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## ESA 07 Rome

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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**Cognitive Consistency,**the Endowment Effect and the Preference Reversal (PR) ESA 05 – Montréal Test of Cognitive Consistency Theory New results on PR 1/16**Standard PR (1)**Which lottery Is preferred? choice CE or WTA Choice P preferred P $ Valuation P preferred CEP > CE$ 2/16**Standard PR (2)**Choice 53% 47% Valuation 20% 80% 39%: P $ CE($) > CE(P) P a failure of transitivity 3/16**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 4/16**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**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 6/16**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. 7/16**Regret theory & PR (1)** u(0) = 0 u(6) = x y(20) = 1 8/16**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**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 10/16**Exp design (2)**11/16**Experimental design (3)**15 sets 4 decisions by set 3 choices: - C or $ - P or $ 2 prices: - price of P (BDM) - Price of $ (BDM) 12/16**PR1 (1)**13/16**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. 14/16**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. 15/16**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@inh.fr . Thank you. 16/16