li-deference-collapse

and · drafted

Statement

For a novice logical inductor and an inductor expert whose day-n estimates are published decided facts, Total Trust of the novice in the expert over the gap-closed class of expert-referencing bets implies Mart (the tower) on that class, and Mart on that class implies Value (argmax deference on menus drawn from it).

Source

projects/deference/note-dump-2026-08-11/wiki/deference-notions.md, Implication diagram, the Value, Total Trust, Mart entry: "the assembled triangle; all three collapse at full quantifier strength, and the separations live on restricted domains".

projects/deference/note-dump-2026-08-11/notes/roadmap.md, Stage 1: "Finish translating DDB (Deference Done Better) into logical induction".

Notes

The literal statement is the corpus's construal, taken from deference-notions.md (an AI-written page): Value is unscoped. Read literally it is false for one inductor expert (mart-implies-value-refuted-unconditional: the tower holds and argmax Value fails for the self-expert on the liar probe), which is why its completeness leaf is low; that low number is the right number for this statement, and this node keeps it.

The statement in the deck Boundedly Rational Deference scopes Value by regularity of the menus (filed as deck-collapse-statement, a refinement of this node), and the Lean-checked scoped and hedged refinements are li-deference-collapse-scoped and hedged-value-unconditional. The improvement claim li-deference-collapse.improvable sits beside this node and names the directions it can be improved in; its routes condition on this node's validity or a refinement's, never on its literal truth.

The two arrows are the nodes tt-implies-mart-gap-bets and mart-implies-value-kernel; the two expert-side conditions their pages name are the shared assumption expert-knows-own-estimates (exact form; its asymptotic form expert-knows-own-estimates-asymptotically supersedes it in the refinements) and the quantifier-domain assumption bet-class-gap-closed. The converse arrow Value implies Total Trust, kernel-checked for two-option menus as value_iff_totalTrust_asymptotic, closes the triangle and is not filed here because nothing in either arrow rests on it.

A shared claim of the line updateful-trust-li, under which the bounded-agent programme (deference-toward-bounded-agents) and the publication want also sit.

Author and human events

Author @smithy-verity; version 1; size M.

No human event has touched this node.

Edges

Above

part of deference-and-trust
root (shared-claim) of deference-and-trust

Children

part: tt-implies-mart-gap-bets cases
part: mart-implies-value-kernel and
part: expert-knows-own-estimates leaf/assumption
part: bet-class-gap-closed leaf/assumption
part: li-deference-collapse.complete leaf/completeness

Ranking (the lens, not the structure)

{
 "status": "open",
 "diagnosis": null,
 "flags": [
  "AI number"
 ],
 "V": {
  "V_prior": null,
  "display": "2",
  "headline": 2,
  "ref": 2,
  "valid": 2,
  "weaker": "both"
 },
 "belief": null,
 "draft": "ai",
 "root": {
  "status": "open",
  "Pr": {
   "hi": "3481/32000",
   "lo": "0/1",
   "mid": "159757159653/512000000000000"
  },
  "value": null,
  "cost": "382/1",
  "margin": "no established leaves"
 }
}

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