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# Among those who cycle most have no regrets - PowerPoint PPT Presentation

Among those who cycle most have no regrets. Michael H. Birnbaum Decision Research Center, Fullerton. Outline. Family of Integrative Contrast Models Special Cases: Regret Theory, Majority Rule (aka Most Probable Winner) Predicted Intransitivity: Forward and Reverse Cycles

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### Among those who cycle most have no regrets

Michael H. Birnbaum

Decision Research Center, Fullerton

• Family of Integrative Contrast Models

• Special Cases: Regret Theory, Majority Rule (aka Most Probable Winner)

• Predicted Intransitivity: Forward and Reverse Cycles

• Pilot Experiment & Planned Work with Enrico Diecidue

• Results: Pilot tests. Comments welcome

• Majority Rule (aka Most Probable Winner)

• Regret Theory

• These can be represented with different functions. I will illustrate with different functions, f.

• These models violate transitivity of preference

• Regret and MR cycle in opposite directions

• However, both REVERSE cycle under permutation over events; i.e., “juxtaposition.”

• Urn: 33 Red, 33White, 33 Blue

• One marble drawn randomly

• Prize depends on color drawn.

• A = (\$4, \$5, \$6) means win \$4 if Red, win \$5 if White, \$6 if Blue.

B = (\$5, \$7, \$3)

C = (\$9, \$1, \$5)

AB: choose B

BC: choose C

CA: choose A

Notation: 222

A’ = (\$6, \$4, \$5)

B’ = (\$5, \$7, \$3)

C’ = (\$1, \$5, \$9)

A’B’: choose A’

B’C’: choose B’

C’A’: choose C’

Notation: 111

Majority Rule Prediction

B = (\$5, \$7, \$3)

C = (\$9, \$1, \$5)

AB: choose A

BC: choose B

CA: choose C

Notation: 111

A’ = (\$6, \$4, \$5)

B’ = (\$5, \$7, \$3)

C’ = (\$1, \$5, \$9)

A’B’: choose B’

B’C’: choose C’

C’A’: choose A’

Notation: 222

Regret Prediction

• Tested via computers (browser)

• Clicked button to choose

• 30 choices (includes counterbalanced choices)

• 10 min. task, 30 choices repeated.

• Each choice in an experiment has a true choice probability, p, and an error rate, e.

• The error rate is estimated from inconsistency of response to the same choice by same person over repetitions

• The proportion of preference reversals between repetitions allows an estimate of e.

• Both off-diagonal entries should be equal, and are equal to:

• Most people are transitive.

• Most common pattern is 112, pattern predicted by TAX with prior parameters.

• However, 2 people were perfectly consistent with MR on 24 choices.

• No one fit Regret theory perfectly.

• Among those few (est. ~10%) who cycle (intransitive), most have no regrets (i.e., they appear to satisfy MR).

• Suppose 5-10% of participants are intransitive. Do we think that they indeed use a different process? Is there an artifact in the experiment? If not, can we increase the rate of intransitivity?

• We plan to test participants from the same pool was used to elicit regret function.

• Assignment: Devise a theorem of integrative interactive contrast model that will lead to self-contradiction (“paradox” of regret theory).

• These contrast models also imply RBI, which is refuted by our data.

• Regret and MR imply intransitivity whose direction can be reversed by permutation of the consequences.

• Very few people are intransitive but a few do indeed appear to be consistent with MR and 2 actually show the pattern in 24 choices.