A discounting framework for trade-offs between risk and delay

Every day we encounter situations in which decisions require trade-offs between the delay to one reward and the likelihood of receiving another reward. The current study was designed to extend a general discounting framework to gain insights into this fundamental trade-off process. Forty-three undergraduates adjusted the probability of receiving an immediate hypothetical monetary reward (either $200 or $10,000) until that probabilistic reward was judged subjectively equal in value to the same reward received with certainty after a delay (ranging from 1 month to 25 years). We replicated previous findings that demonstrated a linear relation between log(delay) and log(odds-against), derived from the subjective probabilistic values. This linear relation was predicted when these choices were analyzed with the hyperboloid functions that describe simple delay and probability discounting in human decision making. Additionally, we extended the discounting framework and showed that the trade-off between risk and delay was well described by a modified hyperboloid discounting model (R²s = .99). These findings suggest that the discounting framework provides a valuable approach for capturing complexities of human decision making.