Some Limitations of “Risk = Threat × Vulnerability × Consequence” for Risk Analysis of Terrorist Attacks

Several important risk analysis methods now used in setting priorities for protecting U.S. infrastructures against terrorist attacks are based on the formula: Risk = Threat x Vulnerability x Consequence. This article identifies potential limitations in such methods that can undermine their ability to guide resource allocations to effectively optimize risk reductions. After considering specific examples for the Risk Analysis and Management for Critical Asset Protection (RAMCAP) framework used by the Department of Homeland Security, we address more fundamental limitations of the product formula. These include its failure to adjust for correlations among its components, nonadditivity of risks estimated using the formula, inability to use risk-scoring results to optimally allocate defensive resources, and intrinsic subjectivity and ambiguity of Threat, Vulnerability, and Consequence numbers. Trying to directly assess probabilities for the actions of intelligent antagonists instead of modeling how they adaptively pursue their goals in light of available information and experience can produce ambiguous or mistaken risk estimates. Recent work demonstrates that two-level (or few-level) hierarchical optimization models can provide a useful alternative to Risk = Threat x Vulnerability x Consequence scoring rules, and also to probabilistic risk assessment (PRA) techniques that ignore rational planning and adaptation. In such two-level optimization models, defender predicts attacker's best response to defender's own actions, and then chooses his or her own actions taking into account these best responses. Such models appear valuable as practical approaches to antiterrorism risk analysis.