Dual Criteria Decisions

1. Dual Criteria Decisions Steffen Andersen Glenn Harrison Morten Lau Elisabet Rutström

3. 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

4. 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?

5. 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…

6. 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

7. 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

8. 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)

9. 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

10. Skewed Distribution of Prizes EV = ₤25,712 Median prizes = [₤750, ₤1,000]

11. 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

12. 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

13. 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

14. 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)

15. 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.

16. 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

24. 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

28. 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

31. 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*