Modelling heterogeneity in decision making processes under uncertainty
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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
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Centre for Transport Studies
Outline
• Background and objectives
• Conceptual approach
• Modelling framework
• Data collection
• Preliminary results and interpretation
• Conclusion
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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)
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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
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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)
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Centre for Transport Studies
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
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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
s
xdsspgxsuf )(()))(((max
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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
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Centre for Transport Studies
Bates et al., (2001)
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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
iiiiiiiii HFSDLSDEVU ][E][E][E
iiiiii
iV
i
HFSDLSDE
eU i
))](exp([E
][E
0
0
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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)
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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
)02.0(063.0 p
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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)