Introduction to the Online Supplement for “Integrating Fragmented Risk Knowledge: Sheaf-Theory for Risk Analysts”
This Online Supplement provides the background and case discussions that underlie the concise summary presented in Table 5 of the main article. Whereas the main text highlights only the essential contrasts between enduring challenges in risk and decision science and the corresponding insights offered by a sheaf-theoretic perspective, the present Supplement expands on those points with fuller explanations, examples, and references. (The references are included at the end of the main article.) The material is organized to parallel the structure of Table 5. Each section develops one or more “backstories” for the challenges listed in the left-hand column—ranging from incoherent individual beliefs and preferences, to difficulties in aggregating expert judgments, to failures of coordination in teams, to obstacles in causal inference, collective choice, and risk governance. For each such challenge, the Supplement illustrates in greater depth why local rationality or consistency may still fail to compose into a globally coherent picture, and how a sheaf-theoretic perspective helps to diagnose and sometimes resolve these failures.
We encourage readers who wish to move beyond the high-level overview of Table 5 to use this Supplement as a guided tour of the diverse domains where fragmentation of knowledge impedes coherence, and where sheaf-theoretic concepts provide new tools that maybe useful in understanding and potentially overcoming these barriers.