Artificial Intelligence Governance of Differential Privacy Budget Allocation in Federated Clinical Learning Under Unmeasured Health Ministry Disclosure Audit Frequency: A Healthcare Privacy-Political Bargaining Evaluation

Differential privacy budget allocation in federated clinical learning is typically treated as a technical parameter to be optimised against model utility. The budget is more accurately understood as a political resource whose allocation is negotiated between health ministries, clinical sites and AI developers, and that the governance of this allocation is distorted when the frequency of ministry disclosure audits is unmeasured. A replication-based evaluation of the before-after-control-impact estimator is used to characterise the operating characteristics of a design that would recover audit-frequency effects under a declared variance structure (between-cluster SD = 6.0, residual SD = 4.5, intraclass correlation = 0.64). Power was estimated across 2000 design cells for cluster counts of 8, 16, 24 and 32 and effect sizes of 3, 5 and 8 percentage points. The analysis indicates that 54 clusters are required for 80 per cent power at a 5 percentage point effect, and that the intraclass correlation of 0.64 substantially constrains what federated designs can detect. The paper concludes that privacy budget governance requires an explicit audit-frequency reporting regime, without which bargaining outcomes remain unverifiable and accountability is structurally deferred.