A trilemma for the lexical utility model of the precautionary principle

Bartha and DesRoches (Synthese 199(3–4):8701–8740, 2021) and Steel and Bartha (Risk Analysis 43(2):260–268, 2023) argue that we should understand the precautionary principle as the injunction to maximise lexical utilities. They show that the lexical utility model has important pragmatic advantages. Moreover, the model has the theoretical advantage of satisfying all axioms of expected utility theory except continuity. In this paper I raise a trilemma for any attempt at modelling the precautionary principle with lexical utilities: it permits choice cycles or leads to paralysis or implies that the smallest value difference that is possible in a context has extreme axiological implications.