I

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Im not overweightIt just needs redistribution

• Michael H. Birnbaum
• California State University, Fullerton

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1967
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1967
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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.

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Paradox Analysis

• Transitivity
• A f B and B f C ? A f C
• Coalescing
• GS (x, p x, q z, r) G (x, p q z, r)
• Restricted Branch Independence

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

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RAM/TAX Models
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RAM Model Parameters
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RAM implies inverse-S
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RAM/TAX ? Violations of Stochastic Dominance
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Which gamble would you prefer to play?
Gamble A Gamble 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
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Which of these gambles would you prefer to play?
Gamble C Gamble 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
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RAM/TAX ? Violations of Stochastic Dominance
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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).
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Questions

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

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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 71 against)
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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 .

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Analysis SD in TAX model
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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

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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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For More Information
mbirnbaum_at_fullerton.edu
http//psych.fullerton.edu/mbirnbaum/
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