Reconciling Introspective Utility with Revealed Preference: Arguments Based on Experimental Eonomics and Prospect Theory Peter P. Wakker; University of Amsterdam ( & Abdellaoui & Barrios; Ecole Normale Supérieure of Cachan) We revisit classical debates ("philosophical") about the interpretation of utility, using modern experimental economics: just measure different utility concepts through controled experiments, and see! Motto: "don't talk but look";

2 Our purpose: Show that choiceless inputs can be useful in economics; revival of old cardinal utility … Many others have pleaded for it in the past and in the present. Special aspect of our plea: Not ad hoc. Not just going back to Bentham. Rather: Link choiceless inputs to revealed preference. Build on, reinforce, revealed preference. Don't abandon it.

1 st appearance of utility: Cramer (1728), Bernoulli (1738) 18 th century 1 st thorough analysis: Bentham (1789); Utility “intuitive.” 3 1. History of Utility

Samuelson (1947, p. 206), about Edgeworth: "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." Utility still intuitive 19 th century Marginal revolution (Jevons 1871, Menger 1871, Walras 1874) Resolved Smith's (1776) paradox of value-in-use versus value-in-exchange. 4

Ordinal revolution: Pareto (1906), Hicks & Allen (1934) 1 st half of 20 th century Utility  choice.  al direct judgment abandoned Baumol 1958, Fisher 1892, Pareto 1906, Slutsky 1915 U ordinal in mathe- matical sense 5 “Utility” is the heritage of Bentham and his theory of pleasures and pains. For us his word is the more acceptable, the less it is entangled with his theory. [Italics from original( Sect14, Chapter 1)]

6 von Neumann-Morgenstern (1944): New hope for cardinal utility? General consensus: cardinal in mathematical sense, not empirical; vNM-U only for risk; for nothing el se. Cardinal utility exists in subfields (risky, welfare, taxation, temporal) but strictly kept there. Ordinal view dominates. (So, no meaning for marginal utility.)

7 First positive results and hope for ordinalism: Hicks & Allen (1934): Market equilibria only need ordinal utility. Samuelson (1938), Houthakker (1950): Preference revealed from market demand. de Finetti (1937), Savage (1954): Choice- basis of subjective beliefs. Debreu (1959): Existence of market equilibrium.

History of utility after 1950: No account of it known to us. There are several accounts of history up to and including ordinal revolution (Stigler 1950, Blaug 1962 & 1997). Yet, many changes since 1950! Time for an update. 8

History of utility after 1950: Allais (1953) & Ellsberg (1961): 9 > < EU First-generation models didn't yet question ordinal position: nonEU. However … Arrow (1951): No good social procedure when only ordinal information. Simon (1955): Bounded rationality; satisficing. Most serious blow for ordinalism: Preference reversals (Lichtenstein & Slovic '71, Grether & Plott '79).

A recent blow. Kahneman (1994, & al.) for intertemporal choice. Big irrationalities: People seemingly prefer prolongation of pain. Shows that: Often, human species cannot integrate over time. Then: No revealed preference. Better resort back to Bentham's "experienced utility." 10

- a property of the commodity? - a property of the consumer? Typical Questions for cardinal utility (not discussed here): 11 Is utility - ultimate index of goodness? -index for other good things (expected offspring …). If child reveals clear preference for candy over medicine, then how about utility thereof? If two persons have different utilities, must it be due to different background/circumstances of an objective kind?

2.Experimental Economics and Utility; Plan of Paper 12 For questions: "Do cardinal and/or ordinal utility exist?" "Are they the same?" experimental economics' answer is: (Try to) measure them, and see! No philosophical contemplations here. A table organizing some utility-related phenomena, and positioning our contribution:

Intertemporal Welfare Risk 13 cardinal utility choiceless Utilities within rectangles are commonly restricted to their domains. Strength of preferences Experienced (Kahneman) Mark Machina, Jun'02: “The word utility has too many meanings. I avoid using the word utility.” We: not more concepts, but fewer. Relate them. choice-based ordinal utility Market equilibria : Relation obtained in this paper.

First, measure utility through risky decisions (choice-based). -Empirical problems for traditional EU; have frustrated utility measurements. - Can be fixed using prospect theory (Bleichrodt, Pinto, & Wakker 2001, Management Science). Next, measure utility through strength of preference; direct judgments (choiceless). Finally, compare these utilities. 3. Plan of paper 14

1 st utility measurement: Tradeoff (TO) method (Wakker & Deneffe 1996) Completely choice-based. 4. The Experiment 15

 ( U(t 1 )  U(t 0 ) ) =  ( U(2000)  U(1000) )  U(1000) +  U(t 1 ) =  U(2000) +  U(t 0 ); _ ( U(2000)  U(1000) ) Tradeoff (TO) method t2t t 1 ~     t6t t 5   ~     (= t 0 ) EU = U(t 2 )  U(t 1 ) = = = U(t 6 )  U(t 5 ) = U(t 1 )  U(t 0 ) =   _ ( U(2000)  U(1000) )    _ ( U(2000)  U(1000) )      6,000   ~ 200,000 t 1 18, 1 curve

? ? ? Tradeoff (TO) method 17 _ ( U(2000)  U(1000) ) t2t t 1 ~     t6t t 5   ~     (= t 0 ) EU = U(t 2 )  U(t 1 ) = = = U(t 6 )  U(t 5 ) = U(t 1 )  U(t 0 ) =   _ ( U(2000)  U(1000) )   _ ( U(2000)  U(1000) )     12,000   ~ 200,000 t 1 Prospect theory: weighted prob s (even unknown prob s ) 11 22 11 22 11 22 ! ! ! 21, curves; then 23, CE 1/3

1 0 U $ 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. 18

2 nd utility measurement: Strength of Preference (SP) Based on direct judgment, not choice-based. 19

For which s 2 is ?s2s2 Strength of Preference (SP) 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 ~* For which s 3 is ?s3s3 t1t0t1t0 s2s2 ~*

CE 2/3 (EU) CE 2/3 (PT) corrects CE 2/3 (EU) FF CE 1/3 CE 2/3 (PT) SP TO Utility functions (group averages) 0 1/6 2/6 3/6 4/6 5/6 1 7/6 U t 0 = FF5, t 6 = FF26,068 22, nonTO,nonEU 24, power? 26, which th? PT! (then TO)) 28,concl 25, CE 2/3 23, CE 1/3 TO(PT) = TO(EU) CE 1/3 (PT) = CE 1/3 (EU) (gr.av.)

Question: Could this identity have resulted because the TO method does not properly measure choice-based risky utility? 22 (And, after answering this, what about nonEU?)

Certainty equivalent CE 1/3 (with good-outcome probability 1/3) 3 d utility measurement: t0t0 t 6   c2c2 ~ t0t0 c 2   c2c2 t 6   EU U(c 2 ) = 1/3 U(c 1 ) = 1/9 U(c 3 ) = 5/9 23 For which c 2 : ? c1c1 ~ For which c 1 : ? c3c3 ~ For which c 3 : ? 21, curves & RDU & PT (for gr.av.) 21, curves Prominent econo- mist on inverse-S, in famous public speech: "It is not universal. But if I had to bet, I would bet on this one." (Chris Starmer, June 24, 2005).

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

Certainty equivalent CE 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 : ? 21, curves 2/3 (with good-outcome probability 2/3)

And, EU is violated. 26 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; 27 16,TOmethod 1/3 w(2/3) =.51 2/3.51 We re-analyze preceding measurements in terms of prospect theory; first TO.

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 28 Under one risky utility, U CE 2/3 = U CE 1/3 = U TO RDU PT :

Gilboa & Schmeidler (2001), "A Cognitive Model of Individual Well-Being," Social Choice and Welfare 18, 269–288. 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. Tinbergen, Jan (1991), “On the Measurement of Welfare,” Journal of Econometrics 50, 7  13. van Praag, Bernard M.S. (1968), "Individual Welfare Functions and Consumer Behavior.” North-Holland, Amsterdam, Interest in choiceless inputs in economics: 29 Especially useful if choice anomalies are prominent. We: relate choiceless inputs to revealed preference. Show how choiceless inputs can reinforce revealed preference!

30 Experimental economics has shed new light on classical debates about utility: Don't talk but look.

Appendix on Analysis of Data All analyses with ANOVA (so, correcting for individual variation). We tested on raw data, and on parametric fittings. Parametric fittings of utility of: 1.Power (CRRA); 2.Exponential (CARA); 3.We developed a one-parametric subfamily of Saha's expo-power satisfying economic desiderata; first presented in ESA- Amsterdam, October Later used by Holt & Laury (2002). 31