The preference reversal with a single lottery: A Paradox to Regret Theory Serge Blondel INH Angers

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The preference reversal with a single
lotteryA Paradox to Regret Theory Serge
Blondel (INH Angers CES Paris 1)Louis
Lévy-Garboua (CES Paris 1)
ESA 07 Rome
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Cognitive Consistency, the Endowment Effect and
the Preference Reversal (PR) ESA 05 Montréal
Test of Cognitive Consistency Theory
New results on PR
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Standard PR (1)
Which lottery Is preferred? ? choice ? CE or WTA
Choice P preferred ? P ?
Valuation P preferred ? CEP gt CE
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Standard PR (2)
Choice 53 47
Valuation 20 80
39 P ? ? CE() gt CE(P) ? P ? a failure of
transitivity
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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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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
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CMS 04 81 50 33.7 3.3
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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 AB(1000,1/62000,1/6.6000,1/6
)
? If you choose A you will? regret 5000
probability 1/6? rejoice 1000 probability 5/6
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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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Regret theory PR (1)
? u(0) 0 ? u(6) x ? y(20) 1
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Regret theory PR (2)
? Hypotheses concave utility
u(y)(y/20)0.8 gt u(0)0, u(6)x.382,
u(20)1 R(z) -z² if zlt0, R(z) ? z² ? 0
otherwise ? P ? ? .9(.382) .3(.382-1)² gt .3 -
.6(.382)² ? 0.229 gt 0.224 ? CEP / (CEP).8
- 0.9 CEP.8 -(6/20)6.8² 0.343 - 0.1
-(CEP).8² ? CEP 5.08 ? CE / (CE).8 -
0.3 (CE).8 -1² 0.3 - 0.7 -(CE)8² ?
CE 5.26 gt CEP ? Regret theory is consistent
with PR.
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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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Exp design (2)
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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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PR1 (1)
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PR1 (2)
39 (6,.9) ? (20,.3) ? CE (20,.3) gt CE(6,.9) ?
(6,.9)
40 (5,1) ? (20,.3) ? CE (20,.3) gt (5,1)
? A simpler version of PR 2 decisions instead of
3 ? One lottery PR1
? Standard PR with P(yP,p) and (y,s) ?
sgt0.6 do not reduce PR sets 1 (.8) and 2 (.7)
? PR is a more general phenomenon than the
original one.
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Regret theory PR1
40 (5,1) ? (20,.3) ? CE (20,.3) gt (5,1)
? u(0)0 and u(20)1 ? (5,1) ?(20,.3) ?
u(5)0.3Ru(5)-1 gt 0.3-0.7R(-u(5)) ? CE /
u(CE) 0.3 Ru(CE)-1 0.3 0.7 Ru(CE) ?
gt CElt5 Regret theory is inconsistent with PR1.
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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 serge.blondel_at_inh.fr . ? Thank you.
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