Tail-Sensitive Social Risk Evaluation and the Fragility–Resilience Wedge: A Static Welfare Benchmark for Sustainable-Development Risk Governance

Resilience investments may provide their greatest benefits during severe disruptions, while benefit-generating activities may also create their largest losses in those states. This paper examines when differences in evaluating adverse states lead to different choices of productive intensity and costly resilience. A static welfare model compares a decentralised decision criterion with a specified social criterion applied to the same physical loss technology. The social criterion is treated as a conditional benchmark rather than a uniquely correct weighting of uncertain outcomes. A Fragility–Resilience Wedge arises when the social criterion places relatively greater marginal weight on severe losses, intensity disproportionately increases losses in those states, and resilience provides comparatively greater protection there. The wedge can be positive, zero, or reversed depending on this alignment. A numerical example comparing expectation-based decentralised evaluation with conditional value-at-risk quantifies the wedges, illustrates boundary and reversal cases, and examines sensitivity to stronger upper-tail weighting. Stronger conclusions about complete allocations require additional curvature, interaction, uniqueness, and monotone-selection conditions. The framework therefore provides a static diagnostic for resilience-oriented risk governance in sustainable-development settings while leaving intertemporal welfare, resilience accumulation, and other dynamic sustainability mechanisms for future research.