Expected Utility and Non-expected Utility Models of Risky Choice: a New Framework and Estimation Results
J Polak, S Hess, Xiang Liu, Centre for Transport Studies, Imperial College London, UK
We propose a new approach to modelling choice under uncertainty combining key features of classical expected utility theory, non-expected utility theory and classical random utility theory.
In recent years there has been a growing recognition that conventional models of travellers? decision making need to be extended to accommodate the fact that travellers are often uncertain regarding the outcome of their decisions. The classical approach to the study of risky choice is expected utility theory (EUT). At last year's AET Conference, Polak and Liu proposed a framework for integrating EUT and random utility theory (RUT) in a consistent fashion and showed that models developed within the expected random utility theory (ERUT) framework have empirical advantages compared to existing ad hoc applications of EUT to risky transport choice contexts. However, EUT is known to have several weaknesses as a descriptive theory of human behaviour and many alternative theories have been proposed. In related work reported at last year's IATBR Conference, Michea and Polak, compared EUT models with models derived from a number of alternative theories of risky choice including Prospective Reference Theory, Weighted Utility Theory, Rank-dependent EUT and Cumulative Prospect Theory. Although there is considerable diversity amongst these alternative, non-expected utility theories (NEUT), they all share a common feature which is that they relax the assumption, fundamental to EUT, that when evaluating risky prospects, decision makers manipulate probabilities strictly according to the laws of probability. The results reported in Michea and Polak indicate that some of these NEUT models can offer significant empirical improvement compared to EUT models.
However, despite this recent progress, a number of important issues remain outstanding. This paper focuses on three of these issues. The first is that NEUT based approaches have to date not been properly integrated with RUT. The second is that in all the work undertaken to date, researchers have only considered situations in which there is one source of uncertainty affecting choice outcomes, whereas in reality risky outcomes typically arise from the interaction of many different sources of uncertainty. The third is that the empirical evidence in the literature to date regarding the relative performance of EUT, ERUT and NEUT models is based on a very limited number of datasets.
In this paper we set out an extension of the ERUT framework of Polak and Liu which can accommodate NEUT models. The resulting non-expected random utility theory (NERUT) framework subsumes all the existing models and provides a basis for systematic empirical comparison of alternative approaches to the treatment of risky choice. We apply this framework to compare EUT and a number of NEUT models using data from a recently completed stated preference exercise, which investigated the effect of travel time variability on mode and time of day choice. In this work, two linked exercises were carried out; the first involving within mode and between mode comparisons in which respondents were exposed to options characterised by a single source of uncertain travel times. The second exercise involved within mode comparisons in which options were characterised by two sources of travel time uncertainty. This enables us to explore not only whether or not the uncertain options within a risk prospect are evaluated on the basis of their mathematical expectation but also whether different sources of uncertainty are combined according to the law of probability. We present a range of empirical results and discuss the implications of these results for the valuation of changes in travel time variability.
Association for European Transport