It is one of the cornerstones of behavioral economics[1][2] and its brain-basis is actively being studied by neuroeconomics researchers.
Given two similar rewards, humans show a preference for one that arrives in a more prompt timeframe.
Humans are said to discount the value of the later reward, by a factor that increases with the length of the delay.
[4] Hyperbolic discounting is an alternative mathematical model that agrees more closely with these findings.
[5] According to hyperbolic discounting, valuations fall relatively rapidly for earlier delay periods (as in, from now to one week), but then fall more slowly for longer delay periods (for instance, more than a few days).
These indifferences reflect annual discount rates that declined from 277% to 139% to 63% as delays got longer.
The most important consequence of hyperbolic discounting is that it creates temporary preferences for small rewards that occur sooner over larger, later ones.
Individuals using hyperbolic discounting reveal a strong tendency to make choices that are inconsistent over time – they make choices today that their future self would prefer not to have made, despite knowing the same information.
[7] 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.
[10] Nor does it depend on human culture; the first preference reversal findings were in rats and pigeons.
[11][12][13] Many 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.
[14][15] For instance, when offered the choice between $50 now and $100 a year from now, many people will choose the immediate $50.
Hyperbolic discounting has also been found to relate to real-world examples of self-control.
[16][17][18] Some evidence suggests pathological gamblers also discount delayed outcomes at higher rates than matched controls.
Likewise, some have suggested that high-rate hyperbolic discounting makes unpredictable (gambling) outcomes more satisfying.
[14] 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.
Both participants know that they can invest the money they receive today in a savings plan that gives them an interest of r. Both of them realize that they should take x dollars immediately if the future value of the savings plan will yield more than y dollars n days later.
Therefore, the minimum value of x (the number of dollars in the immediate choice) that suffices to be greater than that amount will be much smaller than the hyperbolic discounter thinks, with the result that they will perceive x-values in the range from
inclusive as being too small and, as a result, irrationally turn those alternatives down when they are in fact the better investment.
From this one can see that the two models of discounting are the same "now"; this is the reason for the choice of interest rate parameters k. However, when D is much greater than 1,
where β and δ are constants between 0 and 1; and D is the delay in the reward, but now it takes only integer values.
[25] More recently these observations about discount functions have been used to study saving for retirement, personal income [26] to drug addiction.,[27] borrowing on credit cards, and procrastination.
[28][29] Hyperbolic discounting has also been offered as an explanation of the divergence between privacy attitudes and behaviour.
An article from 2003 noted that this pattern might be better explained by a similarity heuristic than by hyperbolic discounting.
[31] Subjects have also reported changing relative preferences as they see more details of what they are choosing—a “temporal construal” effect.
[33] However, although these observations depart from exponential discounting, they do not entail preference reversal as time from the choice to the earlier reward increases.
Arousal of appetite or emotion does sometimes lead to preference reversal, and this has been the most widely accepted alternative to a simply hyperbolic function: hyperboloid or quasi-hyperbolic discounting fuses exponential curves with an arousal bump as a visceral reward becomes imminent.
The most obvious objection to hyperbolic discounting is that many or most people learn to choose consistently over time in most situations.
Similarly, a 2014 paper criticized the existing studies for mostly using data collected from university students and being too quick to conclude that the hyperbolic model of discounting is correct.
[35] Human experiments have frequently reported wide between-subject variations.