Is there Some Format in Which CPT Violations are

Attenuated?

Michael H. BirnbaumDecision Research CenterCalifornia State University,

Fullerton

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Stochastic Dominance

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P(x ≥ t | A) ≥ P(x ≥ t | B)∀ t ⇒ A f B

If A stochastically dominates B, the probability of choosing B over A should not be signicantly greater than 1/2.

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Analysis of Stochastic Dominance

• 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)• Consequence Monotonicity:

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′ G = (x, p;y,q; ′ z ,r) f G = (x, p;y,q;z,r); ′ z f z

′ ′ G = (x, p; ′ y ,q;z,r) f G; ′ y f y

′ ′ ′ G = ( ′ x , p;y,q;z,r) f G; ′ x f x

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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 $9605 blues to win $1405 whites to win $12

85 reds to win $9605 blues to win $9010 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 $9605 greens to win $9605 blues to win $1405 whites to win $12

85 reds to win $9605 greens to win $9005 blues to win $1205 whites to win $12

90% choose C over D

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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 before the experiment, using parameters fit to previous data.

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Questions

• Is there some format in which CPT can be saved?

• We seek a format in which people satisfy stochastic dominance, show no event-splitting effects (violations of coalescing), and satisfy lower and upper cumulative independence.

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Birnbaum & Navarrete (1998)

.05 .05 .90 .10 .05 .85$12 $14 $96 $12 $90 $96

70% violations with 4 tests; n = 100. Similar results were obtained by Birnbaum, Patton, & Lott (1999) who used the same format with 5 new tests; n = 110.

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I: .05 to win $12 J: .10 to win $12 .05 to win $14 .05 to win $90 .90 to win $96 .85 to win $96

Birnbaum & Martin (2003): 74%

This study had a financial incentive; 6% of participants would win the prize of one of their chosen gambles. There were 74% violations, and 68% violated on this choice AND satisfied it in the split form.

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Web Format (1999): 67%

5. Which do you choose?

I: .05 probability to win $12 .05 probability to win $14 .90 probability to win $96 OR J: .10 probability to win $12 .05 probability to win $90 .85 probability to win $96

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Reversed Order: 63%

5. Which do you choose?

I: .90 probability to win $96 .05 probability to win $14 .05 probability to win $12 OR

J: .85 probability to win $96 .05 probability to win $90 .10 probability to win $12

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Pie Charts: 65%, 66%

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Tickets Format: 71%

I: 90 tickets to win $96 05 tickets to win $14 05 tickets to win $12

OR

J: 85 tickets to win $96 05 tickets to win $90 10 tickets to win $12

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List Format: 61%, 64%

I: $96, $96, $96, $96, $96, $96, $96, $96, $96, $96, $96, $96, $96, $96, $96, $96, $96, $96 $14 $12

OR

J: $96, $96, $96, $96, $96, $96, $96, $96, $96, $96, $96, $96, $96, $96, $96, $96, $96 $90 $12, $12

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Semi-Split List: 56%*

I: $96, $96, $96, $96, $96, $96, $96, $96, $96, $96, $96, $96, $96, $96, $96, $96, $96, $96 $14 $12 ORJ: $96, $96, $96, $96, $96, $96, $96, $96, $96, $96, $96, $96, $96, $96, $96, $96, $96 $90 $12, $12

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Marbles: 70%, 76%. Framing: not significant

5. Which do you choose?

I: 90 red marbles to win $96 05 blue marbles to win $14 05 white marbles to win $12 OR

J: 85 red marbles to win $96 05 blue marbles to win $90 10 white marbles to win $12

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Decumulative Probability Format: 80% Violations

5. Which do you choose?

I: .90 probability to win $96 or more .95 probability to win $14 or more 1.00 probability to win $12 or more OR

J: .85 probability to win $96 or more .90 probability to win $90 or more 1.00 probability to win $12 or more

(This had a significantly higher rate of violation)

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New Formats not published as of 1-25-05

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Unaligned Table: Coalesced

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Unaligned Table: Split

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Aligned Table: Coalesced

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Aligned Table: Split Form

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Violations of SD: from Web: Spring, 2004

• New Tickets Format 84% 04%• Unaligned Table 81% 12%• Aligned Table 72% 08%• Violations of SD in coalesced and

split forms--Choices 5 and 11.(No. Participants: 433-- between-Ss: 141, 141, 151)

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Summary: 23 Studies of SD, 8653 participants

• Huge effects of splitting vs. coalescing of branches-70% vs 10%

• Small effects of education, gender• Very Small effects of probability

format, displays• Miniscule effects of event framing

(framed vs unframed)

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Summary

No format has yet been found that leads to data compatible with CPT.

Many of the formats that have been used by others have been tested, and violations of SD have been found with all.

Similar results with tests of UCI, LCI, and coalescing

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Next Program: Testing Models of SD violation

• Are people just following some heuristic such as averaging the consequences and not attending to probability?

• Tests between TAX and RAM.• It will turn out that TAX beats RAM

and that both beat the heuristic.

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For More Information:

http://psych.fullerton.edu/mbirnbaum/

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

mbirnbaum@fullerton.edu