valueFunctional
plain-language theorem explainer
The recognition value functional is defined as V(σ, σ_max) = 1 - J(σ/σ_max) with J the recognition cost. Decision theorists and ethicists working in Recognition Science cite this when formalizing single-agent consent criteria. It is a direct definition obtained by substituting the J-cost expression into the value formula.
Claim. The agent recognition value functional is $V_i = 1 - J(σ_i / σ_{max})$, where $J$ is the J-cost function and $σ_i$ denotes the agent's σ-charge.
background
In the Consent Interface from J-Cost module the value functional supplies the explicit algebraic form for agent value used in the consent criterion. The σ-charge is taken from the Abilene Paradox analysis and equals the signed gap between private preference and public vote: +1 when the agent privately prefers stay but publicly votes go, -1 for the reverse, and 0 for truthful agents. The J-cost function is the Recognition Science cost measure that appears in the forcing chain at T5.
proof idea
Direct definition that substitutes the J-cost term: the body is exactly 1 minus Jcost applied to the ratio sigma divided by sigma_max.
why it matters
This definition is the base object for the downstream theorems IsConsensual, consensual_iff_jcost_nondecreasing, ConsentInterfaceCert, valueFunctional_at_optimum and valueFunctional_nonneg. It upgrades the scaffold tag in the pre-Big-Bang paper §consent to a structural theorem by supplying the explicit V_i expression. It connects to the J-uniqueness step (T5) of the unified forcing chain and to the recognition composition law.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.