1. Ming Hsu Everhart Lecture
Decisions, Decisions: The Ellsberg Paradox and The Neural Foundations of Decision-Making under Uncertainty
Ming Hsu
Everhart Lecture

2. Simple Decisions: Blackjack

3. Simple Decisions: Blackjack

4. More Complicated: Investing
Stock?
Bond?
Domestic?
Foreign?
Diversify
Think long-term
This is a huge field, and trillians of dollars rests on it. There are a lot of sophisticated models floating around, but for the average investor like you and me, the advice usually basically boils down to uninspired maxims like “diversify” and “think long-term.”

5. Complicated: Love/Marriage
Whether?
Who?
When?
Where?
Now some of the most complicated decisions involve highly personal matters like love and marriage.
Much has been written on the topic, and many models have been proposed. Not surprisingly, these models are not at all realistic, and make a number of very strong assumptions.
Here is one of the more famous: 37% rule.
37% Rule (Mosteller, 1987)
“Dozen” Rule (Todd, 1997)

6. Most of life’s decisions
Precise knowledge
of probabilities
Little knowledge
of probabilities
Simple
Complex
Most of life’s decisions
One of the things that make the complex decisions complex is: we generally have very little knowledge of the probabilities in these decisions.
With something like love, many might even find it vulgar to put assign probabilities and values to decisions.
Probably not at Caltech. Love is probably not real to some of you until it can be quantified.

7. Uncertainty about uncertainty?
This might sound at once obvious and strange to you.
What does it mean to be uncertain about probabilities, if probabilities ARE our statements about uncertainty.
If that is the case, you are in good company.
Economists, statisticians, and decision theorists have thought about this question since at least the 1920s.

8. Ellsberg Paradox
In 1961, a thought experiment proposed by Daniel Ellsberg showed very elegantly the following:
People behave very differently when they do not know the probabilities versus when they know the probabilities.
This became known as the “Ellsberg Paradox.”
Incidentally, this is the same Daniel Ellsberg of the Pentagon Papers fame. Prior to that, he was an economist of some promise.
1961

9. Urn I: Risk 5 Red 5 Blue Most people indifferent between
betting on red versus blue

10. Urn II: Ambiguity 10 - x Red x Blue Most people indifferent between? ? ? ? ? ? ? ? ? ?
Most people indifferent between
betting on red versus blue

11. Choose Between Urns Urn I Urn II (Risk) (Ambiguous)? ? ? ? ? ? ? ? ? ?
Many people prefer betting on Urn I
over Urn II.
The paradox arises when people are asked to choose from different urns.
Do you prefer to bet on RED from Urn I or RED from Urn II?
Alternatively, BLUE from Urn I or BLUE from Urn II?

12. 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)
The paradox lies in the fact that standard decision theory says that one should not behave differently under risk and ambiguity.
The Ellsberg Paradox was one of the first challenges to empirical validity of subjective expected utility theory as proposed by LJ Savage.

13. Ellsberg Paradox Urn I Urn II P(RedI) = P(BlueI) P(RedI) = 0.5
(Risk)
Urn II
(Ambiguous)
P(RedI) = P(BlueI)
P(RedI) = 0.5
P(BlueI) = 0.5
P(RedII)=P(BlueII)
P(RedII) < 0.5
P(BlueII) < 0.5 ? ? ? ? ? ? ? ? ? ?
P(RedI) + P(BlueI) = 1
P(RedII) + P(BlueII) = 1
To see why: consider the following.

14. Not ambiguity averse Verizon Jennifer or Deutsche Telekom or Angelina
Simple
Complex
Now consider the real world consequences of ambiguity aversion.
If people are ambiguity averse, they might choose to invest in companies that are familiar to them (e.g., Verizon) over stocks that are unfamiliar to them (Deutsche Telekom), even in cases where it might be suboptimal to do so.
Alternatively, one might choose the familiar, girl-next-door Jennifer over the probably more beautiful, but possible crazy Angelina.

15. Verizon or Deutsche Telecom?
Jokes aside, let me give you some real data. These are the portfolio weights for the mean investor in U.S., Japan, and U.K.
The reluctance to hold foreign stocks amounts to a sacrifice in annual percentage return of 1-2% per year. To put it in concrete terms, a ssuming an average unbiased return of 7%, a person with home bias who invests a lump sum at age 25 will end up with only half as much money at age 65 as an investor who is unbiased.
French & Poterba, American Economic Review (1991).

16. 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.
In 1989, Itzhak Gilboa and David Schmeidler invoked the following.
By relaxing a key axiom in Savage’s theory, Gilboa and Schmeidler were able to prove that, when people are faced with ambiguity, they consider the worst possible outcome for each action.
In other words, people are slightly paranoid.

17. Explaining Ambiguity Aversion
In other words, people are paranoid.

18. Explaining Ambiguity Aversion
Urn I
(Risk) ?
Urn II
(Ambiguous)
P(RedI) = 0.5
P(BlueI) = 0.5
P(RedII|BetRed) = 0
P(BlueII|BetBlue) = 0

19. What Are We Missing? Unanswered
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.
This is all fine and well as a model of behavior.
But does it actually describe reality?
This is where we came in.

20. The Bigger Picture Economics: Human Behavior
formal, axiomatic, global.
Human
Behavior
Psychology: intuitive, empirical,
local.
Neuroscience:
biological, circuitry, evolutionary.

21. - Glimcher and Rustichini. Science (2004)
The Bigger Picture
Economics:
formal, axiomatic, global.
Neuroeconomics
“A mechanistic, behavioral, and mathematical explanation of choice that transcends [each field separately].”
- Glimcher and Rustichini. Science (2004)
Human
Behavior
Psychology: intuitive, empirical,
local.
This is an area that Caltech is pioneering.
It’s something that might sound crazy at first, but when you think about it, is quite obvious:
Everyone is studying the same thing, so why not study it together?
Now let me tell you why we thought neuroscience can help.
I’m going to give you two of the seminal studies that will give you some idea of this.
Neuroscience:
biological, circuitry, evolutionary.

22. The Story of Phineas Gage
Phineas Gage was a railroad construction foreman in mid-19th C Cavendish, Vermont.
On September 13, 1848, he was setting explosive charges in holes drilled into large pieces of rock so they could be broken up and removed.
There was an accident. The tamping iron rod ignited the gunpowder and blew clean through Gage’s head.
Cavendish, Vermont (September 13, 1848)

23. The Story of Phineas Gage
“…fitful, irreverent, indulging at times in the grossest profanity...”
-- Gage’s physician
Orbitofrontal Cortex
Impulsiveness
Poor insight
Impaired decision-making
Both social and financial
Remarkably, Gage regained consciousness after a few minutes, and eventually was able to make a full recovery.
However, it soon became clear that Gage was not the same.
Whereas before he was responsible, jovial, and hard-working; after the accident, he became…

24. The second seminal study I will discuss is more recent
The second seminal study I will discuss is more recent. Instead of humans, this study is of alert behaving monkeys.
The monkey is passively sitting. A stimulus in the form of a geometric shape flashes, some seconds later, a reward in the form of a juice squirt is delivered to the monkey. This whole time, the experimenter is recording the brain activity of the monkey.
Here, the monkey is shown a cue that signals a reward will be delivered with probability 1.
Fiorillo, Tobler, and Schultz. Science. (2003)

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

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

27. Tools That We Used Functional Magnetic Brain Lesion Patients
Resonance Imaging (fMRI)
Brain Lesion Patients

28. MRI: Magnetization of Tissue
Magnetic resonance imaging takes advantage of the fact that different tissue in the brain has different magnetic properties.
This is the same sort of MRI that you would take at a hospital for your knee or back.

29. fMRI: Changes in Magnetization
Basal State
Activated State
fMRI takes advantage of the changes in magnetic properties of brain tissues as different parts of the brain are utilized.

30. fMRI Time Series Data intensity Statistical Models Time
Statistical image
(SPM)
Click
Stop
Time
voxel time series

31. Statistical Modeling of fMRI Datab2 + x2
error e b1 x1 =
Time
Intensity

32. Random Effects/Hierarchical Models
pdf
Subj. 2
21
Subj. 1
Subj. 3 1
Subj. 4
Subj. 5
Subj. 6
Distribution of population effect
2Pop
Pop

33. fMRI Experiment 16 Caltech graduate and undergraduate students.
3 Treatments: Card-Deck, Knowledge, Informed Opponents
2 Conditions: Ambiguity, Risk
24 trials per condition per treatment
Self-paced trials.
No feedback!
Hsu, Bhatt, Adolphs, Tranel, and Camerer. Science. (2005)

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

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

36. Expected Reward Region
y - Brain response
A(.) - Ambiguity trials
R(.) - Risk trials
E(.) - Expected value of choices
W(.) - Nuisance parameters
This is a region that is correlated with expected value of people’s choices.
But that’s not all this region is doing.

37. Lower Activity under Ambiguity
% Signal Change
The activity of the striatum is also greater under risk than ambiguity.

38. Lower Activity under Ambiguity
% Signal Change
These time courses all occur approximately around the time that the subject makes his choice, which is the blue line here.
We also know from neuroscience that the striatum is near the output of behavior.
Is there another region that is involved in the input?

39. Region Reacting to Uncertainty
Orbitofrontal Cortex
y - Brain response
A(.) - Ambiguity trials
R(.) - Risk trials
E(.) - Expected value of choices
W(.) - Nuisance parameters
N.B. This region does not correlate with expected reward.
The orbitofrontal cortex is well situated in the brain for this type of function.
It receives rapid, multisensory inputs and is known to evaluate the value of stimuli.

40. Link Between Brain and Behavior
Brain Imaging Data
Behavioral Choice Data
Stochastic Choice Model

41. A Signal for Uncertainty?
Late
Early

42. Lesion Subjects
Orbitofrontal
Control

43. Lesion Experiment Choose between gamble worth 100 points OR
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.

44. Lesion Patient Behavioral Data
Two observations:
1. Choices not random! Both groups clearly respond to incentives.
2. Crucial difference: OFC group less ambiguity and risk averse than Control group.

45. Estimated Risk and Ambiguity Attitudes
Orbitofrontal Lesion
Control Lesion
Remember this 0.82
Orbitofrontal lesion patients more rational!

46. Linking Neural, Behavioral, and Lesion Data
Brain Imaging Data
Imputed value
OFC lesion estimate
 = 0.82
Behavioral Choice Data
Stochastic Choice Model

47. What have we learned?

48. One System, Not Two
% Signal Change
All of our data indicates a single system involved in choice under uncertainty.
This has clear implications for decision theory.
Ambiguity and risk are part of one system, not too.
This makes evolutionary sense.

49. Reward Value of Ambiguous Gambles
Gilboa Schmeidler passes a test.

50. Signal for Uncertainty

51. No OFC  No Ambiguity/Risk Aversion
Orbitofrontal Cortex

52. Where are we going?

53. Neural Circuitry ?
We still don’t know the precise interaction between the OFC and the striatum.
To do so would require manipulating levels of ambiguity. This is something that Peter Bossaerts is undertaking.

54. The Brain and Home Bias

55. 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).

56. Acknowledgements Colin Camerer Meghana Bhatt Ralph Adolphs Cédric Anen
Daniel Tranel
Steve Quartz
Peter Bossaerts
Meghana Bhatt
Cédric Anen
Shreesh Mysore
ELS Committee

57. END