I’m not overweight It just needs redistribution Michael H. Birnbaum California State University, Fullerton.

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Presentation transcript:

I’m not overweight It just needs redistribution Michael H. Birnbaum California State University, Fullerton

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.

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:

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

RAM/TAX  Violations of Stochastic Dominance

Which gamble would you prefer to play? Gamble AGamble B 90 reds to win $96 05 blues to win $14 05 whites to win $12 85 reds to win $96 05 blues to win $90 10 whites to win $12 70% of undergrads choose B

Which of these gambles would you prefer to play? Gamble CGamble D 85 reds to win $96 05 greens to win $96 05 blues to win $14 05 whites to win $12 85 reds to win $96 05 greens to win $90 05 blues to win $12 05 whites to win $12 90% choose C over D

RAM/TAX  Violations of Stochastic Dominance

Violations of Stochastic Dominance Refute CPT/RDU, predicted by RAM/TAX Both RAM and TAX models predicted this violation of stochastic dominance in advance of the experiment, using parameters fit to other data. These models do not violate transparent dominance (Consequence monotonicity or probability monotonicity).

Questions How “often” do RAM/TAX models predict violations of Stochastic Dominance? Are these models able to predict anything?

Do RAM/TAX models imply that people should violate stochastic dominance? Rarely. Only in special cases. Consider “random” 3-branch gambles: *Probabilities ~ uniform from 0 to 1. *Consequences ~ uniform from $1 to $100. Consider pairs of random gambles. 1/3 of choices involve Stochastic Dominance, but only 1.8 per 10,000 are predicted violations by TAX. Random study of 1,000 trials would unlikely have found such violations by chance. (Odds: 7:1 against)

Can RAM/TAX account for anything? No. These models are forced to predict violations of stochastic dominance in the special recipe,, given the facts that people are (a) risk-seeking for small p and (b) risk-averse for medium to large p in two-branch gambles.

Analysis: SD in TAX model

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.

For More Information: Download recent papers from this site. Follow links to “brief vita” and then to “in press” for recent papers.