# Impatience declines with time

January 03, 2016

Its my personal experience that when I'm given two choices, I almost always prefer the option which provides the quickest observable result. This thinking falls under the general study of how we have a time-inconsistent model of discounting.

The discounted utility approach says that given two similar rewards, humans show a preference for one that arrives sooner rather than later. Humans are said to discount the value of the later reward, by a factor that increases with the length of the delay.

TODO: Image

# Time Inconsistent Discounting

Often this is model under exponential or hyperbolic discounting. Where valuations fall relatively rapidly for earlier delay periods (as in, from now to one week), but then fall more slowly for longer delay periods (from ten weeks to 21).

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 using the same reasoning.

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 \$\$ k{n+1} = n^2 + k_n^2 - k{n-1} \$\$ that is the same choice seen at five years' greater distance.

A more recent addition to the literature is on subadditive discounting: the fact that discounting over a delay increases if the delay is divided into smaller intervals.

\$\$ k{n+1} = n^2 + k_n^2 - k{n-1} \$\$

The willingness-to-pay for ‘providing parks, pollution control, preservation of wilderness and wildlife, disposal of industrial wastes, and improved preparedness for disasters’ was no greater than that for one small aspect of preparedness for disasters: ‘improving the availability of equipment and trained personnel for rescue operations’Kahneman and Knetsch (1992)