## Risk Aversion and Route Choice Decisions

### Authors

A de Palma, N Picard, Universite de Cergy Pontoise, France

### Description

### Abstract

The engineers often focus on standard drivers conditions, which are representative of one (or a collection) of average days. The choice models used are often probabilistic (random utility or discrete choice models). In the conventional approach, the probability is just the expression the analyst?s imperfect knowledge. Here, we consider a second reason, fundamentally different which justifies a probabilistic approach. Most of the time, when routes are congested, the actual travel time is not equal to the average travel time. We show here that the drivers? utility functions are non-linear in travel time, so that the average travel time does not provide a good enough statistic. As a consequence, the value of time, which measures the individual cost associated with the travel time incurred does not convey enough information to represent users' preferences.

We extend the basic approach used in transportation, by considering non-linear utility functions and stochastic travel time. The preferences for the route with the shortest average travel time but with the highest variability varies across individuals: some individuals prefer the shortest expected travel time, while others prefer to use routes with longest expected travel time, but better travel time reliability. Preference for avoiding travel time variability depends, a priori, on the individual socio-economic characteristics, attitudinal factors, and the purpose of the trip (for example, one driver will be more risk averse if she goes to the airport than if she goes for shopping).

We assume that the ranking of the random choices can be achieved with a concave utility function (except for risk lovers). We use the simplest formulations (starting with the well-known constant risk aversion specifications). To estimate the main parameter of the model, the degree of risk aversion, we used telephone interview and collected information for about 4000 individuals. They were asked to choose between risk-free (constant travel time) alternatives and risky (random travel time) alternatives. Three lotteries were successively proposed, depending on the observed travel time and on the answers to the previous lotteries. The succession of answers allows to determine, for each individual, an interval for risk aversion. The econometric model we use corresponds to the ordered probit formulation, based on the idea that people having a higher degree of risk aversion tend to choose less favorable lotteries. For example, the more risk averse individuals chose the constant travel time at the first lottery. So they were proposed a more favorable lottery and also chose the constant travel time for this second lottery. In that case, the third lottery proposed was even more favorable : the more risk averse still chose the lottery, whereas the less risk averse chose the random travel time. Those people who chose the random travel time at the first lottery (respectively the second one) were proposed a less favorable lottery for the second choice (resp. the third one).

The continuous latent variable reflecting the degree of risk aversion in the ordered probit model is assumed to depend on socio-economic characteristics, so the estimation of the model allows to measure the impact of these characteristics on risk aversion. The way risk aversion enters the latent variable depends on the utility function chosen by the econometrician and we will test different specifications.

Finally, we explore two implications of the estimation of drivers? risk aversion. First, we compute the certain equivalent which is the value of the expected travel time that gives the same utility level as in the case of a random travel time (with a smaller expected travel time if drivers are risk averse). Second, using the estimates of the value of time and based on the compensating variation approach, we are able to compute the cost associated with stochastic travel time. This computation is especially important for the design of ATIS, since it allows to associate a money value to the provision of information.

Key Words: route choice, expected utility theory, discrete choice model, risk aversion, compensating variations

#### Publisher

Association for European Transport