Dual Criteria Decisions

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Dual Criteria Decisions

• Steffen Andersen
• Glenn Harrison
• Morten Lau
• Elisabet Rutström

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Single Criteria Models of Decisions

• Utility or expected utility
• 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
• Prospect theory with editing and then evaluation
  stage
• Similarity criteria, and then EU

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Dual Criteria Models Motivation

• Mixtures of EU and PT
• Could be interpreted as two criteria that the
  same decision-maker employs for a given choice
• Psychological literature
• Lopes SP/A model
• Heuristics and cues, emphasis on plural
• Capital city cue?
• Natural language cue?

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Lopes SP/A Model

• Designed from observation of skewed bets
• The shape of the distribution of outcomes seemed
  to matter
• Subjects had preferences for long-shots over
  symmetric bets, with same EV
• Same as obscure arguments by Allais
• Two criteria emerged from verbal protocols
• Security Potential (SP) criteria
• Aspiration (A) criteria
• How are these combined?
• Weighted average, so ends up as a single criteria
  model

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SP Criterion, Just RDEU

• Decision weights
• Cumulative probabilities used to weight utility
  of prospects
• Interpreted as probability of at least X
• Same as Quiggin, JEBO 1982
• Special case may be RDEV, the dual-risk model
  of Yaari Econometrica 1987
• Used by Tversky Kahneman in cumulative prospect
  theory, JRU 1992

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A Criterion, Just An Income Threshold

• Weights given to outcome to reflect extent to
  which they achieve some subjective threshold
• Fuzzy sets Lopes Oden, JMathPsych 1999
• Some probability weight is all we need

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Aside Income Thresholds

• NY city taxi drivers
• Tend to quit early on busy days, once they meet
  their threshold tend to work longer on slow days
• Shouldnt they substitute labor time from slow
  days to these busy days?
• 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
• Stadium vendors (Oettinger, JPE 1999)
• Bicycle messengers (Fehr Goette, AER 2007)

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Deal Or No Deal

• Natural experiment with large stakes
• Simple rules, nothing strategic
• Replicated from task to task
• UK version
• Prizes from 1p up to 250,000 (460k)
• Average earnings 16,750 in our sample
• Divers demographics in sample
• Limited demographics observable
• Some sample selection?
• N461

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Skewed Distribution of Prizes
EV 25,712 Median prizes 750, 1,000
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Dynamic Sequence

• Pick one box for yourself
• Round 1
• Open 5 boxes
• Get an offer 15 of EV of unopened prizes
• Round 2, 3, 4, 5, 6
• Open 3 boxes per round
• Offer 24, 34, 42, 54, 73 of EV
• Round 7
• Only 2 boxes left

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Optimal Choices Under EUT

• In round 1, compare U of certain offer to
• EU of virtual lottery from saying ND, D
• EU of virtual lottery from saying ND, ND, D
• EU of virtual lottery from saying ND, ND, ND, D
• EU of virtual lottery from saying ND, ND, ND, ND,
  D
• EU of virtual lottery from saying ND, ND, ND, ND,
  ND, D
• EU of 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
• Prob(ND) Fmax (EU) - U(offer)
• Easy to extend to non-EUT models
• Close approximation of fully dynamic solution

See our Risk Aversion in Game Shows paper for
details
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Applying Various Models

• EUT
• Expo-power with IRRA
• CRRA when allow for asset integration
• Subjects are not myopic
• CPT
• Significant evidence of probability weighting
• No evidence of loss aversion
• What is the true reference point??

See our Dynamic Choice Behavior in a Natural
Experiment paper for details
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The SP Criterion

• Utility function
• CRRA u(x) x(1-r)/(1-r) for r?1
• Probability weighting
• ?(p) p? / p? (1-p)?1/?
• Decision weights
• wi ?(pipn) - ?(pi1pn) i1,,n-1
• wn ?(pn)
• Overall RDEU or SP criterion
• RDUi ? wi u(xi)

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The Aspiration Function

• Pick some über-flexible cdf
• Monotone increasing
• Continuous
• No real priors here
• Cumulative non-central Beta distribution
• Three parameters
• Orrible to see written out in daylight
• But an intrinsic function in Stata, GAUSS etc.

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How To Combine SP and A?

• Mixture modeling
• View SP as one psychological process
• View A as another psychological process
• Occurs within subject, for each choice
• Illustrates why we are so agnostic on this in
  Weddings modeling
• Likelihoods
• Likelihood of choice if using SP only
• Likelihood of choice if using A only
• Weighted, grand likelihood of SP/A

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Lab Experiments

• Lab as complement to field
• More controls, such as the task design
• 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
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Lab Design

• UCF student subjects
• N125 in total, over several versions
• Normal procedures
• Prizes presented in nominal game-show currency
• Exchange rate converts to 250 maximum
• Subjects love playing this game

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Conclusions

• Dual criteria models
• 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
• 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