Testing Heuristic Models of Risky Decision Making

1. Testing Heuristic Models of Risky Decision Making Michael H. Birnbaum California State University, Fullerton

2. Outline • Priority Heuristic • New Critical Tests: Allow each person to have a different LS with different parameters • Four tests: Interaction, Integration, Transitivity, & Priority Dominance.

3. Priority Heuristic • Brandstätter, et al (2006) model assumes people do NOT weight or integrate information. • Examine dimensions in order • Only 4 dimensions considered. • Order fixed: L, P(L), H, P(H).

4. PH for 2-branch gambles • First: minimal gains. If the difference exceeds 1/10 the (rounded) maximal gain, choose by best minimal gain. • If minimal gains not decisive, consider probability; if difference exceeds 1/10, choose best probability. • Otherwise, choose gamble with the better highest consequence.

5. Priority Heuristic examples

6. PH Reproduces Some Data… Predicts 100% of modal choices in Kahneman & Tversky, 1979. Predicts 85% of choices in Erev, et al. (1992) Predicts 73% of Mellers, et al. (1992) data

7. …But not all Data • Birnbaum & Navarrete (1998): 43% • Birnbaum (1999): 25% • Birnbaum (2004): 23% • Birnbaum & Gutierrez (in press): 30%

8. Problems • No attention to middle branch, contrary to results in Birnbaum (1999) • Fails to predict stochastic dominance in cases where people satisfy it in Birnbaum (1999). Fails to predict violations when 70% violate stochastic dominance. • Not accurate when EVs differ. • No individual differences and no free parameters. Different data sets have different parameters. Delta > .12 & Delta < .04.

9. Modification: • Suppose different people have different LS with different parameters.

10. Family of LS • In two-branch gambles, G = (x, p; y), there are three dimensions: L = lowest outcome (y), P = probability (p), and H = highest outcome (x). • There are 6 orders in which one might consider the dimensions: LPH, LHP, PLH, PHL, HPL, HLP. • In addition, there are two threshold parameters (for the first two dimensions).

11. New Tests of Independence • Dimension Interaction: Decision should be independent of any dimension that has the same value in both alternatives. • Dimension Integration: indecisive differences cannot add up to be decisive. • Priority Dominance: if a difference is decisive, no effect of other dimensions.

12. Taxonomy of choice models

13. Priority Heuristic Implies • Violations of Transitivity • Satisfies Interactive Independence: Decision cannot be altered by any dimension that is the same in both gambles. • No Dimension Integration: 4-choice property. • Priority Dominance. Decision based on dimension with priority cannot be overruled by changes on other dimensions. 6-choice.

14. Dimension Interaction

15. Family of LS • 6 Orders: LPH, LHP, PLH, PHL, HPL, HLP. • There are 3 ranges for each of two parameters, making 9 combinations of parameter ranges. • There are 6 X 9 = 54 LS models. • But all models predict SS, RR, or ??.

16. Results: Interaction n = 153

17. Analysis of Interaction • Estimated probabilities: • P(SS) = 0 (prior PH) • P(SR) = 0.75 (prior TAX) • P(RS) = 0 • P(RR) = 0.25 • Priority Heuristic: Predicts SS

18. Probability Mixture Model • Suppose each person uses a LS on any trial, but randomly switches from one order to another and one set of parameters to another. • But any mixture of LS is a mix of SS, RR, and ??. So no LS mixture model explains SR or RS.

19. Dimension Integration Study with Adam LaCroix • Difference produced by one dimension cannot be overcome by integrating nondecisive differences on 2 dimensions. • We can examine all six LS Rules for each experiment X 9 parameter combinations. • Each experiment manipulates 2 factors. • A 2 x 2 test yields a 4-choice property.

20. Integration Resp. Patterns

21. 54 LS Models • Predict SSSS, SRSR, SSRR, or RRRR. • TAX predicts SSSR—two improvements to R can combine to shift preference. • Mixture model of LS does not predict SSSR pattern.

22. Choice Percentages

23. Test of Dim. Integration • Data form a 16 X 16 array of response patterns to four choice problems with 2 replicates. • Data are partitioned into 16 patterns that are repeated in both replicates and frequency of each pattern in one or the other replicate but not both.

24. Data Patterns (n = 260)

25. Results: Dimension Integration • Data strongly violate independence property of LS family • Data are consistent instead with dimension integration. Two small, indecisive effects can combine to reverse preferences. • Replicated with all pairs of 2 dims.

26. New Studies of Transitivity • LS models violate transitivity: A > B and B > C implies A > C. • Birnbaum & Gutierrez tested transitivity using Tversky’s gambles, but using typical methods for display of choices. • Also used pie displays with and without numerical information about probability. Similar results with both procedures.

27. Three of Tversky’s (1969) Gambles • A = ($5.00, 0.29; $0, 0.71) • C = ($4.50, 0.38; $0, 0.62) • E = ($4.00, 0.46; $0, 0.54) Priority Heurisitc Predicts: A > C; C > E, but E > A. Intransitive. TAX (prior): E > C > A

28. Tests of WST (Exp 1)

29. Results-ACE

30. Summary • Priority Heuristic’s predicted violations of transitivity are rare. • Dimension Interaction violates any member of LS models including PH. • Dimension Integration violates any LS model including PH. • Data violate mixture model of LS. • Evidence of Interaction and Integration compatible with models like EU, CPT, TAX.