1. Violations of Stochastic Dominance Michael H. Birnbaum California State University, Fullerton

2. RAM/TAX  Violations of Stochastic Dominance

3. 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

4. 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

5. 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).

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

7. 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)

8. 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.