Summary: To accommodate the observed pattern of risk-aversion and risk-seeking, as well as common violations of expected utility (e.g., the certainty effect), we introduce and characterize a weighting function according to which an event has greater impact when it turns impossibility into possibility, or possibility into certainty, than when it merely makes a possibility more or less likely. We show how to compare such weighting functions (of different individuals) with respect to the degree of departure from expected utility, and we present a method for comparing an individual’s weighting functions for risk and for uncertainty.