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".

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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.

• 1st appearance of utility:Cramer (1728), Bernoulli (1738)

18th century

• 1st thorough analysis:Bentham (1789);Utility “intuitive.”

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1. History of Utility

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 intuitive19th 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).

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• Ordinal revolution:Pareto (1906), Hicks & Allen (1934)

1st half of 20th century

• Utility choice.

al direct judgment abandonedBaumol 1958, Fisher 1892, Pareto 1906, Slutsky 1915

U ordinal in mathe-matical sense

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“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:

6von 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.)

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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.

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!

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9History 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).

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."

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- a property of the commodity?- a property of the consumer?

Typical Questions for cardinal utility(not discussed here):

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• Is utility

• 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

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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:

Intertemporal

Welfare

Risk

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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-basedordinal utility

Market equilibria

: Relation obtained in this paper.

happiness

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 paper14

1st utility measurement:Tradeoff (TO) method(Wakker & Deneffe 1996)

Completely choice-based.

4. The Experiment15

(U(t1)U(t0)) = (U(2000) U(1000))

U(1000) + U(t1) = U(2000) + U(t0);

_ (U(2000) U(1000))

Tradeoff (TO) method

t2

1000 2000

t1

~

t6

1000 2000

t5

~

1000 2000

5000

(= t0)

EU

=U(t2) U(t1) ==

.

.

.

=

U(t6) U(t5) =

U(t1) U(t0) =

.

.

.

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_ (U(2000) U(1000))

_ (U(2000) U(1000))

6,000

~ 200,000 t1

18, 1 curve

?

?

?

Tradeoff (TO) method17

_ (U(2000) U(1000))

t2

1000 2000

t1

~

t6

1000 2000

t5

~

1000 2000

5000

(= t0)

EU

=U(t2) U(t1) ==

.

.

.

=

U(t6) U(t5) =

U(t1) U(t0) =

.

.

.

_ (U(2000) U(1000))

_ (U(2000) U(1000))

12,000

~ 200,000 t1

Prospect theory:weighted probs

(even unknown probs)

1

2

1

2

1

2

!

!

!

21, curves; then 23, CE1/3

1

0

U

$

Normalize: U(t0) = 0; U(t6) = 1.

t0t1 t6

1/6

t5

5/6

t4

4/6

t3

3/6

t2

2/6

Consequently:U(tj) = j/6.

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2nd utility measurement:

Strength of Preference (SP)

Based on direct judgment,

not choice-based.

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For which s2 is ?s2

Strength of Preference (SP)

For which s6 is s6s5 ~* t1t0?

.

.

.

We assume:

U(s2) – U(t1) = U(t1) – U(t0)

U(s3) – U(s2) = U(t1) – U(t0)

U(s6) – U(s5) = U(t1) – U(t0)

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.

.

.

t1t0t1 ~*

For which s3 is ?s3 t1t0s2 ~*

CE2/3(EU)

CE2/3(PT) corrects CE2/3 (EU)

FF

CE1/3

CE2/3(PT)SP

TO

Utility functions (group averages)

0

1/6

2/6

3/6

4/6

5/6

1

7/6

U

t0= FF5,000

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t6= FF26,068

22, nonTO ,nonEU

24, power? 26, which th? PT! (then TO)) 28,concl25, CE2/3

23, CE1/3

TO(PT) = TO(EU)CE1/3(PT) = CE1/3 (EU) (gr.av.)

Question:

Could this identity have resulted becausethe TO method does not properly measurechoice-based risky utility?

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(And, after answering this, what about nonEU?)

Certainty equivalent CE1/3

(with good-outcome probability 1/3)

3d utility measurement:

t0

t6

c2 ~

t0

c2

c2

t6

EU

U(c2) = 1/3

U(c1) = 1/9

U(c3) = 5/9

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For which c2: ?

c1 ~For which c1: ?

c3 ~For which c3: ?

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.".

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Questions

• Could this identity have resulted because our experiment is noisy (cannot distinguish anything)?

• How about violations of EU?

Certainty equivalent CE4th utility measurement:

t0

t6

d2 ~

t0

d2

d2

t6

CE2/3(EU):

U(d2) = 2/3

U(d1) = 4/9

U(d3) = 8/9

CE2/3(PT) (gr.av):

U(d2) = .51

U(d1) = .26

U(d3) = .76

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d3 ~For which d3: ?

d1 ~For which d1: ?

For which d2: ?

21, curves 21, curves

2/3

(with good-outcome probability 2/3)

And, EU is violated.

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So, our experiment does have the statistical power to distinguish.

Which alternative theory to use?

Prospect theory.

p

w

1

1

0 1/3

Fig. The common probability weighting function.w(1/3) = 1/3;

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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.

5. Conclusions

Under EU: usual discrepancies for risky ut.,

UCE2/3 UCE1/3 , UTO

Risky choice-based U = riskless choiceless U??

However:

= USP

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Under one risky utility, UCE2/3 = UCE1/3 = UTO

RDUPT

:

• Fox, Craig R. & Amos Tversky (1998), "A Belief-Based Account of Decision under Uncertainty," Management Science 44, 879895.

• 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. Ecs 150,1836.

• Ladyard (2005), "Happiness, Lessons from a New Science." Penguin, London.

• Tinbergen, Jan (1991), “On the Measurement of Welfare,” Journal of Econometrics 50, 713.

• 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!

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

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