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Among those who cycle most have no regrets

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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.

A = ($4, $5, $6)

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

A = ($4, $5, $6)

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

- 240 Undergraduates
- 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.