Probabilistic discounting in “certain gain–uncertain loss” and “certain loss–uncertain gain” conditions

Studies on probabilistic discounting typically involve choosing between two outcomes of the same sign (i.e., positive or negative). Commonly, participants are given a choice between a smaller, certain gain and a larger, but uncertain gain, or (less commonly) the options may be a certain, smaller loss and an uncertain, but larger loss. In contrast, participants in this study had to make yes/no decisions as to whether they would accept a financial offer involving a combination of both a gain and a loss. This offer could be either a certain gain which, when accepted, could bring an uncertain larger loss, or a certain loss which, when accepted, could bring an uncertain larger gain. Despite the substantial differences between the alternatives posed in the present study and those in typical discounting studies, the same hyperboloid discounting function that describes the choice between certain and uncertain gains also accurately described choice in the situations presented in the present study. In addition, steeper discounting was observed with a larger uncertain gain than with a smaller uncertain gain. No amount effect was revealed with uncertain losses.