & Plan — Although Representation, Specification & Plan can support this mechanism, the frozen evidence makes its operative form the act that sets time-indexed minimum acceptable values above the fallback and constrains future accept-or-walk decisions; the alternative is therefore secondary rather than defining.
Review outcome: Adjudicated after independent review; high confidence.
Origin Attribution¶
Primary origin: Economics & Finance
Origin pattern: Single lineage
Present-day reach: Multi-domain
Rationale: Reservation values and time-varying walkaway thresholds are canonical bargaining and decision-economic concepts.
Related originating lineages:
- Operations Research — Dynamic decision analysis materially shaped horizon-indexed threshold schedules.
Review resolution: Both blind reviewers agree that economics_finance is the primary historical origin. Explicit reconciliation of alternate origin disagreement adopts reviewer_a's evidence: Reservation values and time-varying walkaway thresholds are canonical bargaining and decision-economic concepts. The selected record uses alternates=operations_research, origin_mode=single_lineage, and domain_reach=multi_domain; the other review proposed alternates=organizational_management, origin_mode=single_lineage, and domain_reach=multi_domain. The selected combination better preserves the mechanism-specific formative lineages and calibrated scope; broader present-day use is not treated as proof of additional historical origin.
Review outcome: Reconciled after independent review; high confidence.
Notes¶
[n1] Reservation value (reservation wage in labor-search models) — the threshold an option must clear for a searcher to stop and accept rather than keep looking. In a finite-horizon search the reservation value is not constant; it declines as the remaining horizon shortens, which is exactly the falling curve a reservation value table tabulates. ↩