--- slug: "MarginalValueRule" name: "MarginalValueRule" type: "Strategy" layer: "Mind" ref: "MarginalValueRule#6611" sema_id: "sema:MarginalValueRule#mh:SHA-256:661109205c507b2c26d683d091de7f8b782bf2d6c2e9192373b242a9b078ac71" tags: ["Mind","Strategy"] updated: 2026-11-11 mindscape: "bootstrap" index_url: https://mindscape.world/scapes/bootstrap.json url: https://mindscape.world/bootstrap/MarginalValueRule/ related: ["Budget","Estimate","PathwayMemory","RecursionDive","SunkCostIgnore","Build","CollaborativeWritingProtocol","ConceptualDecomposition","FractalIntelligence","HumanEmulatorProtocol","MandatoryAbstraction","MetaProtocols","SolverDecomposition","TruthseekingProtocol"] --- # MarginalValueRule Deepen only while expected improvement plus an exploration credit, divided by incremental cost, exceeds a domain threshold Layer: Mind · Category: Strategy ## Mechanism The economic governor of depth for a [RecursionDive](https://mindscape.world/scapes/bootstrap/RecursionDive.md). At any node, it deepens if and only if the expected improvement from going deeper, plus an exploration credit U(n), divided by the incremental cost, exceeds a domain-appropriate threshold θ and budget remains. Improvement and cost come from an [Estimate](https://mindscape.world/scapes/bootstrap/Estimate.md) grounded where possible in [PathwayMemory](https://mindscape.world/scapes/bootstrap/PathwayMemory.md) records of what deepening similar problems has yielded and cost; without such history the estimate falls back to a calibrated prior, and without that to a fixed exploration budget spent on shallow probes. Incremental cost includes the interface load of an added boundary, such as translation, serialization, routing, synthesis, monitoring and semantic loss, and the value term credits any error or risk reduction that makes that load worthwhile. U(n) is inversely proportional to how much Pathway Memory exists at the node, so rarely visited nodes receive a temporary subsidy and the rule trades exploration against exploitation. θ is not a fixed depth limit: another problem or later evidence may justify more detail. Across sibling branches, the remaining [Budget](https://mindscape.world/scapes/bootstrap/Budget.md) goes to the branch with the highest ratio until no branch clears θ or the budget runs out, so problems get precision in proportion to their stakes. ## Invariants - Deepens if and only if (expected improvement + U(n)) / incremental cost exceeds θ and budget remains. - Incremental cost includes the interface load of the added boundary. - θ is set for the domain, not by depth: it does not rise level by level. - Never approves a dive that exceeds the remaining [Budget](https://mindscape.world/scapes/bootstrap/Budget.md). - Compares future value only; prior investment does not count ([SunkCostIgnore](https://mindscape.world/scapes/bootstrap/SunkCostIgnore.md)). ## Failure modes - Overestimation: Expected value is too optimistic, wasting budget on low-value dives. - Underestimation: Expected value is too pessimistic, stopping too early on valuable problems. - Sunk Cost Fallacy: Continuing to invest because of prior investment, not future value. - Exploration starved: U(n) is left out, so rarely visited nodes are never deepened and their Pathway Memory never forms. - Interface load ignored: the cost of an added boundary is left out, so the rule deepens where the boundary costs more than it adds. ## Parameters - `theta` (Ratio, (0.0, inf)): Domain-appropriate threshold that the value-to-cost ratio must exceed; not a fixed depth limit. ## Signature - `Budget(RecursionDive)` ## Builds on - [Budget](https://mindscape.world/scapes/bootstrap/Budget.md) (Infrastructure; References) - [Estimate](https://mindscape.world/scapes/bootstrap/Estimate.md) (Mind; References) - [PathwayMemory](https://mindscape.world/scapes/bootstrap/PathwayMemory.md) (Mind; References) - [RecursionDive](https://mindscape.world/scapes/bootstrap/RecursionDive.md) (Mind; References) - [SunkCostIgnore](https://mindscape.world/scapes/bootstrap/SunkCostIgnore.md) (Mind; References) ## Used by - [Build](https://mindscape.world/scapes/bootstrap/Build.md) (Mind; References) - [CollaborativeWritingProtocol](https://mindscape.world/scapes/bootstrap/CollaborativeWritingProtocol.md) (Mind; Composes with) - [ConceptualDecomposition](https://mindscape.world/scapes/bootstrap/ConceptualDecomposition.md) (Mind; References) - [FractalIntelligence](https://mindscape.world/scapes/bootstrap/FractalIntelligence.md) (Mind; Composes with) - [HumanEmulatorProtocol](https://mindscape.world/scapes/bootstrap/HumanEmulatorProtocol.md) (Mind; Composes with) - [MandatoryAbstraction](https://mindscape.world/scapes/bootstrap/MandatoryAbstraction.md) (Mind; References) - [MetaProtocols](https://mindscape.world/scapes/bootstrap/MetaProtocols.md) (Mind; Composes with) - [SolverDecomposition](https://mindscape.world/scapes/bootstrap/SolverDecomposition.md) (Mind; References) - [TruthseekingProtocol](https://mindscape.world/scapes/bootstrap/TruthseekingProtocol.md) (Mind; Composes with) ## Identity - Sema ID: `sema:MarginalValueRule#mh:SHA-256:661109205c507b2c26d683d091de7f8b782bf2d6c2e9192373b242a9b078ac71` - Ref: `MarginalValueRule#6611` - Supersedes: - `sema:MarginalValueRule#mh:SHA-256:a46a39374cd046def6d2457b87ce2a426fe1e4b957494ff4a5b62d28665e159e` - `sema:MarginalValueRule#mh:SHA-256:314d8f02234530572de34b8f0616021e51e166f2341b9a5c40491e81f7ce5201` - `sema:MarginalValueRule#mh:SHA-256:eebb10656ec6d554fa7bba3a98b2b9ba1207d58b31d0a794563605595af0f026` - `sema:MarginalValueRule#mh:SHA-256:48c4d6b123db9fc25e08f32e0fb90578713dd71ed65ce7e31e9bce9bc7769e80` - `sema:MarginalValueRule#mh:SHA-256:ffe1bb67e5d273f3acf3cb92876189b68752befd2ab6d0bfa406fb1929c4a17b` - `sema:MarginalValueRule#mh:SHA-256:3499c9b3a581cfbf59ce0ebfe7443d67099132c34d019fafc24219208d671438` ## Links - [Pattern page](https://mindscape.world/bootstrap/MarginalValueRule/) - [View in the interactive graph](https://mindscape.world/bootstrap/#MarginalValueRule) - [JSON](https://mindscape.world/scapes/bootstrap/MarginalValueRule.json) - [Index of all patterns](https://mindscape.world/scapes/bootstrap.json)