Structural limits of single-barrier reform in algorithmic recourse: A formal series-system model with implications for digital health

Algorithmic decision systems mediate access to healthcare, credit, employment and housing, yet individuals who experience adverse decisions face multi-stage barriers when seeking recourse. We formalize these barriers as a series-structured system with 11 empirically parameterized stages across three layers (data integration, data accuracy and institutional access) and prove that single-barrier interventions are bounded by baseline system success. Under baseline parameterization derived from federal datasets and peer-reviewed algorithmic audit studies, end-to-end recourse probability is 0.0018%. Removing any single barrier yields negligible improvement (<0.02%). Factorial decomposition reveals that the three-way cross-layer interaction accounts for 87.6% of achievable improvement, illustrated by Shapley attribution, Sobol sensitivity analysis and bootstrap resampling (n = 1,000) within prespecified perturbation ranges. Introducing dependence among the stage pass-events with a Gaussian-copula analysis (latent correlation up to ρ = 0.5), while preserving each marginal pass probability, leaves the comparative conclusion-single-layer reform yields far less than coordinated reform-intact, while a repeated-attempt topology attenuates it, delimiting the model's domain of validity. These findings are properties of the modeled system rather than empirical measurements of real recourse pathways; they yield testable hypotheses for digital-health governance-chiefly that single-layer fairness interventions are structurally unlikely to produce large absolute gains-pending validation against observed recourse data.