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The concept of risk acceptance is defined, analysed and applied within a recently developed statistical framework for non-expected utility theory (non-EU) based on conceptions of status quo-dependent decision making under uncertainty. First, an outline of this framework is given, and its possible extension to decisions with multiple objectives is discussed. Explicit definitions of various risk acceptance attitudes are introduced, the exact probability-dependent utility function is derived, and basic properties of marginally acceptable risk are discussed along with examples and applications. These include, among other things, the observed variability of risk acceptance attitudes, voluntary and involuntary risk-taking, aversion to catastrophic risks with low probabilities but large potentials for damage, and observed societal attitudes toward technological risks. The results indicate that basic risk acceptance patterns familiar from psychometric and social studies of risk are, to some considerable extent, utility-oriented attitudes. Their notorious variability can be attributed, in systematic ways, to varying 'pragmatic' constraints on decision making, notably the aspirations, prospects and extant exposure to risk (status quo, economic and other) of decision makers. The final section emphasizes the significance of the non-EU results for risk management practices. Methodological issues connected with the interpretation of observed patterns of individual and societal risk bearing in terms of utility maximization will also be addressed.