Dual Criteria DecisionsDual Criteria Decisions

Steffen AndersenGlenn Harrison

Morten LauElisabet Rutström

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

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?

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…

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

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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Alternative Aspiration Functions

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 Shouldn’t 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)

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?

N=461

Skewed Distribution of Prizes

EV = ₤25,712 Median prizes = [₤750, ₤1,000]

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

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) = Φ[max (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

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

The SP Criterion

Utility function CRRA: u(x) = x(1-r)/(1-r) for r≠1

Probability weighting ω(p) = pγ / [pγ + (1-p)γ]1/γ

Decision weights wi = ω(pi+…+pn) - ω(pi+1+…+pn) i=1,…,n-1

wn = ω(pn)

Overall RDEU or SP criterion RDUi = ∑ wi × u(xi)

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.

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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Prize (Worst to Best)

Figure 1: Decision Weights under RDU

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Figure 1: Decision Weights under RDU

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Figure 1: Decision Weights under RDU

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SP Weighting Functionã=.664

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Aspiration WeightsFigure 2: SP/A Weighting and Aspiration Functions

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

Lab Design

UCF student subjects

N=125 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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SP Weighting Functionã=.308

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Aspiration Weights

Figure 7:SP/A Weighting and Aspiration Functions

With Lab Responses

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*