This essay examines drivers’ subjective beliefs of congestion as a way of explaining their route choices. We examine subjective belief in a setting where the penalty for a late arrival is
variable and is contingent on the extent of delay, such that a longer delay incurs additional
penalty on the driver. This continuous penalty setting complements the discrete penalty setting
that is examined in Chapter 1. This is consistent with route choice models that simply subtract
the value of the travel time from the value of the trip (Small (1982); Jackson and Jucker (1982)).
The primary research question in this essay is: if the penalty for a late arrival is a varying
amount, does belief formation differ compared to when the penalty is a fixed amount? Recall
from Chapter 1, where the penalty is a fixed amount, that we observe belief adjustment only
when the underlying congestion risk is low. This behavior is said to be expected under an
endogenous information environment, as it is in the context of driving, where information about
a route can only be obtained if one drives on that route. Thus, in a scenario where the underlying
congestion risk is low and subjects start with a prior belief of low congestion, they are more
likely to drive on the route and are able to obtain more information and result in more belief
adjustment. Here in the continuous penalty setting, will we observe the same pattern of
There are reasons to believe that the consequences of delay (here referred to as late
penalties) affect which route an individual may select. For example, an individual whose
purpose of the trip is to attend a conference meeting faces a different delay consequence than
another individual whose purpose of the trip is to catch a flight. For the first individual, the
consequence of delay is missing part of the meeting, where the longer the delay the more
information is missed; for the second individual, the consequence of delay is missing the flight
and the loss of the entire value of the trip. The first scenario exemplifies a penalty that is
continuous with longer delay incurring additional penalty, whereas the second scenario
exemplifies a penalty that is discrete with a fixed amount. Even if no appointment is being
missed, fully or partially, the fact that more of the individual's valuable time is wasted sitting in
traffic reduces the utility of the trip.
To examine behavior in a setting where the late penalty is continuous calls for an
experimental design that has variability in arrival times so that the extent of delay varies. In the
experiment subjects are asked to make route choices using a driving simulator, and the amount of
time it takes to complete the drive varies depending on route selection, the congestion scenario
on the uncertain route, and how the subjects drive on the simulator. In this way, the arrival times
along with late penalties are induced as continuous variables.
Commuters from the Atlanta and Orlando metropolitan areas are recruited to participate
in this experiment. The field subjects are asked to make binary choices over two routes: one has
an uncertain level of congestion risk, the other has no congestion risk. We elicit subjects’ perceptions of the probability, p, that there is congestion on the uncertain route. This probability
is known to the experimenter, but not to the subjects. Four levels of this probability are used:
stays constant throughout the session for that subject. We also elicit each subject’s perceptions of the amount of time it takes to travel on the route that has an uncertain congestion risk when
there is actually congestion vs. no congestion, and the amount of time it takes to travel on the
route that has no congestion risk. The route choices are made using driving simulators, and
subject’s subjective probabilities of the uncertain risk of congestion, as well as their subjective probabilities of the travel time distributions, are inferred through the route choices they make.
The latent subjective probabilities are estimated controlling for risk attitudes which are estimated
from separate tasks with binary lottery choices.
In this continuous penalty setting, the results indicate that subjects are able to discern the
difference between low-congestion and high-congestion risks, which is the same result as
reported in a discrete penalty setting. In terms of learning (or belief adjustment), however, we
draw different conclusions from those in Chapter 1. In the discrete penalty setting, we saw
adjustments in beliefs over time in the lowest risk scenario. In this essay we compare the
standard deviations of the estimated travel time belief distributions as an indication of whether
more is learnt in the low risk scenario than the high risk scenario. We do not see a significant
difference across treatments in these standard deviations.