being motivated to change their behavior and do indeed seek treatment (e.g., Etter, Perneger, & Ronchi, 1997; Hogue, Dauber, & Morgenstern, 2010), but later voluntarily drop out of treatment to resume drug use or relapse despite successfully completing treatment (e.g., McKay, Franklin, Patapis, & Lynch, 2006). This may be explained by delay discounting because, as noted above, hyperbolic/hyperboloid discounting means that changes in value are not constant over time (Ainslie, 2001; Frederick, Loewenstein, & O'Donoghue, 2003). More specifically, rewards appear to both disproportionately lose and gain value based on temporal proximity (either as the time to receipt approaches or as initial delays are implemented), which quantitatively predicts a change in overall preference from a larger delayed reward to a smaller immediate reward as it becomes temporally near at hand (i.e., a preference reversal). Moreover, the more steeply hyperbolic the individual’s discounting curve, the more likely this is to happen. Thus, hyperbolic discounting provides a mathematical model for preference reversals from outcomes that have larger long-term benefits to those that are smaller, but immediately available (for more comprehensive reviews, see Ainslie, 2001 and Odum, 2011a, b).
