Web-Based Program of Research on Risky Decision Making Michael H. Birnbaum California State University, Fullerton

2001

1967

Web-Based Research Series of Studies tests classical and new paradoxes in decision making. People come on-line via WWW (some in lab). Choose between gambles; 1 person per month (about 1% of participants) wins the prize of one of their chosen gambles. Data arrive 24-7; sample sizes are large; results are clear.

Allais “Constant Consequence” Paradox Called “paradox” because preferences contradict Expected Utility. A: $1M for sure  B:.10 to win $2M.89 to win $1M.01 to win $0 C:.11 to win $1M  D:.10 to win $2M.89 to win $0.90 to win $0

Expected Utility (EU) Theory A  B  u($1M) >.10u($2M) +.89u($1M) +.01u($0) Subtr..89u($1M):.11u($1M) >.10u($2M)+.01u($0) Add.89u($0):.11u($1M)+.89u($0) >.10u($2M)+.90u($0)  C  D. So, Allais Paradox refutes EU.

Cumulative Prospect Theory/ Rank-Dependent Utility (RDU)

Cumulative Prospect Theory/ RDU Tversky & Kahneman (1992) CPT is more general than EU or (1979) PT, accounts for risk-seeking, risk aversion, sales and purchase of gambles & insurance. Accounts for Allais Paradoxes, chief evidence against EU theory. Accounts for certain violations of restricted branch independence. Nobel Prize in Economics (2002)

RAM/TAX Models

RAM Model Parameters

RAM implies inverse- S

Allais “Constant Consequence” Paradox Can be analyzed to compare CPT vs RAM/TAX A: $1M for sure  B:.10 to win $2M.89 to win $1M.01 to win $0 C:.11 to win $1M  D:.10 to win $2M.89 to win $0.90 to win $0

Allais Paradox Analysis Transitivity: A  B and B  C  A  C Coalescing: GS = (x, p; x, q; z, r) ~ G = (x, p + q; z, r) Restricted Branch Independence:

A: $1M for sure  B:.10 to win $2M.89 to win $1M.01 to win $0 A ’ :.10 to win $1M  B:.10 to win $2M.89 to win $1M.89 to win $1M.01 to win $1M.01 to win $0 A ” :.10 to win $1M  B’:.10 to win $2M.89 to win $0.89 to win $0.01 to win $1M.01 to win $0 C:.11 to win $1M  D:.10 to win $2M.89 to win $0.90 to win $0

Decision Theories and Allais Paradox Branch Independence CoalescingSatisfiedViolated SatisfiedEU, CPT* OPT* RDU, CPT* ViolatedSWU, OPT*RAM, TAX

Allais Paradoxes Do not hinge on large, hypothetical prizes. Do not depend on consequence of $0. Do not require choice between “sure thing” and 3-branch gamble. Largely independent of event-framing Best explained as violation of coalescing (violations of BI run in opposition).

Case against CPT/RDU Violations of Stochastic Dominance Violations of Coalescing (Event-Splitting) Violations of 3-Upper Tail Independence Violations of Lower Cumulative Independence Violations of Upper Cumulative Independence

More Evidence against CPT/RDU/RSDU Violations of Restricted Branch Independence are opposite predictions of inverse-S weighting function needed to explain the Allais Paradoxes. Violations of distribution independence favor RAM over TAX and also opposite of predictions of CPT with inverse-S.

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