Pure hyperbolic discount curves predict "eyes open" self-control

The models of internal self-control that have recently been proposed by behavioral economists do not depict motivational interaction that occurs while temptation is present. Those models that include willpower at all either envision a faculty with a motivation ("strength") different from the motives that are weighed in the marketplace of choice, or rely on incompatible goals among diverse brain centers. Both assumptions are questionable, but these models' biggest problem is that they do not let resolutions withstand re-examination while being challenged by impulsive alternatives. The economists' models all attempt to make a single equilibrium preference predictable from a person's prior incentives. This was the original purpose of these models' hyperboloid ("beta-delta") delay discount functions, which have been widely justified by the assumption that a person's intertemporal inconsistency (impulsiveness) can be accounted for by the arousal of appetite for visceral rewards. Although arousal is clearly a factor in some cases of intertemporal inconsistency, it cannot be blamed for others, and furthermore does not necessarily imply hyperboloid discounting. The inadequacy of beta-delta functions is particularly evident in models of internal self-control. I have reviewed several of these models, and have argued for a return to pure hyperbolic discount function as originally proposed, the relatively high tails of which can motivate a recursive process of self-prediction and thereby the formation of self-enforcing intertemporal contracts. Such a process does not require a separately motivated faculty of will, or incompatible goals among brain centers; but it also does not permit the prediction of unique preferences from prior incentives.