Decision-Preserving Diagnostic Compression: When Knowing the Mismatch Is Not Enough
Abstract
**A correct diagnosis need not be a sufficient decision representation:** it may identify what changed while discarding distinctions needed to decide how to intervene. We study this gap between diagnostic recovery and intervention sufficiency by treating diagnosis as a compression of legal pre-decision information . For a fixed action set, we characterize when this compression preserves action-selectable value and decompose the headroom over the best fixed intervention into representation loss, rule defect, and delivered value. In the binary case, representation loss admits an exact mechanism: opposing action advantages cancel within diagnosis cells. This population distinction also creates an identification problem. We introduce the Counterfactual Adaptation Audit (CAA), which ties each empirical claim to its estimand, information regime, identifying contrast, and status. In a controlled adaptation study, the diagnostic target is recovered near-affinely, intervention preference changes sharply with mismatch source, and a prespecified source-matched rule achieves privileged opportunity value (95% CI ) over the best fixed intervention. Yet the estimator-derived diagnostic becomes available only after one candidate action has been executed, leaving legal pre-decision and unidentified. The resulting boundary is structural: information can be recoverable and decision-relevant without being preserved in a form, and available at a time, that can change the decision.
est. 32% chance this paper gets accepted at ICLR 2027.
What do you think this paper will get?
All positions stay anonymous.