Water-filling vs the fixed-oversight paradigm

The same review effort, allocated two ways across a set of delegated tasks. The Minimum Sufficient Oversight Principle distributes authority by the Euler-Lagrange rule; the baseline paradigm reviews everything uniformly. MSO meets the same delivery target at the least governance cost ∫α²√g — and the gap grows with task heterogeneity.

Delivery target p_min0.42

Task heterogeneity (σ spread)0.30

MSO cost ∫α²√g

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uniform cost

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MSO saves

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delivery ∫α·σ

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Governance cost by policy (same delivery — lower is better)

Per-task authority α* (MSO concentrates oversight 1−α on the weak tasks)

authority α (MSO) oversight 1−α · tick = uniform α

Task allocation (endogenous scope: which tasks to delegate)

Minimum coverage0%

Computed by mso-core.js (solveMSO, selectScope) — the water-filling solver and scope selection are pinned to minimal_oversight.allocation by the parity test. Water-filling is the constrained minimum of the Fisher-weighted oversight integral, so MSO never costs more than uniform; with all tasks equal it equals uniform, and the advantage grows as competence varies.