Theory of Decision Making under
Uncertainty
Based on papers by Itzhak Gilboa, Massimo Marinacci, Andy
Postlewaite, and David Schmeidler
IDC Herzliya
Dec 29, 2013
Risk and Uncertainty
I
Dual use of probability: empirical frequencies in games of
chance and a subjective tool to quantify beliefs
Risk and Uncertainty
I
Dual use of probability: empirical frequencies in games of
chance and a subjective tool to quantify beliefs
I
Dates back to Pascal and Leibniz (cf. Pascal’s Wager)
Risk and Uncertainty
I
Dual use of probability: empirical frequencies in games of
chance and a subjective tool to quantify beliefs
I
Dates back to Pascal and Leibniz (cf. Pascal’s Wager)
I
1921 Knight , (Keynes) – risk, uncertainty
Risk and Uncertainty
I
Dual use of probability: empirical frequencies in games of
chance and a subjective tool to quantify beliefs
I
Dates back to Pascal and Leibniz (cf. Pascal’s Wager)
I
1921 Knight , (Keynes) – risk, uncertainty
I
1931 Ramsey, de Finetti – subjective probability
Risk and Uncertainty
I
Dual use of probability: empirical frequencies in games of
chance and a subjective tool to quantify beliefs
I
Dates back to Pascal and Leibniz (cf. Pascal’s Wager)
I
1921 Knight , (Keynes) – risk, uncertainty
I
1931 Ramsey, de Finetti – subjective probability
I
1954 Savage "The crowning glory"
Risk and Uncertainty
I
Dual use of probability: empirical frequencies in games of
chance and a subjective tool to quantify beliefs
I
Dates back to Pascal and Leibniz (cf. Pascal’s Wager)
I
1921 Knight , (Keynes) – risk, uncertainty
I
1931 Ramsey, de Finetti – subjective probability
I
1954 Savage "The crowning glory"
I
Uncertainty = or Knightian Uncertainty
Risk and Uncertainty
I
Dual use of probability: empirical frequencies in games of
chance and a subjective tool to quantify beliefs
I
Dates back to Pascal and Leibniz (cf. Pascal’s Wager)
I
1921 Knight , (Keynes) – risk, uncertainty
I
1931 Ramsey, de Finetti – subjective probability
I
1954 Savage "The crowning glory"
I
Uncertainty = or Knightian Uncertainty
I
Objectivity – interpersonal concept, convincing others
Digression
I
For which audience(s) the economic theorists writes?
Digression
I
For which audience(s) the economic theorists writes?
I
Economics is an empirical science
Digression
I
For which audience(s) the economic theorists writes?
I
Economics is an empirical science
I
Convince, persuade, rhetoric
Digression
I
For which audience(s) the economic theorists writes?
I
Economics is an empirical science
I
Convince, persuade, rhetoric
I
Axioms
theory
from Classical Greece to contemporary decision
Digression
I
For which audience(s) the economic theorists writes?
I
Economics is an empirical science
I
Convince, persuade, rhetoric
I
Axioms
theory
I
von Neumann and Morgenstein, Savage
from Classical Greece to contemporary decision
Rationality
I
Economic decision is rational if it optimizes the agent’s
preferences,
Rationality
I
Economic decision is rational if it optimizes the agent’s
preferences,
I
As long as the preferences are consistent
Rationality
I
Economic decision is rational if it optimizes the agent’s
preferences,
I
As long as the preferences are consistent
I
De gustibus non est disputandum
Rationality
I
Economic decision is rational if it optimizes the agent’s
preferences,
I
As long as the preferences are consistent
I
De gustibus non est disputandum
I
In case of risk or uncertainty the agent should maximize
expected utility with respect to the known or subjective
probability
Rationality
I
Economic decision is rational if it optimizes the agent’s
preferences,
I
As long as the preferences are consistent
I
De gustibus non est disputandum
I
In case of risk or uncertainty the agent should maximize
expected utility with respect to the known or subjective
probability
I
This is the accepted view of economic theory
Rationality
I
Economic decision is rational if it optimizes the agent’s
preferences,
I
As long as the preferences are consistent
I
De gustibus non est disputandum
I
In case of risk or uncertainty the agent should maximize
expected utility with respect to the known or subjective
probability
I
This is the accepted view of economic theory
I
or majority of economic theorists and game theorists.
Rationality and Objectivity
I
The de…nition we use:
Rationality and Objectivity
I
The de…nition we use:
I
A mode of behavior is irrational for a given decision maker, if,
when the decision maker behaves in this mode, and is then
exposed to the analysis of her behavior, she regrets it (feels
embarrassed).
Rationality and Objectivity
I
The de…nition we use:
I
A mode of behavior is irrational for a given decision maker, if,
when the decision maker behaves in this mode, and is then
exposed to the analysis of her behavior, she regrets it (feels
embarrassed).
I
In other words, an act is rational (or objectively rational) if
the decision maker can convince others that she optimized her
goals.
Rationality and Objectivity
I
The de…nition we use:
I
A mode of behavior is irrational for a given decision maker, if,
when the decision maker behaves in this mode, and is then
exposed to the analysis of her behavior, she regrets it (feels
embarrassed).
I
In other words, an act is rational (or objectively rational) if
the decision maker can convince others that she optimized her
goals.
I
Like Objectivity this is an interpersonal concept – convincing
others
Rationality and Objectivity
I
The de…nition we use:
I
A mode of behavior is irrational for a given decision maker, if,
when the decision maker behaves in this mode, and is then
exposed to the analysis of her behavior, she regrets it (feels
embarrassed).
I
In other words, an act is rational (or objectively rational) if
the decision maker can convince others that she optimized her
goals.
I
Like Objectivity this is an interpersonal concept – convincing
others
I
An act is subjectively rational if the decision maker can not be
convinced by others that she failed to optimize her goals.
The Bayesian approach
I
Four tenets of Bayesianism in economic theory
The Bayesian approach
I
Four tenets of Bayesianism in economic theory
I
Formulation of a state space, where each state “resolves all
uncertainty”
The Bayesian approach
I
Four tenets of Bayesianism in economic theory
I
Formulation of a state space, where each state “resolves all
uncertainty”
I
Prior Probability: (i) Whenever a fact is not known, one
should have probabilistic beliefs about its possible values.
The Bayesian approach
I
Four tenets of Bayesianism in economic theory
I
Formulation of a state space, where each state “resolves all
uncertainty”
I
Prior Probability: (i) Whenever a fact is not known, one
should have probabilistic beliefs about its possible values.
I
(ii) These beliefs should be given by a single probability
measure de…ned over the state space
The Bayesian approach
I
Four tenets of Bayesianism in economic theory
I
Formulation of a state space, where each state “resolves all
uncertainty”
I
Prior Probability: (i) Whenever a fact is not known, one
should have probabilistic beliefs about its possible values.
I
(ii) These beliefs should be given by a single probability
measure de…ned over the state space
I
Updating of the prior according to Bayes rule
The Bayesian approach
I
Four tenets of Bayesianism in economic theory
I
Formulation of a state space, where each state “resolves all
uncertainty”
I
Prior Probability: (i) Whenever a fact is not known, one
should have probabilistic beliefs about its possible values.
I
(ii) These beliefs should be given by a single probability
measure de…ned over the state space
I
Updating of the prior according to Bayes rule
I
When facing a decision problem, one should maximize
expected utility
The Bayesian approach
I
Four tenets of Bayesianism in economic theory
I
Formulation of a state space, where each state “resolves all
uncertainty”
I
Prior Probability: (i) Whenever a fact is not known, one
should have probabilistic beliefs about its possible values.
I
(ii) These beliefs should be given by a single probability
measure de…ned over the state space
I
Updating of the prior according to Bayes rule
I
When facing a decision problem, one should maximize
expected utility
I
(ii)* Sometimes the prior is posited on the consequences.
Background
I
Undoubtedly, the Bayesian approach is immensely powerful
and successful
Background
I
Undoubtedly, the Bayesian approach is immensely powerful
and successful
I
It is very good at representing knowledge, belief, and intuition
Indeed, it is a …rst rate tool to reason about uncertainty
(cf. “paradoxes”)
Background
I
Undoubtedly, the Bayesian approach is immensely powerful
and successful
I
It is very good at representing knowledge, belief, and intuition
Indeed, it is a …rst rate tool to reason about uncertainty
(cf. “paradoxes”)
I
Used in statistics, machine learning and computer science,
philosophy (mostly of science), and econometrics...
Background
I
Undoubtedly, the Bayesian approach is immensely powerful
and successful
I
It is very good at representing knowledge, belief, and intuition
Indeed, it is a …rst rate tool to reason about uncertainty
(cf. “paradoxes”)
I
Used in statistics, machine learning and computer science,
philosophy (mostly of science), and econometrics...
I
However, in most of these, only when the prior is known.
Background
I
Undoubtedly, the Bayesian approach is immensely powerful
and successful
I
It is very good at representing knowledge, belief, and intuition
Indeed, it is a …rst rate tool to reason about uncertainty
(cf. “paradoxes”)
I
Used in statistics, machine learning and computer science,
philosophy (mostly of science), and econometrics...
I
However, in most of these, only when the prior is known.
I
Typically, for a restricted state space where the set of
parameters does not grow with the database
Background
I
Undoubtedly, the Bayesian approach is immensely powerful
and successful
I
It is very good at representing knowledge, belief, and intuition
Indeed, it is a …rst rate tool to reason about uncertainty
(cf. “paradoxes”)
I
Used in statistics, machine learning and computer science,
philosophy (mostly of science), and econometrics...
I
However, in most of these, only when the prior is known.
I
Typically, for a restricted state space where the set of
parameters does not grow with the database
I
By contrast, in economics, it has been applied to very large
spaces
Non-Bayesian decisions
A
I
a
b
c
7
0
3
B = AC
0
7
3
Ellsberg’s Paradox
I
One urn contains 50 black and 50 red balls
I
Another contains 100 balls, each black or red
I
Do you prefer a bet on the known or the unknown urn?
I
Many prefer the known probabilities. People often prefer
known to unknown probabilities
I
This is inconsistent with the Bayesian approach
Ellsberg’s Paradox
I
One urn contains 50 black and 50 red balls
I
Another contains 100 balls, each black or red
I
Do you prefer a bet on the known or the unknown urn?
I
Many prefer the known probabilities. People often prefer
known to unknown probabilities
I
This is inconsistent with the Bayesian approach
I
Still, many insist on this choice even when the inconsistency
and Savage’s axioms are explained to them
Symmetry and Reality
I
Ellsberg’s paradox may be misleading
If one wishes to be Bayesian, it is easy to adopt a prior in
this example (due to symmetry)
Symmetry and Reality
I
Ellsberg’s paradox may be misleading
If one wishes to be Bayesian, it is easy to adopt a prior in
this example (due to symmetry)
I
But this is not the case in real life examples of wars, stock
market crashes, etc.
Symmetry and Reality
I
Ellsberg’s paradox may be misleading
If one wishes to be Bayesian, it is easy to adopt a prior in
this example (due to symmetry)
I
But this is not the case in real life examples of wars, stock
market crashes, etc.
I
Indeed, my critique was based on the cognitive implausibility
of the Bayesian approach, and not on the results of an
experiment