Hyperbolic Discounting - Observations

Observations

The phenomenon of hyperbolic discounting is implicit in Richard Herrnstein's "matching law," which states that when dividing their time or effort between two non-exclusive, ongoing sources of reward, most subjects allocate in direct proportion to the rate and size of rewards from the two sources, and in inverse proportion to their delays. That is, subjects' choices "match" these parameters.

After the report of this effect in the case of delay, George Ainslie pointed out that in a single choice between a larger, later and a smaller, sooner reward, inverse proportionality to delay would be described by a plot of value by delay that had a hyperbolic shape, and that when the larger, later reward is preferred, this preference can be reversed by reducing both rewards' delays by the same absolute amount. That is, for values of x for which under current conditions it would be obviously rational to prefer x dollars in (n + 1) days over one dollar in n days (e.g., x = 3), a large subset of the population would (rationally) prefer the former alternative given large values of n, but even among this subset, a large (sub-)subset would (irrationally) prefer one dollar in n days when n = 0. Ainslie demonstrated the predicted reversal to occur among pigeons.

A large number of subsequent experiments have confirmed that spontaneous preferences by both human and nonhuman subjects follow a hyperbolic curve rather than the conventional, "exponential" curve that would produce consistent choice over time. For instance, when offered the choice between $50 now and $100 a year from now, many people will choose the immediate $50. However, given the choice between $50 in five years or $100 in six years almost everyone will choose $100 in six years, even though that is the same choice seen at five years' greater distance.

Hyperbolic discounting has also been found to relate to real-world examples of self-control. Indeed, a variety of studies have used measures of hyperbolic discounting to find that drug-dependent individuals discount delayed consequences more than matched nondependent controls, suggesting that extreme delay discounting is a fundamental behavioral process in drug dependence. Some evidence suggests pathological gamblers also discount delayed outcomes at higher rates than matched controls. Whether high rates of hyperbolic discounting precede addictions or vice-versa is currently unknown, although some studies have reported that high-rate discounting rats are more likely to consume alcohol and cocaine than lower-rate discounters. Likewise, some have suggested that high-rate hyperbolic discounting makes unpredictable (gambling) outcomes more satisfying.

The degree of discounting is vitally important in describing hyperbolic discounting, especially in the discounting of specific rewards such as money. The discounting of monetary rewards varies across age groups due to the varying discount rate. The rate depends on a variety of factors, including the species being observed, age, experience, and the amount of time needed to consume the reward.