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The preference reversal with a single lottery: A Paradox to Regret Theory Serge Blondel (INH Angers & CES Paris 1) Louis Lévy-Garboua (CES Paris 1). ESA 07 Rome. Cognitive Consistency, the Endowment Effect and the Preference Reversal (PR) ESA 05 – Montréal. Test of Cognitive

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The preference reversal with a single lottery:A Paradox to Regret TheorySerge Blondel (INH Angers & CES Paris 1)Louis Lévy-Garboua (CES Paris 1)

ESA 07 Rome

slide2

Cognitive Consistency,

the Endowment Effect

and the Preference Reversal (PR)

ESA 05 – Montréal

Test of Cognitive

Consistency Theory

New results

on PR

1/16

slide3

Standard PR (1)

Which lottery

Is preferred?

 choice

 CE or WTA

Choice P preferred  P  $

Valuation P preferred  CEP > CE$

2/16

slide4

Standard PR (2)

Choice 53% 47%

Valuation 20% 80%

39%: P  $  CE($) > CE(P)  P

 a failure of transitivity

3/16

slide5

Previous studies (1)

Survey of studies :

 real payment

 only gains

 choice and selling price with BDM method

Lichtenstein and Slovic (1971) replicated:

Lichtenstein and Slovic (1973) : Casino

 Grether and Plott (1979), Reilly (1982), Pommehrene et al. (1982) : incentives

 Tversky et al. (1990), Cubitt et al. (2004) : experimental methods

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slide6

Previous studies (2)

p min (%) s max (%) PR (%) Rev PR (%)

LS 71 80.5 50 32.1 4.8

LS 73 58.3 50 38.2 5.2

GP 79 (NI) 80.5 50 29 5.7

GP 79 (I) 80.5 50 26.3 8.4

PSZ 82 (1) 80.5 50 23.3 6.7

PSZ 82 (2) 80.5 50 29 8

R 82 (1) 80.5 58.3 14.5 19.1

R 82 (2) 80.5 58.3 20.5 16.5

LSS 89 60 40 30.1 16.1

TSK 90 [I] 81 50 45 4

5/16

CMS 04 81 50 33.7 3.3

slide7

Regret theory (1)

1 2 3 4 5 6

A 1000 2000 3000 4000 5000 6000

B 6000 1000 2000 3000 4000 5000

 Will you choose A or B?

A and B are equivalent if you consider both independently:

A=B=(1000,1/6;2000,1/6;….;6000,1/6)

If you choose A you will: regret 5000: probability 1/6 rejoice 1000: probability 5/6

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slide8

Regret theory (2)

Regret theory (Loomes and Sugden 1982, Bell 1982):

 Regret / rejoicing

 Regret aversion

Regret theory can explain:

 Coexistence of insurance and gambling

 Reflection effect

 Allais paradox

Loomes and Sugden (1983) and Bell (1982) have

shown that regret theory is consistent with PR.

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slide9

Regret theory & PR (1)

 u(0) = 0

 u(6) = x

 y(20) = 1

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slide10

Regret theory & PR (2)

Hypotheses: * concave utility u(y)=(y/20)0.8

=> u(0)=0, u(6)=x=.382, u(20)=1 * R(z) = -z² if z<0, R(z) =  z² 0 otherwise

 P  $  .9(.382) + .3(.382-1)² > .3 - .6(.382)²

 0.229> 0.224

 CEP / (CEP).8 - 0.9 [CEP.8 -(6/20)6.8]² = 0.343 - 0.1 [-(CEP).8]²

 CEP = 5.08

 CE$ / (CE$).8 - 0.3 [(CE$).8 -1]² = 0.3 - 0.7 [ -(CE$)8]²

 CE$ = 5.26 > CEP

 Regret theory is consistent with PR.

9/16

slide11

Experimental design (1)

 2 sessions, total time one hour.

32 subjects, 22 years old in average, students

1. 10 euros

2. Personal information

3. 30 prices (BDM procedure) in random order

4. 45 choices in random order

5. one decision drawn among the 75 ones

6. The decision drawn is played

7. The subject is paid

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slide13

Experimental design (3)

15 sets

4 decisions by set

 3 choices: - C or $

- P or $

 2 prices: - price of P (BDM)

- Price of $ (BDM)

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slide14

PR1 (1)

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slide15

PR1 (2)

39%: (6,.9)  (20,.3)  CE (20,.3) > CE(6,.9)  (6,.9)

40%: (5,1)  (20,.3)  CE (20,.3) > (5,1)

A simpler version of PR: 2 decisions instead of 3

 One lottery: PR1

Standard PR with P=(yP,p) and $=(y$,s):

 s>0.6 do not reduce PR: sets 1 (.8) and 2 (.7)

PR is a more general phenomenon than the original one.

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slide16

Regret theory & PR1

40%: (5,1)  (20,.3)  CE (20,.3) > (5,1)

 u(0)=0 and u(20)=1

 (5,1) (20,.3)  u(5)+0.3R[u(5)-1] > 0.3-0.7R(-u(5))

 CE$ / u(CE$) + 0.3 R[u(CE$)-1] = 0.3 + 0.7 R[u(CE$)]

 => CE$<5 : Regret theory is inconsistent with PR1.

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slide17

Conclusions

 Lichtentein & Slovic (1971) have been extensively replicated, as if the initial framing was more favourable to the apparition of PR: the phenomenon appears more general.

 Average rates of PR (36%) and PR1 (30%) are in the range of previous studies.

 PR1 is consistent with cognitive consistency theory (Blondel & Lévy-Garboua 2006).This theory also explains other phenomenon as WTA/WTP gap. More information: [email protected] .

 Thank you.

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