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Reconciling Introspective Utility with Revealed Preference: Experimental Arguments based on Prospect Theory

This paper explores the concept of utility and its measurement through experimental economics. It discusses the historical development of utility theory, the problems with traditional utility measurement, and how prospect theory can offer new insights. The paper presents the tradeoff method and strength of preference method as alternative approaches to measuring utility. The experiment conducted shows discrepancies between different utility theories and suggests that prospect theory may provide a better framework.

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Reconciling Introspective Utility with Revealed Preference: Experimental Arguments based on Prospect Theory

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  1. 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.

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

  3. 3 19th century 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." • Utility still intuitive • Marginal utilityJevons (1871), Menger (1871), Walras (1874) • Resolved Smith's (1776) paradox of value-in-use versus value-in-exchange.

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

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

  6. 6 This lecture, why here, why now? This topic has been studied by theoretical economists, philosophers, and, nowadays, because it is so outdated, by historians.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!

  7. 7 3. Plan of paper 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.

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

  9. d1  (U(2000)-U(1000)) (U(2000)-U(1000))   _ _ d1 d1   d2 d2  ~  2000 2000 1000 1000 d2 ~ =   . . .   = 9 Tradeoff (TO) method & RDU & PT: EU 2000 1000 _ 2/3 U(t1)-U(t0)= (U(2000)-U(1000)) ~ 1/3 5000 t1? (=t0) = U(t2)-U(t1)= t1 t2 ? . . . U(t6)-U(t5)= t5 t6?

  10. 1 U 5/6 4/6 3/6 2/6 1/6 0 t2 t3 t4 t5 FF 10 Consequently: U(tj) = j/6. Normalize: U(t0) = 0; U(t6) = 1. t1 t0 t6

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

  12. 12 Strength of Preference (SP) We assume: U(s2) – U(t1) = U(t1) – U(t0) For which s2 is ? s2 t1 t1t0 ~* For which s3 is s3s2 ~* t1t0? U(s3) – U(s2) = U(t1) – U(t0) . . . . . . For which s6 is s6s5 ~* t1t0? U(s6) – U(s5) = U(t1) – U(t0)

  13. CE2/3(PT) CE2/3(EU) SP CE1/3 TO t0= FF5,000 t6= FF26,068 13 7/6 1 U 5/6 4/6 3/6 2/6 1/6 0 FF Utility functions (for mean values). 14 16 18 20

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

  15.   For which c2:    ? t0 c1 For which c1: ~ ? c2 c2 c3 For which c3: ~ ? t6 15 3d utility measurement: Certainty equivalent CE1/3 (with good-outcome probability 1/3) EU (& RDU & PT gr.av.): t0 c2 U(c2) = 1/3 ~ t6 U(c1) = 1/9 U(c3) = 5/9 13

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

  17. For which d2: ?   d1 For which d1: ~ ?   d3 For which d3: ~ ?  17 4th utility measurement: Certainty equivalent CE2/3 (with good-outcome probability 2/3) CE2/3(EU): CE2/3(PT) (gr.av): t0 d2 U(d2) = 2/3 U(d2) = .51 ~ t6 t0 U(d1) = 4/9 U(d1) = .26 d2 d2 U(d3) = 8/9 U(d3) = .76 t6 13 13

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

  19. 1/3 p 19 1 w 1 0 Figure. The common weighting fuction w(1/3) = 1/3; w(2/3) = .51 17

  20. Under one risky utility, UCE2/3 = UCE1/3 = UTO = USP However: RDU : PT 20 5. Conclusions Under EU : usual discrepancies for risky ut., UCE2/3  UCE1/3 , UTO Risky choice-based U = riskless choiceless U??

  21. 21 Interest in choiceless inputs in economics: • 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. Ecs 150,18-36. • van Praag, Bernard M.S. (1968),"Individual Welfare Functions and Consumer Behavior.”North-Holland, Amsterdam, 1968. Especially useful if choice anomalies are prominent. Our finding can be considered a reinforcement of revealed preference!

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

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