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New Paradoxes of Risky Decision Making that Refute Prospect Theories

New Paradoxes of Risky Decision Making that Refute Prospect Theories. Michael H. Birnbaum Fullerton, California, USA. Outline. I will review tests between Cumulative Prospect Theory (CPT) and Transfer of Attention eXchange (TAX) model.

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New Paradoxes of Risky Decision Making that Refute Prospect Theories

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  1. New Paradoxes of Risky Decision Making that Refute Prospect Theories Michael H. Birnbaum Fullerton, California, USA

  2. Outline • I will review tests between Cumulative Prospect Theory (CPT) and Transfer of Attention eXchange (TAX) model. • Emphasis will be on critical properties that test between these two non-nested theories.

  3. Cumulative Prospect Theory/ Rank-Dependent Utility (RDU)

  4. “Prior” TAX Model Assumptions:

  5. TAX Parameters For 0 < x < $150 u(x) = x Gives a decent approximation. Risk aversion produced by d. d = 1 .

  6. Non-nested Models

  7. CPT and TAX nearly identical inside the prob. simplex

  8. Testing CPT TAX:Violations of: • Coalescing • Stochastic Dominance • Lower Cum. Independence • Upper Cumulative Independence • Upper Tail Independence • Gain-Loss Separability

  9. Testing TAX Model CPT: Violations of: • 4-Distribution Independence (RS’) • 3-Lower Distribution Independence • 3-2 Lower Distribution Independence • 3-Upper Distribution Independence (RS’) • Res. Branch Indep (RS’)

  10. Stochastic Dominance • A test between CPT and TAX: G = (x, p; y, q; z) vs. F = (x, p – q; y’, q; z) Note that this recipe uses 4 distinct values of consequences. It falls outside the probability simplex defined on three consequences. CPT  G, TAX F We can test if violations due to “error”

  11. Violations of Stochastic Dominance 122 Undergrads: 59% repeat the violation (BB) 28% Pref Reversals (AB or BA) Estimates: e = 0.19; p = 0.85 170 Experts: 35% repeat violations 31% Reversals Estimates: e = 0.20; p = 0.50 Chi-Squared test reject H0: p < 0.4

  12. Pie Charts

  13. Aligned Table: Coalesced

  14. Summary: 23 Studies of SD, 8653 participants • Large effects of splitting vs. coalescing of branches • Small effects of education, gender, study of decision science • Very small effects of probability format, request to justify choice. • Miniscule effects of event framing (framed vs unframed)

  15. Lower Cumulative Independence R:39%S:61% .90 to win $3 .90 to win $3 .05 to win $12 .05 to win $48 .05 to win $96 .05 to win $52 R'':69%S'':31% .95 to win $12 .90 to win $12 .05 to win $96 .10 to win $52

  16. Upper Cumulative Independence R':72%S':28% .10 to win $10 .10 to win $40 .10 to win $98 .10 to win $44 .80 to win $110 .80 to win $110 R''':34%S''':66% .10 to win $10 .20 to win $40 .90 to win $98 .80 to win $98

  17. Summary: UCI & LCI 22 studies with 33 Variations of the Choices, 6543 Participants, & a variety of display formats and procedures. Significant Violations found in all studies.

  18. S’: .1 to win $40 .1 to win $44 .8 to win $100 S: .8 to win $2 .1 to win $40 .1 to win $44 R’: .1 to win $10 .1 to win $98 .8 to win $100 R: .8 to win $2 .1 to win $10 .1 to win $98 Restricted Branch Indep.

  19. S’: .10 to win $40 .10 to win $44 .80 to win $100 S2’: .45 to win $40 .45 to win $44 .10 to win $100 R’: .10 to win $4 .10 to win $96 .80 to win $100 R2’: .45 to win $4 .45 to win $96 .10 to win $100 3-Upper Distribution Ind.

  20. S’: .80 to win $2 .10 to win $40 .10 to win $44 S2’: .10 to win $2 .45 to win $40 .45 to win $44 R’: .80 to win $2 .10 to win $4 .10 to win $96 R2’: .10 to win $2 .45 to win $4 .45 to win $96 3-Lower Distribution Ind.

  21. Gain-Loss Separability

  22. Notation

  23. Wu and Markle Result

  24. Birnbaum & Bahra--% F

  25. Summary: Prospect Theories not Descriptive • Violations of Coalescing • Violations of Stochastic Dominance • Violations of Gain-Loss Separability • Dissection of Allais Paradoxes: viols of coalescing and restricted branch independence; RBI violations opposite of Allais paradox.

  26. Summary-2

  27. Summary-3

  28. Results: CPT makes wrong predictions for all 12 tests • Can CPT be saved by using different formats for presentation? More than a dozen formats have been tested. • Violations of coalescing, stochastic dominance, lower and upper cumulative independence replicated with 14 different formats and thousands of participants.

  29. Implications • Results indicate that neither PT nor CPT are descriptive of risky decision making. • TAX correctly predicts the violations of CPT. CPT implies violations of TAX that either fail or show the opposite pattern from predicted by CPT.

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