Aspiration Level, Probability of Success and Failure, and Expected Utility

Several studies have shown that aspiration levels are a relevant aspect of decision making. We develop a model that takes this into account. We include the overall probabilities of success and failure, i.e. the probabilities of reaching and not reaching the aspiration level, into an expected utility representation. This turns out to be equivalent, in a mathematical sense, to expected utility with a discontinuous utility function. We give a behavioral foundation to the proposed model and provide conditions to determine the relative weights of the overall probabilities of success and failure. The model leads to several predictions that fit empirical evidence. Most notably, an aspiration level reinforces loss aversion, can account for simultaneous risk-averse and risk-seeking behavior, and can explain choices violating the mean-variance approach