Serialization Tax in Shared-Latent Exchangeable Decisions

Itemwise calibration does not guarantee calibration of the decision it feeds. Many systems output one score per item in a partially observed group, but the downstream action asks whether enough hidden items cross a threshold: show a slate, defer a panel decision, or inspect a batch. If those hidden items share an unresolved user, patient, or batch state, averaging that state before aggregation preserves means but makes the aggregate posterior too concentrated. We call this failure the serialization tax. For Bernoulli de Finetti posteriors, the exact hidden-count law dominates any independent completion with the same total predictive mean in convex order, yielding variance, total-variation, threshold, and Bayes-value gaps. The same interface loss extends to non-binary outcomes through empirical-measure Laplace functionals and to heterogeneous slates through a shared-covariance identity. TaxScore turns the theory into a routing rule: use cheap marginal interfaces when hidden-block ambiguity is far from the decision boundary, and propagate a shared posterior sample when it is near. On pre-specified, hidden-label-free MovieLens 1M/10M audits, replacing Transformer count heads with existing stochastic shared-latent heads improves high-TaxScore negative log-likelihood (NLL)/utility from $0.673/0.696$ to $0.629/0.723$ and from $0.670/0.691$ to $0.639/0.715$; routing richer heads only on flagged slates gives $0.006$-$0.012$ full-population utility gains.