Decisions, Decisions:
The Ellsberg Paradox and
The Neural Foundations of
Decision-Making under Uncertainty
Ming Hsu
Everhart Lecture
Simple Decisions: Blackjack
Simple Decisions: Blackjack
More Complicated: Investing
Stock?
Bond?
Diversify
Think long-term
Domestic?
Foreign?
Complicated: Love/Marriage
Whether
?
Who?
When?
Where?
37% Rule (Mosteller, 1987)
“Dozen” Rule (Todd, 1997)
Precise knowledge
of probabilities
Little knowledge
of probabilities
Simple
Complex
Most of life’s decisions
Uncertainty about uncertainty?
Ellsberg Paradox
1961
Urn I: Risk
5 Red
5 Blue
Most people indifferent between
betting on red versus blue
Urn II: Ambiguity
10 - x Red
x Blue
? ? ? ?? ? ?
? ? ?
Most people indifferent between
betting on red versus blue
Choose Between Urns
Urn I
Urn II
(Risk)
(Ambiguous)
? ? ? ?? ? ?
? ? ?
Many people prefer betting on Urn I
over Urn II.
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(RedI) = P(BlueI)
Urn I
P(RedI) = 0.5
(Risk)
P(BlueI) = 0.5
Urn II
P(RedII)=P(BlueII)
(Ambiguous) P(Red ) < 0.5
II
? ? ? ?? ? ?
? ? ?
P(RedI) + P(BlueI) = 1
P(RedII) + P(BlueII) = 1
P(BlueII) < 0.5
Verizon
or
Deutsche Telekom
Jennifer
or
Angelina
Not ambiguity
averse
Simple
Complex
Verizon or Deutsche Telecom?
Portfolio Weights: U.S., Japan, and U.K. Investors
Proportion of portfolio
1
0.9
Canada
Germany
France
U.K.
Japan
U.S.
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
U.S.
Japan
French & Poterba, American Economic Review (1991).
U.K.
Explaining Ambiguity Aversion
Like physicists, economists like laws of nature
(Law of Demand, Walras’ Law, etc.)
Murphy’s Law
If anything can go wrong, it will.
People consider the worst possible
outcome of each action.
Explaining Ambiguity Aversion
Explaining Ambiguity Aversion
Urn I
Urn II
(Risk)
(Ambiguous)
? ? ? ?? ? ?
? ? ?
P(RedI) = 0.5
P(RedII|BetRed) = 0
P(BlueI) = 0.5
P(BlueII|BetBlue) = 0
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 decisionmaking process?
How are the relevant variables interpreted and
choices produced?
Look in the brain.
The Bigger Picture
Economics:
formal, axiomatic, global.
Human
Behavior
Psychology: intuitive,
empirical,
local.
Neuroscience:
biological, circuitry,
evolutionary.
The Bigger Picture
Economics:
formal,
axiomatic, global.
Neuroeconomics
Human
Behavior
“A mechanistic,
behavioral, intuitive,
and
Psychology:
mathematical explanation
empirical,
of choice that transcends
local.
[each field separately].”
- Glimcher and Rustichini.
Neuroscience:
Science (2004)
biological, circuitry,
evolutionary.
The Story of Phineas Gage
Cavendish, Vermont (September 13, 1848)
The Story of Phineas Gage
“…fitful, irreverent, indulging at
times in the grossest profanity...”
-- Gage’s physician
Orbitofrontal Cortex
• Impulsiveness
• Poor insight
• Impaired decisionmaking
• Both social and financial
Fiorillo, Tobler, and Schultz. Science. (2003)
Fiorillo, Tobler, and Schultz. Science. (2003)
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
fMRI Time Series Data
intensity
Statistical Models
Click
Stop
Statistical image
(SPM)
voxel time series
Time
= b1
Intensity
+ b2
x1
x2
+
error
Statistical Modeling of fMRI Data
e
pdf
Random Effects/Hierarchical Models
Subj. 1
0
21
b1
Subj. 2
Subj. 3
Subj. 4
Subj. 5
Subj. 6
Distribution of
population effect
2Pop
bPop
fMRI Experiment
Hsu, Bhatt, Adolphs, Tranel, and Camerer. Science. (2005)
fMRI Experiment
Hsu, Bhatt, Adolphs, Tranel, and Camerer. Science. (2005)
fMRI Experiment
Hsu, Bhatt, Adolphs, Tranel, and Camerer. Science. (2005)
Expected Reward Region
y i,t,vj    b amb A(i, j,t)  b riskR(i, j,t)
E(i, j,t)  W (i, j,t,v)  ei,t,vj
y
A(.)
R(.)
E(.)
W(.)
- Brain response
- Ambiguity trials
- Risk trials
- Expected value of choices
- Nuisance parameters
a
% Signal Change
Lower Activity under Ambiguity
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TIF
are ne
% Signal Change
Lower Activity under Ambiguity
TIF
are ne
Region Reacting to Uncertainty
y i,t,vj    b amb A(i, j,t)  b riskR(i, j,t)
E(i, j,t)  W (i, j,t,v)  ei,t,vj
y
A(.)
R(.)
E(.)
W(.)
Orbitofrontal Cortex
b
amb
b
risk
- Brain response
- Ambiguity trials
- Risk trials
- Expected value of choices  N.B. This region does not
correlate with expected reward.
- Nuisance parameters
Link Between Brain and Behavior
Brain Imaging Data
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are
Behavioral Choice Data
Stochastic Choice Model
A Signal for Uncertainty?
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?
Late
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Lesion Subjects
Orbitofrontal
Control
Lesion Experiment
100 Cards
50 Red
50 Black
100 Cards
x Red
100-x Black
Choose between gamble worth 100 points
OR
Sure payoffs of 15, 25, 30, 40 and 60 points.
Lesion Patient Behavioral Data
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Estimated Risk and Ambiguity Attitudes
Orbitofrontal Lesion
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Control Lesion
Orbitofrontal lesion patients more rational!
Linking Neural, Behavioral, and Lesion Data
Brain Imaging Data
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Imputed value
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OFC lesion estimate
 = 0.82
Behavioral Choice Data
Stochastic Choice Model
What have we learned?
% Signal Change
One System, Not Two
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Reward Value of Ambiguous Gambles
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Signal for Uncertainty
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No OFC 
No Ambiguity/Risk Aversion
Orbitofrontal Cortex
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Where are we going?
Neural Circuitry
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?
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The Brain and Home Bias
Portfolio Weights: U.S., Japan, and U.K. Investors
Proportion of portfolio
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Canada
Germany
France
U.K.
Japan
U.S.
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
U.S.
Japan
U.K.
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).
Acknowledgements
Colin Camerer
Ralph Adolphs
Daniel Tranel
Meghana Bhatt
Cédric Anen
Shreesh Mysore
Steve Quartz
Peter Bossaerts
ELS Committee
END