Decisions, Decisions: The Ellsberg Paradox and The Neural Foundations of Decision-Making under Uncertainty Ming Hsu Everhart Lecture
Dec 28, 2015
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
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.)
Explaining Ambiguity Aversion
Explaining Ambiguity Aversion
? ? ? ? ??? ???
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)
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
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
1
Pop
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, 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
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% 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.
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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
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Brain Imaging Data
Behavioral Choice Data Stochastic Choice Model
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Link Between Brain and Behavior
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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
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Estimated Risk and Ambiguity Attitudes
Orbitofrontal Lesion
Control Lesion
Orbitofrontal lesion patients more rational!
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Linking Neural, Behavioral, and Lesion Data
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Brain Imaging Data
Behavioral Choice Data Stochastic Choice Model
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Imputed value
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OFC lesion estimate = 0.82
What have we learned?
One System, Not Two
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% S
igna
l Cha
nge
Reward Value of Ambiguous Gambles
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Signal for Uncertainty
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No OFC No Ambiguity/Risk Aversion
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Orbitofrontal Cortex
Where are we going?
Neural Circuitry
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??
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.
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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
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