This paper characterizes properties of chance attitudes (nonadditive measures). It does so for decision under uncertainty (unknown probabilities), where it assumes choquet expected utility, and for decision under risk (known probabilities), where it assumes rank-dependent utility. It analyzes chance attitude independently from utility. All preference conditions concern simple violations of the sure-thing principle. Earlier results along these lines assumed richness of both outcomes and events. This paper generalizes such results to general state spaces as in schmeidler's model of choquet expected utility, and to general outcome spaces as in gilboa's model of choquet expected utility.