The first part of this paper gives an overview of the dominating approach within economic theory on individual decision making under uncertainty or risk - the expected utility (EU) theory. The theory has increasingly been criticised, and some of the empirical violations of the theory are reviewed. In spite of a number of paradoxes, and the descriptive and predictive difficulties of the EU theory, it remains the dominating approach within economic theory. This paper presents and discusses two alternative, non-expected utility approaches, which fit better with observed behaviour in different experiments and real-life situations.

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