Vierordt's law

Karl von Vierordt (1868) was the first to record a law of time perception which relates perceived duration to actual duration over different interval magnitudes, and according to task complexity.

Vierordt's law is "a robust phenomenon in time estimation research that has been observed with different time estimation methods" Fortin. C and Rousseau. R. (1998). It states that, retrospectively, "short" intervals of time tend to be overestimated, and "long" intervals of time tend to be underestimated. The other major paradigm of time estimation methodology measures time prospectively.

The cut-off point between what is considered "short" and "long" - and therefore between overestimation and underestimation - is between 2 and 10 minutes depending on the task e.g. Yarmey.A.D. (2000). The percentage of underestimation grows as task duration increases.

The law is relatively unknown outside psychophysics and is not cited in the Transport Planning literature, which relies heavily on the Valuation of Time Savings http://www.its.leeds.ac.uk/projects/WBToolkit/Note10.htm.

(Note to avoid controversy: Vierordt law is irrelevant to the economic appraisal of transport infrastructure on account of the Constant Unit Value of time (CUV) assumption, which states that the same unit value should be assigned to time changes irrespective of the size or sign of the change [see para 3.27 http://www.dft.gov.uk/stellent/groups/dft_econappr/documents/page/dft_econappr_610340-03.hcsp#TopOfPage ]. However, at least one group of researchers have pointed out the possible importance of asymmetric variation of VTTS distributions:

"For purposes of investment appraisal, it is acceptable to use "average" figures for VTTS, which could mean mode or median figures for the variations in VTTS in the population are asymmetric [...] in terms of individuals' actual willingness to pay and modify their behavior, it may be necessary to recognize that small time savings might not be valued the same as larger blocks of time" Zhang et al. (2004).

There is, in other words, evidence (not yet understood or fully accepted) that "the unit value of time is lower for small travel-time savings and falls with the length of the trip" Zhang et al. (2004). This is a well-known and sometime widely debated controversy in Transport Planning know as "the small travel time savings controversy". Interestingly 3 minutes used to be considered a "small" time saving. Now it is about 10. )