Figure 1.

Preference reversal.

Because of the hyperbolic nature of the curves describing time discounting of a small and a large reward, the curves cross over (preference reversal). At time t₁, the large reward seems more important than the small, immediate reward. At t₂, taking the small, immediate, reward is rational. According to George Ainslie:

“a hyperbolic discounter who faces a choice between smaller-sooner (SS) and larger-later (LL) rewards will evaluate them roughly in proportion to their objective size – their values at zero delay – when both are distant, but value the SS reward disproportionately when it is close. Thus she will have an innate tendency to form temporary preferences for SS rewards, purely as a function of elapsing time”. (Ainslie 2005).