Modelling heterogeneity in decision making processes under uncertainty

1. 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. Outline • Background and objectives • Conceptual approach • Modelling framework • Data collection • Preliminary results and interpretation • Conclusion

3. 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. 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. 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. Conceptual framework

7. 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. 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. Bates et al., (2001)

10. 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. 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. 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. 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)