The standard axioms of expected utility, by construction, are insensitive to rare events. That is, the continuity assumption states that for lotteries which differ only in a sufficiently small (of positive measure) number of cases, decisions over these lotteries must be equivalent. Rare events, however, are important to decisionmakers. Rather than consider reactions to these events as irrational, Chichilnisky proposes replacing the monotone continuity assumption in classical expected utility theory with an assumption of sensitivity to rare events. She shows that such a choice model requires the Axiom of Choice, unlike classical theory.
“The Topology of Fear,” Chichilnisky, 2009