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Among those who cycle most have no regrets Michael H. Birnbaum Decision Research Center, Fullerton

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Outline 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

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Integrative, Interactive Contrast Models

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Assumptions

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Special Cases Majority Rule (aka Most Probable Winner) Regret Theory These can be represented with different functions. I will illustrate with different functions, f.

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Majority Rule Model

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Regret Model

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Predicted Intransitivity These models violate transitivity of preference Regret and MR cycle in opposite directions However, both REVERSE cycle under permutation over events; i.e., “juxtaposition.”

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Concrete Example 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.

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Majority Rule Prediction 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

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Regret Prediction 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

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Pilot Test 240 Undergraduates Tested via computers (browser) Clicked button to choose 30 choices (includes counterbalanced choices) 10 min. task, 30 choices repeated.

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ABC Design Results

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True and Error Model Assumptions 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

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One Choice, Two Repetitions AB A B

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Solution for e The proportion of preference reversals between repetitions allows an estimate of e. Both off-diagonal entries should be equal, and are equal to:

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Estimating e

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Estimating p

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Testing if p = 0

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A’B’C’ Results

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ABC X A’B’C’ Analysis

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ABC-A’B’C’ Analysis

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Results 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.

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Results: Continued 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?

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Advice Welcome: Our Plans 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.

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Summary 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.

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