CoverageCap: Exact Value-of-Information Calculator for Query and Data Budgets

Concept

A decision-desk tool with one wedge: the exact worth of the next query.

Inputs: a finite decision table — candidate states of the world with rational prior weights (base rates, historical counts), the actions on the table, and each action's payoff in each state (several acceptable answers are supported via the paper's multiple-answer reward extension); plus an information budget, stated either as K symbols of unrestricted information (what a vendor's cleverest K-symbol report could convey) or I realizable yes/no point-membership checks (the tests, lookups, or verifications the buyer can actually order).

Outputs:

• The ceiling: the optimal value of the best K-symbol message, which the paper shows equals weighted maximum K-point coverage — the most any K units of information could ever add to expected payoff.
• The realizable value: what I actual yes/no checks can deliver — weighted maximum (I+1)-point coverage — along with the specific optimal set of checks or fields to buy.
• The gap between the two, i.e., the 'packaging premium' a data vendor could only capture by sending computed summaries rather than raw answers — a concrete number for contract negotiation.
• A marginal-value curve with an explicit stop point: the budget at which additional queries add exactly zero, so the team knows when to stop commissioning work.

Scope guard: the formulas are exact for finite state spaces with rational priors — the natural shape of underwriting, diligence, and triage decisions — not open-ended analytics; the tool says so rather than extrapolating.

Why now

• The new paper [0] establishes, for an arbitrary rational prior, that the optimal value of a deterministic K-symbol encoder–decoder pair is exactly weighted maximum K-point coverage — turning 'what is this information worth to my decision' from a consulting abstraction into a computable optimization with known algorithms.
• The same paper pins the realizable value of I perfect point-membership inspections at weighted maximum (I+1)-point coverage and extends the free-message analysis to multiple-answer reward objectives, so the calculator can show both the oracle ceiling and the achievable value under the buyer's actual test menu.
• The core results are machine-checked in Lean 4 with explicit witnesses, so the calculator's value formulas can ship with formal correctness proofs — a differentiator when the output justifies spend to auditors or regulators.
• Converging older evidence [1] shows that what a learner can extract depends on the structure of the observation system, not just the number of queries — reinforcing the tool's premise that information must be valued at the buyer's real observation grade, not an idealized oracle.