1. Using Modern Nonexpected Utility Theories for Risky Decisions and Modern Tools from Experimental Economics to Revisit Classical Debates in Economics, and to Restore the Classical Utility Concept Peter P. Wakker; Erasmus University Rotterdam (& Abdellaoui & Barrios; Ecole Normale Supérieure of Cachan) Utility central in economics. - We review history and classical debates ("ordinal revolution"). - We bring novelty, using modern nonexpected utility and modern experimental economics, rather than philosophy & armchair speculation. Motto: "don't talk but look".

2. 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.

3. 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

4. Samuelson (1947, p. 206), about such views: "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  1870: the marginal revolution (Jevons 1871, Menger 1871, Walras 1874) Resolved Smith's (1776) paradox of value-in-use versus value-in-exchange (e.g. the "water-diamond" paradox). 4

5. 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)] Logical positivism: everything falsifiable. No metaphysics. In psychology: behaviorism. In economics:

6. 6 von Neumann-Morgenstern (1944) with expected-utility for risky decisions, and utility cardinal in mathematical sense: New hope for cardinality in empirical sense? General consensus: Cardinal in mathematical sense, not empirical neoclassical; vNM-U only for risk; not for welfare evaluations etc. Cardinal utility exists in subfields (risky, welfare, taxation, temporal) but strictly kept there. Ordinal view dominates. (So, no meaning for utility differences.)

7. 7 First there were positive results and hope for ordinalism: Hicks & Allen (1934): Market phenomena 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.

8. 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 occurred since 1950. Time for an update! 8

9. 9 History of utility after 1950: Allais (1953) & Ellsberg (1961): > < 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).

10. A new, 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

11. - 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?

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

13. 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. happiness

14. 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

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

16.  ( 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 t2t2 1000 2000 t 1 ~     t6t6 1000 2000 t 5   ~   1000 2000 5000   (= t 0 ) EU = U(t 2 )  U(t 1 ) = =...... = U(t 6 )  U(t 5 ) = U(t 1 )  U(t 0 ) =...... 16   _ ( U(2000)  U(1000) )    _ ( U(2000)  U(1000) )      6,000   ~ 200,000 t 1 18, 1 curve

17. ? ? ? Tradeoff (TO) method 17 _ ( U(2000)  U(1000) ) t2t2 1000 2000 t 1 ~     t6t6 1000 2000 t 5   ~   1000 2000 5000   (= 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

18. 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

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

20. 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 ) 20...... t1t0t1t0 t1t1 ~* For which s 3 is ?s3s3 t1t0t1t0 s2s2 ~*

21. 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 = FF5,000 21 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.)

22. 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?)

23. 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 (Chris Starmer, June 24, 2005) on inverse-S: "It is not universal. But if I had to bet, I would bet on this one.".

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

25. 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 ) =.76 25 d3d3 ~ For which d 3 : ? d1d1 ~ For which d 1 : ? For which d 2 : ? 21, curves 2/3 (with good-outcome probability 2/3)

26. And, EU is violated. 26 So, our experiment does have the statistical power to distinguish. Which alternative theory to use? Prospect theory.

27. p w 1 1 0 1/3 Fig. The common probability weighting function. w(1/3) = 1/3; 27 16,TOmethod 1/3 w(2/3) =.51 2/3.51 We re-analyze the preceding measurements (the curves you saw before) in terms of prospect theory; first TO.

28. 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 :

29. Fox, Craig R. & Amos Tversky (1998), "A Belief-Based Account of Decision under Uncertainty," Management Science 44, 879  895. Gilboa & Schmeidler (2001), "A Cognitive Model of Individual Well-Being," Social Choice and Welfare 18, 269–288. Kahneman (1994), "New Challenges to the Rationality Assumption," Journal of Instit. & Theor. Ec s 150,18  36. Ladyard (2005), "Happiness, Lessons from a New Science." Penguin, London. 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, 1968. 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. 30 Experimental economics has shed new light on classical debates about utility: Don't talk but look.

31. 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 2000. Later used by Holt & Laury (2002). 31