Artificial Intelligence Governance of Public Hospital Capital Budget Allocation Models Under Unmeasured Legislative Committee Amendment Log Authority: A Healthcare Political Budgetary Estimation

Legislative committee amendment logs record changes to capital budget lines but not the authority under which those changes are made, leaving a gap between the formal appropriation and the informal governance that shapes hospital capital allocation. The framework specifies how AI-assisted allocation models can be governed when the committee record is incomplete, and it derives the conditions under which the design can detect a three, five or eight percentage-point effect. A replication-based power analysis was conducted across 2000 design cells with between-cluster standard deviation of 6.0, residual standard deviation of 4.5 and an intraclass correlation of 0.64. The analysis indicates that 54 clusters are required to detect a five percentage-point effect at 80 per cent power, and that the minimum detectable effect declines as cluster count rises from 8 to 32. The contribution is a governance framework that makes the unmeasured authority parameter explicit and a design-characterisation that bounds what can be inferred from committee amendment logs when that parameter is absent.