Graham Loomes, University of Warwick
Undergraduate at Essex 1967-70
Modelling Decision Making:
Combining Economics, Psychology and Neuroscience
Thanks to many co-authors over the years – Bob Sugden
and Mike Jones-Lee in particular
For today’s talk, thanks to Dani Navarro-Martinez,
Andrea Isoni and David Butler
Thanks to ESRC for a Professorial Fellowship; more
recently, the ESRC Network for Integrated Behavioural
Science; and the Leverhulme Trust ‘Value’ Programme
Graham Loomes, University of Warwick
Undergraduate at Essex 1967-70
Modelling Decision Making:
Combining Economics, Psychology and Neuroscience
A number of things attracted me to Essex
Progressive attitudes
Impressive people
Common first year involving Econ Gov Soc Stats
No Psych, unfortunately (and still none at u/g level . . . ?)
Positive economics: emphasis on evidence
Downside: de-emphasised internal processes – what went
on in the head was (then) unobservable ‘black box’ activity
Upside: favoured empirical testing
For decision making under risk, (S)EU model ruled in
economics
As if assign subjective ‘utility’ to payoffs and weight by
probabilities and decide according to expectation
But the evidence contradicted the theory in certain
‘phenomenal’ or ‘paradoxical’ respects
But actually ‘positive’ economists didn’t do much testing
(one or two notable exceptions)
Most testing was done by psychologists and statisticians
(and the odd engineer)
And clear gaps between economists’ models and
observed behaviour were apparent from the early days
(and stubbornly persist)
Models
Behaviour
Deterministic
Probabilistic
Parsimonious/restricted
Multi-faceted
Procedurally invariant
Sensitive to
framing/procedure
What if we were starting from what we know now?
Summarise some key facts
Choices are systematically probabilistic over some range
Option B:
£40, 0.8; 0, 0.2
Option A:
X, 1
Response times (RTs) are related to these probabilities,
as are judgments of difficulty / confidence
Option B:
£40, 0.8; 0, 0.2
Option A:
X, 1
Decision making involves brain activity that looks like the
sampling and accumulation of evidence until an action is
triggered
How might that apply to risky choice?
I offer you a choice between
Lottery A: 90% chance of £15; 10% chance of 0
Lottery B: 35% chance of £50; 65% chance of 0
on the understanding that the one you pick will be
played out and you will get paid (or not) accordingly
Which one do you pick?
How did you reach that decision?
Lottery A: 90% chance of £15; 10% chance of 0
Lottery B: 35% chance of £50; 65% chance of 0
A fairly general model (with some eyetracking support)
entails numerous (often repeated) binary comparisons:
Positive payoff comparison is evidence for B
Chance of 0 is evidence for A
Not just a matter of the direction of the argument but
also the force – involving judgments sampled from
memory and/or perception which may vary in strength
from sample to sample
The process of sampling and accumulating evidence has
often been represented as follows:
Accumulator value
τ
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Sample number
Up favours A, down favours B
Vertical axis represents force / valence
Choice made when accumulated evidence reaches threshold
More evenly balanced, liable to more vacillation, longer RT
and greater judged difficulty
Natural variability even when same action triggered
Accumulator value
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Sample number
29
With some sequences possibly leading to a different
choice
Accumulator value
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Sample number
29
Same choice made independently on 10 occasions:
A chosen 7 times, B chosen 3 times
Intrinsic variability, not error – simulations
Accumulator value
τ
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Sample number
29
Often such models are depicted in terms of a fixed
threshold
An alternative is to suppose that choice is triggered
when we feel ‘confident enough’ about the imbalance of
evidence
This involves trading off between the level of confidence
we feel we want and the amount of time spent
deliberating (and the opportunity costs entailed –
mind/time/attention is a scarce resource – Simon)
So modelling individual decision making as a process
requires us to specify:
What he/she samples
How the evidence is weighed and accumulated
What the stopping/trigger rule is
Boundedly Rational Expected Utility Theory – BREUT
Aim: to illustrate the idea by taking the industry standard
model and embedding it in a deliberative process
(Other models/assumptions are available . . . e.g.
Busemeyer & Townsend’s 1993 Decision Field Theory –
the pathbreaking application to preferential choice)
What he/she samples
The sampling frame is the underlying acquired set of
various memories/impressions/perceptions of relative
subjective values of payoffs, represented by a set of vNM
utility functions (say, a distribution of coefficients of RRA)
A draw entails picking a u(.) at random and applying it to
the pair of options under consideration
How the evidence is weighed and accumulated
A sampled u(.) corresponds with a preference for A or B –
the direction on the vertical axis
But what about the strength of the evidence?
Proxied by the CE difference: + for A, – for B
As sampling progresses, mean and variance are updated
What the stopping/trigger rule is
When the options are first presented, the null hypothesis
is that neither is preferred: that there is zero imbalance of
evidence either way
This is maintained until rejected with sufficient confidence
An individual may be characterised as having an initial
desired level of confidence which he/she lowers as time
passes in order to make this decision and gets on to the
next decision / rest of life
Some Results/Implications
1. Observed choices do not necessarily reveal the
structure of underlying preferences
EU is not the only possible ‘core’ – can embed other
assumptions – but BREUT shows that underlying
preferences can ALL be vNM and yet modal choices in
‘Common Ratio Effect’ pairs violate independence:
£30, 1 preferred to £40, 0.8 in more than 50% of choices
Yet £40, 0.2 is the modal choice over £30, 0.25
This pattern has done more than any other to discredit
independence – yet it COULD be compatible with core EU
Challenge to RP
2. Can’t just stick a noise term on each option
Variability of the kind discussed here is intrinsic, so a simple
‘add-on’ error term cannot capture it adequately
Two lotteries B and
C, each 50% likely
to be chosen when
paired with sure A6
BREUT allows
different
frequencies versus
other sure sums
Contrary to Luce
formulation
B
C
It might seem that all we need is to allow eC to have higher
variance than eB. But when the As are lotteries with a bigger
payoff range than B and C . . .
B
C
It might seem that all we need is to allow eC to have higher
variance than eB. But when the As are lotteries with a bigger
payoff range than B and C . . .
The two curves flip
positions
But that would
entail eC having a
lower variance
than eB.
So independent
add-on noise
model ruled out
C
B
3. Context/frame/procedure effects are endemic
If sampling and accumulation are key, anything which
influences the process may affect the outcome
Equivalence tasks compared with choice tasks: how is the
‘response mode’ influential? Do we ‘anchor and adjust’?
Reference/endowment effects – WTP vs WTA: does
endowment change the initial null?
Range-frequency effects in multiple choice lists: do these
edit/overwrite our sampling frames (as in DbS)?
3. Context/frame/procedure effects are endemic
Lab experiments may show effects most sharply – but all
these effects may have ‘real world’ counterparts
People may be most susceptible in contexts where they are
least familiar/experienced – but these are important nonmarket areas (e.g. health, safety, environment) where
survey elicitation informs policy
Since ALL production of responses involves SOME process,
can we separate ‘true preference’ from ‘procedural bias’?
Concluding Remarks
Parsimonious deterministic models played their role in the days when
we knew little about brain processes and when limited computing
power made analytical results desirable
But we now have dozens of such models, each only accounting for a
subset of behaviour and with considerable overlap/redundancy
Crucially, they neglect the reality of probabilistic responses. This
cannot be ‘fixed’ by some arbitrary add-on noise (which in any case
provides no explanation for the RT/difficulty/confidence data)
The ‘positive’ future lies in multiple-influence probabilistic processbased models harnessing computing power and simulation methods
to integrate insights from psychology and neuroscience with the social
sciences
Graham Loomes, University of Warwick
Undergraduate at Essex 1967-70
Modelling Decision Making:
Combining Economics, Psychology and Neuroscience