Posterior-Based Decision Stability under Cross-City Stress Testing in Urban Flood Risk Prioritisation

Urban risk prioritisation often requires selecting a small subset of assets for inspection, intervention, or further assessment from a much larger portfolio. Risk models may quantify uncertainty in estimated risk, but the operational decision is discrete: which assets fall inside the selected top-k set, and which remain outside it. Uncertainty in estimated risk is therefore not equivalent to uncertainty in the resulting decision. This paper presents a Bayesian framework for analysing the stability of prioritisation decisions under uncertainty. Rather than treating a ranking as a fixed model output, the framework uses posterior top-k membership probabilities derived from posterior draws to construct decision-stability classes. This separates assets that are robustly prioritised, assets that are robustly excluded, and a smaller review set whose prioritisation changes under posterior uncertainty. The framework is evaluated using a deliberately simplified Bayesian logistic model with exposure and pluvial hazard proxies and a synthetic binary outcome. Experiments include a Rotterdam baseline, controlled perturbation of the hazard representation, and a fixed-specification cross-city stress test in Hamburg and Donostia-San Sebastián. Across the experiments, uncertainty affecting prioritisation membership remains concentrated near the selection boundary rather than diffusing across the full asset population. At comparable approximately 1% prioritisation thresholds, the unstable boundary represents 0.0136% of assets in Rotterdam, 0.0164% in Hamburg, and 0.1676% in Donostia-San Sebastián. The contribution is methodological rather than hydraulic: the framework shows how posterior inference can be propagated through a ranking and selection rule to identify where uncertainty can actually change a prioritisation decision. Development history: The decision-stability formulation used in this preprint was developed by the author and documented in a Phase 1 manuscript in March 2026. That manuscript already treated prioritisation stability as a primary inferential object and implemented posterior top-k membership probabilities together with a borderline decision region for urban flood-risk prioritisation. The Phase 1 manuscript is preserved in the Habnetic research repository.