Behavioural Processes 94 (2013) 9–18 Contents lists available at SciVerse ScienceDirect Behavioural Processes journa l h omepa g e: www.elsevier.com/locate/behavproc The future is risky: Discounting of delayed and uncertain outcomes Marianna Blackburn ∗ , Wael El-Deredy School of Psychological Sciences, University of Manchester, Oxford Road, Manchester M13 9PL, UK a r t i c l e i n f o Article history: Received 23 December 2011 Received in revised form 27 October 2012 Accepted 7 November 2012 Keywords: Delay discounting Uncertainty Subjective value Certainty equivalent a b s t r a c t The world is full of choices where outcomes are both delayed and probabilistic. Whilst the delay dis- counting 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 val- ues 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. © 2012 Elsevier B.V. All rights reserved. 1. Introduction Many choices involve a trade-off between short and long term benefits. For example, adopting and maintaining a healthy lifestyle and saving for a pension require forgoing immediate rewards in favour of more optimal yet delayed benefits. Further, the consequences of such choices are seldom certain. Therefore, understanding how people mange trade-offs involving delayed and uncertain outcomes carries practical implications for encourag- ing future orientated behaviour. Despite the combined presence of delay and uncertainty within most choices, the majority of research has considered these factors in isolation, or made assump- tions about their equivalence. Here we exploit a delay discounting framework to examine how the combined presence of delay and probability impacts on subjective judgement of value. Empirical evidence shows people often prefer to receive rewards that are delivered sooner rather than later, even when the delayed rewards are rationally favourable. Such behavioural pre- ferences can be accounted for by delay discounting (DD), which refers to the devaluation of subjective reward value as a function of the delay until its receipt (Ainslie, 1975). From a normative perspec- tive, subjective value declines according to an exponential function (Eq. (1)), implying a given time delay will have the same impact on ∗ Corresponding author. E-mail address: marianna.cbr@gmail.com (M. Blackburn). value and preference regardless of when it occurs (for a review see Loewenstein and Prelec, 1992). V = Ae -kD (1) where V represents the subjective value of the future reward, A is the amount of expected reward, D is the time delay to its receipt, and k is the individually different parameter governing the rate of devaluation. Exponential decay functions are derived from the assumption that with each additional unit of time, there is a constant proba- bility (i.e. hazard rate) that some event may intervene to prevent an outcome’s receipt (Green and Myerson, 1996; Kagel et al., 1986; Sozou, 1998). In this way, larger values of k that are associated with steeper discounting of future rewards, imply a greater risk (i.e. the probability that reward receipt will be prevented), or a greater sen- sitivity to risk. From this perspective, both time and uncertainty contribute towards future outcome evaluation. However, behavioural evidence has consistently shown that rewards delivered with shorter delays are discounted more steeply that those delivered with longer delays, and are better described according to a hyperbolic model (Mazur, 1987): V = A 1 + kD (2) where V represents the subjective value of the future reward, A is the amount of expected reward, D is the time delay to its receipt, 0376-6357/$ – see front matter © 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.beproc.2012.11.005