1. 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

2. Test of Cognitive Consistency Theory Cognitive Consistency, the Endowment Effect and the Preference Reversal (PR) ESA 05 – Montréal New results on PR 1/16

3. Standard PR (1) Which lottery Is preferred?  choice  CE or WTA ChoiceP preferred  P  $ ValuationP preferred  CE P > CE $ 2/16

4. Standard PR (2) Choice53%47% Valuation20%80% 39%: P  $  CE($) > CE(P)  P  a failure of transitivity 3/16

5. Previous studies (1)  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  Survey of studies :  real payment  only gains  choice and selling price with BDM method 4/16

6. Previous studies (2) LS 71 80.55032.1 4.8 LS 73 58.35038.2 5.2 GP 79 (NI) 80.55029 5.7 GP 79 (I) 80.55026.3 8.4 PSZ 82 (1) 80.55023.3 6.7 PSZ 82 (2) 80.55029 8 R 82 (1) 80.558.314.5 19.1 R 82 (2) 80.558.320.5 16.5 LSS 89 604030.1 16.1 TSK 90 [I] 8150 45 4 CMS 04 8150 33.7 3.3 p min (%)s max (%) PR (%) Rev PR (%) 5/16

7. Regret theory (1)  If you choose A you will:  regret 5000: probability 1/6  rejoice 1000: probability 5/6  A and B are equivalent if you consider both independently: A=B=(1000,1/6;2000,1/6;….;6000,1/6) 6/16 A 100020003000400050006000 B 600010002000300040005000 1 2 3 4 5 6  Will you choose A or B?

8.  Loomes and Sugden (1983) and Bell (1982) have shown that regret theory is consistent with PR.  Regret theory (Loomes and Sugden 1982, Bell 1982):  Regret / rejoicing  Regret aversion 7/16  Regret theory can explain:  Coexistence of insurance and gambling  Reflection effect  Allais paradox Regret theory (2)

9. Regret theory & PR (1)  u(0) = 0  u(6) = x  y(20) = 1 8/16

10. 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) = -z ² if z<0, R(z) =  z ²  0 otherwise  P  $ .9(.382) +.3(.382-1) ² >.3 -.6(.382) ²  0.229 > 0.224  CE P / (CE P ).8 - 0.9 [CE P.8 -(6/20)6.8 ] ² = 0.343 - 0.1 [-(CE P ).8 ] ²  CE P = 5.08  CE $ / (CE $ ).8 - 0.3 [(CE $ ).8 -1] ² = 0.3 - 0.7 [ -(CE $ ) 8 ] ²  CE $ = 5.26 > CE P  Regret theory is consistent with PR. 9/16

11. 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

12. 11/16 Exp design (2)

13. 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

14. PR1 (1) 13/16

15.  A simpler version of PR: 2 decisions instead of 3  One lottery: PR1 39%: (6,.9)  (20,.3)  CE (20,.3) > CE(6,.9)  (6,.9) 40%: (5,1)  (20,.3)  CE (20,.3) > (5,1)  Standard PR with P=(y P,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 PR1 (2)

16. Regret theory & PR1  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. 40%: (5,1)  (20,.3)  CE (20,.3) > (5,1) 15/16

17. 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 & L é vy-Garboua 2006).This theory also explains other phenomenon as WTA/WTP gap.  More information: serge.blondel@inh.fr.serge.blondel@inh.fr  Thank you. 16/16