1. Centre for Transport Studies Modelling heterogeneity in decision making processes under uncertainty Xiang Liu and John Polak Centre for Transport Studies Imperial College London j.polak@imperial.ac.uk www.imperial.ac.uk/cts

2. Centre for Transport Studies Outline Background and objectives Conceptual approach Modelling framework Data collection Preliminary results and interpretation Conclusion

3. Centre for Transport Studies Background (1) Increasing congestion has led to greater uncertainty in system performance, hence –need to understand/model impact on behaviour and –place valuations on changes in uncertainty The design and evaluation of ITS also requires the treatment of information imperfections These (and other) contexts require a theory that describes how travellers choose between alternatives that are defined as probability distributions over possible outcomes This area is under-developed in transport modelling (but growing interest)

4. Centre for Transport Studies Background (2) There are a wide range of theories of choice under uncertainty –Expected utility theory –Regret theory –Prospect theory –Cumulative Prospect theory –and several others… However, two important issues remain –Integration with RUM –Empirical evaluation in transport context

5. Centre for Transport Studies Objectives To provide a coherent utility-based treatment jointly of –Decision makers’ uncertainty (e.g. SEU, PT, CPT) –Modellers’ uncertainty (e.g., RUM) To investigate heterogeneity in decision making under uncertainty (both parametric and as between different styles) and its relationship to observable and unobservable influences To explore these issues in the context of realistic transport decision making contexts (not stylised lotteries)

6. Centre for Transport Studies Conceptual framework

7. Centre for Transport Studies Modelling framework The general framework for these approaches to decision making under uncertainty can be characterised as follows: where x is a vector of decision variables s(x) is a vector representing a state of the world, dependent upon the travellers decision u() is a utility function giving the value to the traveller of the state s(x) p(s) is the (objective) pdf of the states s f() and g() are functions, in general non-linear

8. Centre for Transport Studies Preliminary study Based on SP data collected by Bates, Polak, Jones and Cook (2001) –~200 rail travellers –choice contexts involving alternative rail operators offering services with different levels of travel time uncertainty –trade off of fare, scheduled departure time, headway scheduled travel time and uncertainty in travel time Bates et al. presented expected utility models; in this paper we generalise this to allow for explicit risk aversion/risk proneness We also allow for heterogeneity in attitudes to risk across sample

9. Centre for Transport Studies Bates et al., (2001)

10. Centre for Transport Studies Utility functions (1) Bates et al., (2001) use the following risk neutral expected utility specification, resulting in a LIP MNL/NL model We generalise this to where the parameter is the Arrow-Pratt absolute risk aversion coefficient; implies constant risk aversion whereas implies constant risk proneness

11. Centre for Transport Studies Utility functions (2) Three versions of this model are being developed: –Constant for all travellers (MNL) –Deterministic variation in, via segmentation (MNL) –Deterministic and stochastic variation in (MMNL)

12. Centre for Transport Studies Summary of preliminary results Across the sample as a whole, there is statistically significant evidence of mild risk-proneness Remaining substantive model parameters are largely unaffected compared to Bates et al., results Also evidence of significant heterogeneity in the attitude to risk across the sample - ~ 10% of the sample were risk averse; 90% were risk prone Attitude to risk appears to be systematically related to destination activity

13. Centre for Transport Studies Conclusions It is possible to extend existing RUM theoretic models to accommodate a more sophisticated treatment of uncertainty There are however, several important underlying conceptual and theoretical issues still require serious reflection e.g, ordinal vs cardinal utility scales Beyond this, the current work will be extended in a number of ways: –more general formulations of attitudes to risk (e.g., HARA class models) –exploration of non-SEU models (e.g., RT, PT, CPT)