Self-Consistent Wasserstein Repair under Decision-Dependent Constraints

Constraint-enforcing post-processing is usually evaluated at the decision held fixed while the repair is computed. In batch decision systems, however, repaired scores can determine a new threshold; when that threshold also parameterizes the constraints, feasibility becomes endogenous to the repair itself. We formalize this repair–decision feedback and define self-consistent Wasserstein repair (SCWR) as a best-response equilibrium between a groupwise Wasserstein projection and the decision induced by the repaired scores. For grouped one-dimensional scores with polyhedral constraints, the fixed-decision repair is a weighted isotonic quadratic program. We derive an exact identity that separates frozen-problem optimality from deployment violation, prove equilibrium existence without contraction, and give a computable global certificate for uniqueness and robustness. Locally, equilibrium sensitivity is governed by the resolvent $(I-J{)}^{-1}$ of the repair–decision Jacobian; for a scalar decision the feedback amplification is exactly $1/|1-\chi |$ after factoring out the direct score response. A critical-cone formula covers active-set changes. Under calibration-selected policies with nontrivial feedback, one-shot repair becomes infeasible after re-decision in 94–100% of runs in the main benchmark table, while converged SCWR runs reduce the smooth-decision residual below $10^{-9}$ with $|\Delta \mathrm{AUC}|<10^{-3}$. Across 169 stable perturbation trials, the predicted scalar amplification matches the empirical ratio with $0.59\%$ mean relative error.