Dual Criteria Decisions
Steffen Andersen
Glenn Harrison
Morten Lau
Elisabet Rutström
Single Criteria Models of Decisions
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Utility or expected utility
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EUT
Multi-attribute models reduce to one scalar for each prospect
Non-EUT models such as rank-dependent EU or prospect
theory also boil down to a scalar
Some lexicographic models, but still single criteria at
each sequential stage
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Prospect theory with editing and then evaluation stage
Similarity criteria, and then EU
Dual Criteria Models – Motivation
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Mixtures of EU and PT
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Could be interpreted as two criteria that the same
decision-maker employs for a given choice
Psychological literature
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Lopes SP/A model
Heuristics and cues, emphasis on plural
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Capital city cue?
Natural language cue?
Lopes SP/A Model
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Designed from observation of skewed bets
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The shape of the distribution of outcomes seemed to
matter
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Two criteria emerged from verbal protocols
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Subjects had preferences for long-shots over symmetric
bets, with same EV
Same as obscure arguments by Allais
Security Potential (SP) criteria
Aspiration (A) criteria
How are these combined?
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Weighted average, so ends up as a single criteria
model…
SP Criterion, Just RDEU
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Decision weights
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Cumulative probabilities used to weight utility of
prospects
Interpreted as “probability of at least $X”
Same as Quiggin, JEBO 1982
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Special case may be RDEV, the “dual-risk” model of
Yaari Econometrica 1987
Used by Tversky & Kahneman in cumulative prospect
theory, JRU 1992
A Criterion, Just An Income Threshold
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Weights given to outcome to reflect extent to which
they achieve some subjective threshold
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Fuzzy sets Lopes & Oden, JMathPsych 1999
Some probability weight is all we need
1
.75
.75
Probability
Probability
Alternative Aspiration Functions
1
.5
.5
.25
.25
0
0
0
50000
100000 150000 200000 250000
Prize Value
0
50000
100000 150000 200000 250000
Prize Value
Aside: Income Thresholds
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NY city taxi drivers
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Tend to quit early on busy days, once they meet their
threshold; tend to work longer on slow days
Shouldn’t they substitute labor time from slow days to
these busy days?
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Camerer, Babcock, Lowenstein & Thaler, QJE 1997;
thoroughly critiqued by Farber, JPE 2005
No controls for risk attitudes or discount rates…
No controls for how many days worked…
Others with flexible work hours
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Stadium vendors (Oettinger, JPE 1999)
Bicycle messengers (Fehr & Goette, AER 2007)
Deal Or No Deal

Natural experiment with large stakes
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Simple rules, nothing strategic
Replicated from task to task
UK version
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Prizes from 1p up to ₤250,000 ($460k)
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Average earnings ₤16,750 in our sample
Divers demographics in sample
 Limited demographics observable
 Some sample selection?
N=461
Skewed Distribution of Prizes
EV = ₤25,712
Median prizes = [₤750, ₤1,000]
Dynamic Sequence
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Pick one box for yourself

Round #1
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Open 5 boxes
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Get an offer ≈ 15% of EV of unopened prizes
Round #2, #3, #4, #5, #6
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Open 3 boxes per round
Offer ≈ 24%, 34%, 42%, 54%, 73% of EV
Round #7
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Only 2 boxes left
Optimal Choices Under EUT
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In round #1, compare U of certain offer to

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EU
EU
EU
EU
EU
EU
of
of
of
of
of
of
virtual lottery from saying ND, D
virtual lottery from saying ND, ND, D
virtual lottery from saying ND, ND, ND, D
virtual lottery from saying ND, ND, ND, ND, D
virtual lottery from saying ND, ND, ND, ND, ND, D
just saying ND in every future round
Say ND if any EU exceeds U(offer)
Similarly in round #2, etc.
Likelihood of observed decision in each round
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Prob(ND) = Φ[max (EU) - U(offer)]
Easy to extend to non-EUT models
Close approximation of fully dynamic solution
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See our Risk Aversion in Game Shows paper for details
Applying Various Models
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EUT
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Expo-power with IRRA
CRRA when allow for asset integration
Subjects are not myopic
CPT
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Significant evidence of probability weighting
No evidence of loss aversion
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What is the true reference point??
See our Dynamic Choice Behavior in a Natural Experiment paper for details
The SP Criterion
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Utility function
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ω(p) = pγ / [pγ + (1-p)γ]1/γ
Decision weights
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for r≠1
Probability weighting
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CRRA: u(x) = x(1-r)/(1-r)
wi = ω(pi+…+pn) - ω(pi+1+…+pn) i=1,…,n-1
wn = ω(pn)
Overall RDEU or SP criterion
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RDUi = ∑ wi × u(xi)
The Aspiration Function
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Pick some über-flexible cdf
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Monotone increasing
Continuous
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No real priors here
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Cumulative non-central Beta distribution
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Three parameters
Orrible to see written out in daylight
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But an intrinsic function in Stata, GAUSS etc.
How To Combine SP and A?
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Mixture modeling
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View SP as one psychological process
View A as another psychological process
Occurs within subject, for each choice
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Illustrates why we are so agnostic on this in Weddings
modeling
Likelihoods
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Likelihood of choice if using SP only
Likelihood of choice if using A only
Weighted, grand likelihood of SP/A
Figure 1: Decision Weights under RDU
1
RDU ã=.55
1
.9
.8
.75
.7
.6
ù(p)
Decision
Weight .5
.5
.4
.3
.25
.2
.1
0
0
0
.25
.5
p
.75
1
1
2
3
4
Prize (Worst to Best)
5
Figure 1: Decision Weights under RDU
1
RDU ã=.55
1
.9
.8
.75
.7
.6
ù(p)
Decision
Weight .5
.5
.4
.3
.25
.2
.1
0
0
0
.25
.5
p
.75
1
1
2
3
4
Prize (Worst to Best)
5
Figure 1: Decision Weights under RDU
1
RDU ã=.55
1
.9
.8
.75
.7
.6
ù(p)
Decision
Weight .5
.5
.4
.3
.25
.2
.1
0
0
0
.25
.5
p
.75
1
1
2
3
4
Prize (Worst to Best)
5
Figure 2: SP/ A Weighting and Aspiration Functions
SP Weighting Function
ã=.664
1
.75
ù(p)
Aspiration Weights
1
.75
ç
.5
.5
.25
.25
0
0
0
.25
.5
p
.75
1
0
50000
100000 150000 200000 250000
Prize Value
Lab Experiments
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Lab as complement to field
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More controls, such as the task design
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Different country formats
Different bank offer functions
Information on earnings, especially the distribution
More information about subjects
Is the lab reliable?
See our Risk Aversion in Game Shows paper for details
Lab Design
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UCF student subjects
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N=125 in total, over several versions
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Normal procedures
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Prizes presented in nominal game-show currency
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Exchange rate converts to $250 maximum
Subjects love playing this game
Figure 7:
SP/ A Weighting and Aspiration Functions
With Lab Responses
1
SP Weighting Function
Aspiration Weights
ã=.308
1
.75
ù(p)
.75
ç
.5
.5
.25
.25
0
0
0
.25
.5
p
.75
1
0
50
100
150
Prize Value
200
250
Conclusions
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Dual criteria models
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Way to integrate various criteria, including those with
descriptive and non-normative rationale
Natural use of mixture modeling logic
SP/A is also rank-dependent and sign-dependent
Both criteria in SP/A seem to be used*
Deal Or No Deal
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Not just utility-weighting going on
But there is some utility-weighting
In comparable lab environment subjects seem to use a
very simple decision heuristic*