On the Irrelevance of Prospect Theory in Modelling Uncertainty in Travel Decisions

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On the (Ir)relevance of Prospect Theory in
ModellingUncertainty in Travel Decisions

• Harry Timmermans

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Decision Making Approach

• Riskless versus Risky
• Wide variety of topics in riskless choice
  studies far less in studies of risky choice
• Axiomatic versus nonaxiomatic utility theory

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• Your Subtopics Go Here

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Boundaries of Prospect Theory general criticisms
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General boundaries

• Conceptual issues
• Experimental effects
• Deterministic utility function
• Bias versus bounded rationality

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Conceptual issues

• Information about objective probabilities not
  provided in many choice situations
• Not realistic to assume that individuals first
  assign probabilities and then apply decisions
  weights
• Imperfect and incomplete information is captured
  in beliefs not readily evident that mental
  representation involves uncertainty (risk
  perception?)
• may be conceptually richer to distinguish between
  mental representation, cognitive environment,
  preference structure and choice rule to avoid any
  confounding as potentially done in prospect
  theory.

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Conceptual issues

• Overweighting of small probabilities vs ignored
  in editing phase?
• Prospect theory risk attitude is nothing but a
  descriptive label of the curvature of the utility
  function and the weighted probability function
  presumed to underlie travel choices.
• As choices in certain real world environments do
  not necessarily reflect underlying preferences,
  observed choices in uncertain environments do not
  necessarily depict risk attitudes and
  corresponding decision styles.

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Polak

• Rank-dependent model
• What would have happened if the extreme
  probability cases would not have been part of the
  experiment

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Experimental effects

• Experimental design in Riskless preference and
  choice
• Avoid non-linear effects of anchoring
• Use natural task
• Use common words
• Error theory
• Design experiment to optimize certain
  characteristics
• Systematically trigger respondents to apply
  preference function

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Experimental effects

• Experimental design in Risky choice
• Search for anchoring
• Task is like a quiz
• Difficult to process
• No Error theory
• Design experiment not optimized in any sense
  except to make errors
• No systematic triggers
• evidence of risk aversion may have been
  confounded with errors introduced in
  understanding the experimental task, the framing
  of the task itself, limited information
  processing/bounded rationality in completing the
  task or any other process affecting the
  response-generating process.

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Avineri

• Examples of information processing could be
  typical examples of information integration
  theory and/or psychophysical relationships
• Not relevance to judgement and/or choice

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Deterministic utility function

• Implicitly, prospect theory assumes that when
  faced with replicated identical binary choices,
  subjects will made the same choice. This is in
  contrast with much empirical evidence
• Researchers made additional assumptions
• Utility-max behavior inconsistent?
• Errors are made in activity value function

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Deterministic utility function

• However, no explicit treatment of risk attitude
  in choice rule. There does not seem any inherent
  reason to assume that risk attitudes do not play
  a role in the choice stage of a decision problem.
  
• The estimated parameters of prospect theory (and
  any other deterministic theory) may differ
  substantially depending on the assumptions that
  are made with respect to stochastic choice rule
  that is assumed to capture the error-generating
  process. Evidence of risk aversion may vanish
  when a different stochastic choice rule is
  introduced.

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Schwanen and Ettema

• Consider different valuing functions and decision
  weights
• But these will be highly correlated
• Assumed utility-maximizing behaviour
• Not appealing non rational behaviour in valuing
  function and decision weights not in the choice
  rule
• Tests do not vary the assumption about the
  probabilistic choice rules results depend on
  assumptions made
• Risk attitude in choices assumed identical
  unrealistic assumption
• Lack of statistical test differences are small
  interpretation/evidence may be overrated

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Rose

• Evidence that conclusions depend on the
  assumptions regarding (a)symmetry in the cost
  function

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Bounded rationality?

• many of the examined biases can also be explained
  by the alternative assumption that individuals
  demonstrate bounded rationality.
• prospect theory and cumulative prospect theory
  are difficult to test and apply in practice
  because the editing can be done in so many
  different ways, leaving many more degrees of
  freedom compared to other theories.

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Boundaries of Prospect Theory specific
criticisms in the context of transportation
research
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General boundaries

• Incongruence in decision problem representation
• Ignoring credibility of information (source) and
  underlying control strategy
• Ignoring learning effects
• Gains and losses?
• Ignoring heterogeneity and context effects

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Incongruence in decision problem representation

• In the typical transportation problems,
• respondents are NOT fully informed
• Do not know objective probabilities
• Do not know the values
• Uncertainty may also arise from lack of awareness

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Credibility and control strategy

• Travellers may have reason to believe that the
  information or information source is not credible
  because
• (i) it may be based on imperfect model
  predictions or historical data,
• (ii) it may be not be real-time data,
• (iii) by the time they face the decision to make,
  the information may be old, and/or
• (iv) the information provider may have ulterior
  motives that may not necessarily be in the
  travellers personal interest.
• Han et al have shown that travelers can decipher
  control strategies and act accordingly

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Ignoring learning effects

• (Cumulative) prospect theory has little to say
  about how travellers learn and adapt their
  behaviour to the structure and dynamics of a
  given uncertain environment and to varying
  degrees of awareness, information levels and
  belief strengths.
• Same wrt information exchange and social
  interaction
• Loss aversion does not seem an effective coping
  mechanism against regret!

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Gains and losses?

• No natural reference point
• Shouldnt the application be restricted to
  decisions under risk that involve true
  significant, irreversible losses.
• Is time allocation to travel and different
  activities better conceptualized in terms of
  gains and losses are just as alternative choices?
  

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Gains and losses?

• The potential benefit of differentiating between
  gains and losses is significantly less if the
  decision problem can be realistically
  conceptualized in gains or losses only.
• Reference points are endogeneous, and stochastic,
  situation-dependent
• There is a long history in models of riskless
  choice to use reference points or thresholds to
  model ideal points, variety seeking behaviour,
  inertia/status quo, hybrid utility functions,
  aspects of bounded rationality, relative utility
  theory, historical disposition, latent
  personality traints, and different frames of
  references as a function of accumulated
  experiences.

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Polak

• Endogenous, but not stochastic
• Estimated, but not stated
• Thresholds in utility space?
• Matter of specification?

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Mahmassani

• Construct validity-are these still gains and
  losses?
• Would model behave any differently if the
  specification would be labelled otherwise?

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Chorus et al.

• Reference point is the best of foregone
  alternatives
• Acknowledges
• Choice context
• Impact of choice set composition
• Comments
• Are regrets linear or nonlinear?
• Only the best alternative are multiple/all with
  varying probability weights?
• From regret minimization to regret aversion?

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Heterogeneity and context effects

• No account of
• taste variation
• Context dependency
• Choice set effects
• To raise the bar, several of such effects need to
  be estimated
• Even then, the models would not be embedded in a
  model of activity-travel behavior

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Rose

• One of the first studies in transportation
  research applying MMNL model for gains/losses,
  following Polak, Hensher etc.
• However, choice task is not example of decison
  under uncertainty
• Taste variation but specification utility
  function applies to all individuals

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Conclusions and discussion
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Discussion

• Conceptually
• Some fundamental differences between simple
  gambling behavior under risk and complex travel
  behavior under uncertainty.
• Some mechanisms are poorly addressed, such as
  risk attitudes in choice
• Content validity of these models as a
  manifestation of a theory of travel behavior
  under uncertainty is relatively poor compared to
  alternative theories of travel behavior under
  uncertainty
• Prospect theory is more a data-fitting approach

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Discussion

• Modelling approach
• the 35 years since its introduction have not led
  to much theoretical progress nor to the
  development of advanced operational models
• Curvature can be captured equally well in the
  context of other theories of choice
• Several extensions are deemed necessary do we
  still call this prospect theory?

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Van der Kaa

• Extended prospect theory
• Is this the extension needed
• However,
• Notions seems conflicting
• How to build an operational model
• What makes it prospect theory? Curvature of
  contents
• Notion of consistent intrapersonal behavior?

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Rose, Polak

• Applications of MMNL
• With specific curvature
• However, these specifications have a long
  tradition in other applied sciences
• Do we call this prospect theory or relative
  utility theory or ????

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Relevance

• Yes, in specific contexts such as pricing and
  information provision whether the decision
  problem and context resembles the theory
• No, as a theory of dynamic activity-travel
  behavior under uncertainty and information
  provision.
• However, nonlinearity etc critical for developing
  operational models of choice behavior (see
  Mahmassani)

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Implications

• Think dont flirt with any theory/model
• Nature of problem
• High involvement vs low involvement
• Context?
• Personal or other consequences
• Routine vs non-routine
• Individual vs household
• Social context?
• Choose or develop theory/models that has the most
  appealing mechanisms/concept

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Implications

• Methodological
• Realise that the same mathematical expression can
  be derived from multiple, sometime conflicting
  theories
• There is more than predictive validity

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THANK YOU

• Harry Timmermans