Continuity, catastrophic risk, and severe uncertainty

Abstract The Continuity axiom implies that no catastrophe is so bad that one should not be willing to accept a gamble that might result in that catastrophe, as long as the gamble is sufficiently likely to instead result in some improvement on one’s status quo. The axiom is implied by most normative decision theories, including risk averse alternatives to expected utility theory. We argue that Continuity should be abandoned when evaluating policy options where (a) there is sufficient uncertainty about the correct probabilities, and (b) some options could be catastrophic. However, unlike Bartha and DesRoches (2021) and Steel and Bartha (2023), we argue that there are examples of policy evaluation where, although the outcome could be catastrophic, the relevant probabilities are sufficiently well-grounded such that Continuity should be satisfied.