Governance of infectious disease risks requires understanding of often indeterminate interactions between diverse, complex, open, and dynamic human and natural systems. In the face of these challenges, worldwide policy making affords disproportionate status to “ science-based” risk-assessment methods. These reduce multiple, complex dimensions to simple quantitative parameters of “outcomes” and “probabilities,” and then re-aggregate across diverse metrics, contexts, and perspectives to yield a single ostensibly definitive picture of risk. In contrast, more precautionary or participatory approaches are routinely portrayed as less rigorous, complete, or robust. Yet, although conventional reductive–aggregative techniques provide powerful responses to a narrow state of risk, they are not applicable to less tractable conditions of uncertainty, ambiguity, and ignorance. Strong sensitivities to divergent framings can render results highly variable. Reductive aggregation can marginalize important perspectives and compound exposure to surprise. The value of more broad-based precautionary and participatory approaches may be appreciated. These offer ways to be more rigorous and complete in the mapping of different framings. They may also be more robust than reductive–aggregative appraisal methods, in “opening up” greater accountability for intrinsically normative judgements in decision making on threats like pandemic avian influenza.