On the statistical foundations of non-linear utility theory: The case of status quo-dependent preferences

Abstract An account of non-expected utility is given which resumes concepts of μ – σ -analysis from statistical decision theory and combines them with standard principles of preference theory such as weak order, continuity and stochastic dominance. A three-parameter family of probability-dependent utility functions is specified, which is governed by the decision maker's aspiration level, distribution of present wealth, or status quo, and discount parameter for future risks. The approach offers a simple resolution of the Allais Paradox and explains basic patterns of probability-dependent risk attitudes arising in theoretical and applied decision analysis.

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