The future is risky: discounting of delayed and uncertain outcomes.

The world is full of choices where outcomes are both delayed and probabilistic. Whilst the delay discounting framework provides a platform for examining the relationship between dimensions of time and probability, the majority of research has considered these factors in isolation, or made assumptions about their equivalence. In order to address these issues, we present a novel measurement approach for assessing the discounting of delayed and uncertain outcomes. We conducted two experiments which compared discounting on three types of delay discounting task (standard, uncertain outcome, and uncertain amount) and examined the robustness of using a delayed and uncertain outcome's certainty equivalent relative to its expected value as a method for measuring discount rates. Both experiments demonstrated that discounting is best modelled by a hyperbolic function that describes subjective values relative to their certain equivalents. Moreover, when modelled this way, clear differences emerged between the different aspects of uncertainty (outcome vs. amount) dependent on whether outcomes were delayed gains or losses. This was true for both group and individual delay discounting data, as well as for both outcomes that were uncertain with respect to whether they would occur or not and outcomes that were uncertain with respect to what their magnitude would be when they occurred.