New Paradoxes of Risky Decision Making that Refute Prospect Theories

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

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Presentation transcript:

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. Emphasis will be on critical properties that test between these two non-nested theories.

Cumulative Prospect Theory/ Rank-Dependent Utility (RDU)

“Prior” TAX Model Assumptions:

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

Non-nested Models

CPT and TAX nearly identical inside the prob. simplex

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

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’)

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”

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

Pie Charts

Aligned Table: Coalesced

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)

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 Results shown here are for Birnbaum (1999b) student sample tested in lab. 124 x 2 reps.

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 These results are for the student sample of Birnbaum (1999b), lab sample.

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.

Restricted Branch Indep. S’: .1 to win $40 .1 to win $44 .8 to win $100 S: .8 to win $2 .1 to win $40 R’: .1 to win $10 .1 to win $98 .8 to win $100 R: .8 to win $2 .1 to win $10 Significantly more have the preference pattern SR’ than the reverse RS’. “Median heuristic”-- The median describes this choice, but not details of the study. Choice depends on the values of the consequences. Inverse-S implies RS’ pattern.

3-Upper Distribution Ind. 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 Here, TAX predicts a reversal: R’S2’. Indeed, of 1075 participants, more show this switch Than the opposite switch, predicted by CPT. Here RAM allows no switch. 56% (sig more than half) prefer R’ and 67% (sig more than half) prefer S2’.

3-Lower Distribution Ind. 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 Here, TAX predicts no reversal. Indeed, of 1075 participants, more show this switch Than the opposite switch, predicted by CPT. Here RAM allows no switch. 56% (sig more than half) prefer R’ and 67% (sig more than half) prefer S2’.

Gain-Loss Separability

Notation

Wu and Markle Result

Birnbaum & Bahra--% F

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.

Summary-2 Property CPT RAM TAX LCI No Viols Viols UCI UTI R’S1Viols LDI RS2 Viols 3-2 LDI

Summary-3 Property CPT RAM TAX 4-DI RS’Viols No Viols SR’ Viols UDI RBI RS’ Viols

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.

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.