decisions, decisions: the ellsberg paradox and the neural foundations of decision-making under...

Decisions, Decisions:The Ellsberg Paradox and The Neural Foundations of

Decision-Making under Uncertainty

Decisions, Decisions:The Ellsberg Paradox and The Neural Foundations of

Decision-Making under Uncertainty

Ming Hsu

Everhart Lecture

Ming Hsu

Everhart Lecture

Simple Decisions: Blackjack

Stock?Bond?

Domestic?Foreign?

Stock?Bond?

Domestic?Foreign?

DiversifyThink long-termDiversifyThink long-term

More Complicated: Investing

Whether?Who?When?Where?

Whether?Who?When?Where?

37% Rule (Mosteller, 1987)“Dozen” Rule (Todd, 1997)37% Rule (Mosteller, 1987)“Dozen” Rule (Todd, 1997)

Complicated: Love/Marriage

Little knowledge of probabilities

Little knowledge of probabilities

SimpleSimple ComplexComplex

Most of life’s decisions

Precise knowledge of probabilitiesPrecise knowledge of probabilities

Uncertainty about uncertainty?

Ellsberg Paradox

1961

Urn I: Risk

Most people indifferent between betting on red versus blue

5 Red5 Blue

?

Urn II: Ambiguity

Most people indifferent between betting on red versus blue

? ? ? ??? ???

10 - x Redx Blue

Choose Between Urns

Many people prefer betting on Urn I over Urn II.

? ? ? ? ??? ???

Urn II(Ambiguous)

Urn I(Risk)

Where Is The Paradox?

“…sadly but persistently, having looked into their hearts, found conflict with the axioms and decided … to satisfy their preferences and let the axioms satisfy themselves.”

--Daniel Ellsberg, Quarterly Journal of Economics (1961)

Ellsberg Paradox

P(RedII)=P(BlueII)

P(RedII) < 0.5

P(BlueII) < 0.5? ? ? ? ??? ???

P(RedI) = P(BlueI)

P(RedI) = 0.5

P(BlueI) = 0.5

P(RedI) + P(BlueI) = 1

P(RedII) + P(BlueII) = 1

Urn II(Ambiguous)

Urn I(Risk)

SimpleSimple ComplexComplex

Verizonor

Deutsche Telekom

Jenniferor

Angelina

Not ambiguityaverseNot ambiguityaverse

Portfolio Weights: U.S., Japan, and U.K. Investors

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

U.S. Japan U.K.

Proportion of portfolio

CanadaGermanyFranceU.K.JapanU.S.

Verizon or Deutsche Telecom?

French & Poterba, American Economic Review (1991).

Explaining Ambiguity Aversion

People consider the worst possible outcome of each action.

Murphy’s Law

If anything can go wrong, it will.

Like physicists, economists like laws of nature(Law of Demand, Walras’ Law, etc.)


? ? ? ? ??? ???

Urn II(Ambiguous)

P(RedII|BetRed) = 0

P(BlueII|BetBlue) = 0

P(RedI) = 0.5

P(BlueI) = 0.5

Urn I(Risk)

What Are We Missing?Gilboa & Schmeidler’s model is a model of ambiguity aversion.

There are a number of other models of ambiguity aversion.

Unanswered

Do these models really reflect actual decision-making process?

How are the relevant variables interpreted and choices produced?

Look in the brain.

The Bigger Picture

HumanBehavior

Economics: formal, axiomatic, global.

Psychology: intuitive, empirical, local.

Neuroscience:biological, circuitry, evolutionary.

The Bigger Picture

HumanBehavior

Economics: formal, axiomatic, global.

Psychology: intuitive, empirical, local.

Neuroscience:biological, circuitry, evolutionary.

Neuroeconomics

“A mechanistic, behavioral, and

mathematical explanation of choice that transcends [each field separately].”

- Glimcher and Rustichini. Science (2004)

The Story of Phineas Gage

Cavendish, Vermont (September 13, 1848)

The Story of Phineas Gage

• Impulsiveness

• Poor insight

• Impaired decision-making

• Both social and financial

“…fitful, irreverent, indulging at times in the grossest profanity...”

-- Gage’s physician

Orbitofrontal Cortex

Fiorillo, Tobler, and Schultz. Science. (2003)

Tools That We Used

Brain Lesion Patients Functional Magnetic Resonance Imaging (fMRI)

MRI: Magnetization of Tissue

fMRI: Changes in Magnetization

Basal State

Activated State

Statistical Models

Statistical image(SPM)

voxel time series

intensity

Tim

e

fMRI Time Series Data

Click

Stop

Statistical Modeling of fMRI Data

Tim

e = 2+

x2

+ erro

r

1

x1Intensity

Subj. 1

Subj. 6

Subj. 5

Subj. 4

Subj. 3

Subj. 20

Distribution of population effect

21

2Pop

Random Effects/Hierarchical Models

pdf

1

Pop

fMRI Experiment

Hsu, Bhatt, Adolphs, Tranel, and Camerer. Science. (2005)

Expected Reward Region

€

y i, jt,v = α + β amb A(i, j, t) + β riskR(i, j, t)

+δE(i, j, t) + πW (i, j, t,v) + ε i, jt,v

y - Brain response A(.) - Ambiguity trialsR(.) - Risk trialsE(.) - Expected value of choicesW(.) - Nuisance parameters

Lower Activity under Ambiguity

QuickTime™ and aTIFF (LZW) decompressor

are needed to see this picture.QuickTime™ and a

TIFF (LZW) decompressorare needed to see this picture.

% S

ign

al C

ha

ng

e

Lower Activity under Ambiguity

% S

ign

al C

ha

ng

e

Region Reacting to Uncertainty

€

amb > β risk

N.B. This region does not correlate with expected reward.


are needed to see this picture.Orbitofrontal Cortex

€

y i, jt,v = α + β amb A(i, j, t) + β riskR(i, j, t)

+δE(i, j, t) + πW (i, j, t,v) + ε i, jt,v

y - Brain response A(.) - Ambiguity trialsR(.) - Risk trialsE(.) - Expected value of choicesW(.) - Nuisance parameters


are needed to see this picture.



Brain Imaging Data

Behavioral Choice Data Stochastic Choice Model





Link Between Brain and Behavior






are needed to see this picture.Early

Late??

A Signal for Uncertainty?

Lesion Subjects

Orbitofrontal Control

Lesion Experiment

100 Cards

50 Red50 Black

100 Cards

x Red100-x Black

Choose between gamble worth 100 points OR

Sure payoffs of 15, 25, 30, 40 and 60 points.

Lesion Patient Behavioral Data











Estimated Risk and Ambiguity Attitudes

Orbitofrontal Lesion

Control Lesion

Orbitofrontal lesion patients more rational!



Linking Neural, Behavioral, and Lesion Data



Brain Imaging Data

Behavioral Choice Data Stochastic Choice Model







Imputed value



OFC lesion estimate = 0.82

What have we learned?

One System, Not Two




are needed to see this picture. QuickTime™ and aTIFF (LZW) decompressor


% S

igna

l Cha

nge

Reward Value of Ambiguous Gambles





Signal for Uncertainty



No OFC No Ambiguity/Risk Aversion



Orbitofrontal Cortex

Where are we going?

Neural Circuitry



??

The Brain and Home Bias

Portfolio Weights: U.S., Japan, and U.K. Investors

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

U.S. Japan U.K.

Proportion of portfolio

CanadaGermanyFranceU.K.JapanU.S.



Why Ambiguity Averse?

“…he was a gambler at heart…[and] assumed that he could always beat the odds.”

On Jeffrey Skilling From Bethany McLean and Peter Elkind, Smartest Guys in the Room (2003).

Colin CamererRalph AdolphsDaniel Tranel

Steve QuartzPeter Bossaerts

Meghana BhattCédric AnenShreesh Mysore

ELS Committee

Acknowledgements

decisions, decisions: the ellsberg paradox and the neural foundations of decision-making under...

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