Modelling heterogeneity in decision making processes under uncertainty

Centre for Transport Studies

Modelling heterogeneity in decision making processes under uncertainty

Xiang Liu and John PolakCentre for Transport Studies

Imperial College [email protected]/cts


Outline

• Background and objectives

• Conceptual approach

• Modelling framework

• Data collection

• Preliminary results and interpretation

• Conclusion


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)


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


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)


Conceptual framework

Activity and Travel Attributes

Activity and Travel Primitives

Choice Set Formation Rules

Alternative Activity-Travel

Plans

Subjective Uncertainty

Information Integration Rules

(Incomplete) Knowledge

System Variability

Activity-Travel Plan Decision Rules

Chosen Activity-Travel Plan

Attitudes

Preferences

Partial or Complete Execution of Chosen Activity-Travel Plan

Experience

Non-experiential Information Sources

Objectives and Constraints


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

s

xdsspgxsuf )(()))(((max


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


Bates et al., (2001)


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

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iiiiii

iV

i

HFSDLSDE

eU i

))](exp([E

][E

0

0


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)


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

)02.0(063.0 p


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)

Documents

Modelling heterogeneity in decision making processes under uncertainty