Reconciling Introspective Utility with Revealed Preference: Experimental Arguments Based on Prospect Theory Peter P. Wakker ( & Abdellaoui & Barrios; Ecole Normale Supérieure of Cachan) Les Sixièmes Journées d’Économie Expérimentale How experimental economics can shed new light on the meaning of utility.

1. History of Utility 1 st appearance of utility: Cramer (1728), Bernoulli (1738) 18 th century 1 st thorough analysis: Bentham (1789); Utility “intuitive.” 2

Utility still intuitive 19 th century Marginal utility Jevons (1871), Menger (1871), Walras (1874) 3 Resolved Smith's (1776) paradox of value-in-use versus value-in-exchange. Samuelson (1947, p. 206): "To a man like Edgeworth, steeped as he was in the Utilitarian tradition, individual utility —nay social utility— was as real as his morning jam."

Ordinal revolution: Pareto (1906), Hicks & Allen (1934) 20 th century Utility  choice.  al direct judgment abandoned Baumol 1958, Fisher 1892, Pareto 1906, Slutsky 1915 U ordinal 4

-of commodity? - of consumer? Typical Questions 5 Is utility property Is utility - ultimate index of goodness? -signal for other good things (expected offspring …). If child prefers candy to medicine, then how about utility thereof?

2.This lecture, why here, why now? 6 This topic has been studied by theoretical economists, philosophers, and, nowadays, because it is so outdated, by historians. Why at Sixièmes Journées d’Économie Expérimentale? Because experimental economics can shed new light on this problem!

First, we measure utility for decision under risk (choice-based). The traditional theory, EU, has empirical problems. Has frustrated utility measurements. Problems fixed by means of prospect theory (Bleichrodt, Pinto, & Wakker 2001, Management Science) Next, we measure utility through direct judgments (choiceless). Finally, we compare. 3. Plan of paper 7

1 st utility measurement: Tradeoff (TO) method (Wakker & Deneffe 1996) Completely choice-based, but appeals to direct  al judgments of strength of preferences. 4. The Experiment 8

_ ( U(2000)  U(1000) ) Tradeoff (TO) method t 2 ? t 1 ~     t6?t6? t 5   ~   ~ 1000 t 1 ?     (= t 0 ) EU = U(t 2 )  U(t 1 ) = = = U(t 6 )  U(t 5 ) = U(t 1 )  U(t 0 ) = 11 _ 22 ( U(2000)  U(1000) ) 11 _ 2 & RDU & PT:   11 22

1 0 U FF Normalize: U(t 0 ) = 0; U(t 6 ) = 1. t0t0 t1t1 t6t6 1/6 t5t5 5/6 t4t4 4/6 t3t3 3/6 t2t2 2/6 Consequently: U(t j ) = j/6. 10

2 nd utility measurement: Strength of Preference (SP) Based on direct judgment, not choice-based. 11

For which s 2 is ?s2s2 Strength of Preference (SP) For which s 3 is s 3 s 2 ~* t 1 t 0 ? For which s 6 is s 6 s 5 ~* t 1 t 0 ? We assume: U(s 2 ) – U(t 1 ) = U(t 1 ) – U(t 0 ) U(s 3 ) – U(s 2 ) = U(t 1 ) – U(t 0 ) U(s 6 ) – U(s 5 ) = U(t 1 ) – U(t 0 ) t1t0t1t0 t1t1 ~*

FF CE 2/3 (EU) CE 1/3 CE 2/3 (PT) SP TO Utility functions (for mean values). 0 1/6 2/6 3/6 4/6 5/6 1 7/6 U t 0 = FF5, t 6 = FF26,

Question: Could this identity have resulted because the TO method does not properly measure choice-based risky utility? 14

3 d utility measurement: t0t0 t 6   c2c2 ~ t0t0 c 2   c2c2 t 6   EU (& RDU & PT gr.av.): U(c 2 ) = 1/3 U(c 1 ) = 1/9 U(c 3 ) = 5/9 15 Certainty equivalent CE 1/3 (with good-outcome probability 1/3) For which c 2 : ? c1c1 ~ For which c 1 : ? c3c3 ~ For which c 3 : ? 13

16 Questions Could this identity have resulted because our experiment is noisy (cannot distinguish anything)? How about violations of EU?

4 th utility measurement: t0t0 t 6   d2d2 ~ t0t0 d 2   d2d2 t 6   CE 2/3 (EU): U(d 2 ) = 2/3 U(d 1 ) = 4/9 U(d 3 ) = 8/9 CE 2/3 (PT) (gr.av): U(d 2 ) =.51 U(d 1 ) =.26 U(d 3 ) = d3d3 ~ For which d 3 : ? d1d1 ~ For which d 1 : ? For which d 2 : ? Certainty equivalent CE 2/3 (with good-outcome probability 2/3) 13

And, EU is violated. 18 So, our experiment does have the statistical power to distinguish. Which alternative theory to use? Prospect theory.

p w /3 Figure. The common weighting fuction w(1/3) = 1/3; w(2/3) =

5. Conclusions Under EU : usual discrepancies for risky ut., U CE 2/3  U CE 1/3, U TO Risky choice-based U = riskless choiceless U?? However: = U SP 20 Under one risky utility, U CE 2/3 = U CE 1/3 = U TO RDU PT :

Gilboa & Schmeidler (2000), "A Cognitive Model of Individual Well-Being," Social Choice and Welfare, forthcoming. Fox, Craig R. & Amos Tversky (1998), "A Belief-Based Account of Decision under Uncertainty," Management Science 44, 879  895. Kahneman (1994), "New Challenges to the Rationality Assumption," Journal of Instit. & Theor. Ec s 150,18  36. van Praag, Bernard M.S. (1968), "Individual Welfare Functions and Consumer Behavior.” North-Holland, Amsterdam, Interest in choiceless inputs in economics: Especially useful if choice anomalies are prominent. 21 Our finding can be considered a reinforcement of revealed preference!

22 Experimental economics can shed new light on the interpretation of utility.