The analysis of alternative decisions and the choice of the optimal – in a given sense – decision is an integral part of people’s purposeful activity in all areas of their social life. Many formal approaches have been proposed to solve these problems. One such approach is expected utility theory, which correctly models individuals’ subjective preferences and attitudes to risk. For a very long time this theory was the leading approach for decision making under conditions of risk. However, numerous practical studies have shown its weakness: the theory did not explicitly use subjective perceptions of decision outcome probabilities in optimal decision-making processes. This research has led to the creation and development of approaches to explicitly consider the probabilities of outcomes in decision making. This paper provides a critical analysis of the descriptive properties of expected utility theory and presents various forms of probability weighting functions.