Dear UTSG listmember, 

Continuing from an earlier comment by Tony Fowkes:

I accept the logic that "no harm would have been done by ignoring the SP evidence from  experiments involving small time savings and using a constant unit of time instead", but this reasoning in no way implies that such variation does not exist, or that it might not be larger when measured using some other (non-SP) methodology. Absence of evidence is not evidence of absence. 

As has been stated several times (e.g. Bates and Whelen 2001, and Fowkes 1999), SP is not always the right tool for the job. SP data is equally useless for disproving the CUV approach as it will be for proving any non-CUV hypothesis. If the data thus far obtained is not definitive for settling the CUV / non-CUV debate, or remains controversial, then perhaps a different type of evidence should be sought. Perhaps subjective time is less parsimonious than objective time, and its dimensions cannot be fully captured using paper and pen? 

Since I am not an expert on the limitations of SP, the rest of this email is confined to comments on whether the apparent variation in the unit value of time could be explained by a mechanism that is more complex than that implied by CUV.

For the hypothetical example given by Tony Fowkes in a previous email (an operational scheme with a 4 minute time-saving, perceived by an end-user as a 5 minute time-saving, which is an overestimation of duration), the unit VTTS would be undervalued i.e. each minute of objective time would be diluted by the longer perceived duration of each subjective minute. That scenario would be consistent with Vierordt's law, in this case leading to either a 20 or 25% undervaluation (depending on whether 100% is defined as 5 subjective minutes, or 4 objective minutes).

If Vierordt's law has any merit or relevance to value-of-time theory, we should obtain  undervaluations for small time savings, and overvaluations for large time savings (taking care to note that an overestimation of duration does not lead to an overvaluation of objective time, but to an undervaluation of objective time). 

This [undervaluation], however, is not the theoretical situation described in the literature: it has been asserted that distortions in the value of time (over small time periods) are not only modest (at approx.1%), but are signed as overvaluations (Fowkes 1999 p355). Neither the sign nor the magnitude of a 1% overvaluation are supported by Vierordt's law, hence I am sceptical as to whether this latter phenomenon has been examined in as close detail as the former. 

Relevant details are therefore reproduced here for your convenience. 

For a transport-relevant example, see Yarmey 2000, who states:

"The mean percentage error for shorter invariant events ranged between 23% overestimations for an event lasting 2 minutes 31 seconds (subway ride) to 73% overestimations for an event lasting around 51 seconds (subway ride)" Yarmey (2000) p53.

If Vierordt's law applies to the value of time, these figures would translate into a 23% undervaluation and 73% undervaluation, respectively – consistent with the difference between duration and value noted above. 

Moreover, it is logical to argue that as the time interval gets smaller, the size of any distortion (error) would grow as a proportion of total interval size. For time savings of less than 51 seconds, therefore, we can expect the overestimation to be greater than 73% (i.e. leading to a 73 plus % undervaluation). For time intervals approaching zero, an undervaluation of anywhere between 73 and 99% can reasonably be expected, based on the empirical evidence citd above. 

Fowkes 1999 (wisely) avoids defining how large a small time saving is, hence the figure of 99% undervaluation can be taken arbitrarily as an upper bound which has a modicum of hard empirical support.

The (very interesting) outcome of Vierordt's law is that the (inferred) 99% undervaluation actually confirms Fowkes' original 1% overvaluation (assuming that it is not illogical to claim that a 1% overvaluation is similar, if not identical, to a 99% undervaluation – well, almost).

Despite this congruity, Bates and Whelen (2001) do not cite Vierordt's law in support of option (a) (p 40), opting instead for option (b) [that SP data is unreliable], behavioural VTTS are routinely discarded as too unreliable (Mackie 2001 p97), and Fowkes (1999) has not cited Vierordt's law in support of his own calculation. 

The (inferred) 99% undervaluation (if it were to be found experimentally by some non-SP method) would confirm that downweighting small time-savings is inappropriate – again confirming data which already exists in the transport literature. 

So why is Vierordt's law completely absent from transportation research when it could be used in support of SP data reliability? It could be used in a complementary fashion, instead of as an alternative option.

It is possible to assert that detecting variability in a 99% undervaluation ought to be easier than detecting the same distortion in a 1% overvaluation - the body of data is larger (there is more to vary): 

0.076% to 1% overvaluation = a 14% variation (but is vanishingly small in absolute terms)

75% to 99% undervaluation = a 14% variation (yet is quite large in absolute terms)

Using SP to detect variation in the unit VTTS would be, in the words of Allan Wenban-Smith, like "examining an elephant with a microscope". Conversely, using RP to detect the same apparent variation would be like examining a bacteria through a kaleidoscope – unless the kaleidoscope can be straightened-out. Both approaches have their limitations, but the easier (second) option appears to have been ignored. 

In order to prove – or disprove – the non-CUV hypothesis, a combined, interdisciplinary approach which encapsulates the best of both worlds (and avoids the worst) would be required. The explanatory power of any single technique on its own is not sufficient. 

For all these reasons I still maintain that the absence of Vierordt's law from transportation research is not symptomatic of it being so well-known that noone can be bothered to cite it, merely that it's full significance is yet to be explored . 

Regards 



Michael Nandris

(p.s. I am looking for privately rented accommodation in Budapest, Hungary, for October/Nov/Dec 2003 so as to attend the ECMT conference. Do UTSG listmembers have a friend of a friend who might be able to reccomend an accommodation agency, or point me in the right direction?).

 

References: 

Bates. J. and Whelen. G. (2001) 'Sign and size of time savings' ITS Working paper 561.

Fowkes. T. (1999) 'Issues in evaluation: a justification for awarding all time savings and losses, both small and large, equal unit value in scheme evaluation' In: Accent / Hague 1999. The Value of Travel Time on UK Roads. Report to DETR, London. 

Mackie. P.J. Jara-Diaz. S and Fowkes. A. S. (2001) 'The value of time savings in evaluation' Transportation Research E 37 pp91-106.

Yarmey. A. D. (2000) 'Retrospective duration estimations for variant and invariant events in field situations' Applied Cognitive Psychology 14 pp45-57



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