Theory of Decision Making underUncertainty

Based on papers by Itzhak Gilboa, Massimo Marinacci, AndyPostlewaite, and David Schmeidler

IDC Herzliya

Dec 29, 2013

Risk and Uncertainty

I Dual use of probability: empirical frequencies in games ofchance and a subjective tool to quantify beliefs

I Dates back to Pascal and Leibniz (cf. Pascal’s Wager)I 1921 Knight , (Keynes) — risk, uncertaintyI 1931 Ramsey, de Finetti — subjective probabilityI 1954 Savage "The crowning glory"I Uncertainty = or Knightian UncertaintyI Objectivity — interpersonal concept, convincing others

Risk and Uncertainty

I Dual use of probability: empirical frequencies in games ofchance and a subjective tool to quantify beliefs

I Dates back to Pascal and Leibniz (cf. Pascal’s Wager)

I 1921 Knight , (Keynes) — risk, uncertaintyI 1931 Ramsey, de Finetti — subjective probabilityI 1954 Savage "The crowning glory"I Uncertainty = or Knightian UncertaintyI Objectivity — interpersonal concept, convincing others

Risk and Uncertainty

I Dual use of probability: empirical frequencies in games ofchance 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 probabilityI 1954 Savage "The crowning glory"I Uncertainty = or Knightian UncertaintyI Objectivity — interpersonal concept, convincing others

Risk and Uncertainty

I Dual use of probability: empirical frequencies in games ofchance and a subjective tool to quantify beliefs

I Dates back to Pascal and Leibniz (cf. Pascal’s Wager)I 1921 Knight , (Keynes) — risk, uncertaintyI 1931 Ramsey, de Finetti — subjective probability

I 1954 Savage "The crowning glory"I Uncertainty = or Knightian UncertaintyI Objectivity — interpersonal concept, convincing others

Risk and Uncertainty

I Dual use of probability: empirical frequencies in games ofchance and a subjective tool to quantify beliefs

I Dates back to Pascal and Leibniz (cf. Pascal’s Wager)I 1921 Knight , (Keynes) — risk, uncertaintyI 1931 Ramsey, de Finetti — subjective probabilityI 1954 Savage "The crowning glory"

I Uncertainty = or Knightian UncertaintyI Objectivity — interpersonal concept, convincing others

Risk and Uncertainty

I Dual use of probability: empirical frequencies in games ofchance and a subjective tool to quantify beliefs

I Dates back to Pascal and Leibniz (cf. Pascal’s Wager)I 1921 Knight , (Keynes) — risk, uncertaintyI 1931 Ramsey, de Finetti — subjective probabilityI 1954 Savage "The crowning glory"I Uncertainty = or Knightian Uncertainty

I Objectivity — interpersonal concept, convincing others

Risk and Uncertainty

I Dual use of probability: empirical frequencies in games ofchance and a subjective tool to quantify beliefs

I Dates back to Pascal and Leibniz (cf. Pascal’s Wager)I 1921 Knight , (Keynes) — risk, uncertaintyI 1931 Ramsey, de Finetti — subjective probabilityI 1954 Savage "The crowning glory"I Uncertainty = or Knightian UncertaintyI Objectivity — interpersonal concept, convincing others

Digression

I For which audience(s) the economic theorists writes?

I Economics is an empirical scienceI Convince, persuade, rhetoricI Axioms from Classical Greece to contemporary decisiontheory

I von Neumann and Morgenstein, Savage

Digression

I For which audience(s) the economic theorists writes?I Economics is an empirical science

I Convince, persuade, rhetoricI Axioms from Classical Greece to contemporary decisiontheory

I von Neumann and Morgenstein, Savage

Digression

I For which audience(s) the economic theorists writes?I Economics is an empirical scienceI Convince, persuade, rhetoric

I Axioms from Classical Greece to contemporary decisiontheory

I von Neumann and Morgenstein, Savage

Digression

I For which audience(s) the economic theorists writes?I Economics is an empirical scienceI Convince, persuade, rhetoricI Axioms from Classical Greece to contemporary decisiontheory

I von Neumann and Morgenstein, Savage

Digression

I For which audience(s) the economic theorists writes?I Economics is an empirical scienceI Convince, persuade, rhetoricI Axioms from Classical Greece to contemporary decisiontheory

I von Neumann and Morgenstein, Savage

Rationality

I Economic decision is rational if it optimizes the agent’spreferences,

I As long as the preferences are consistentI De gustibus non est disputandumI In case of risk or uncertainty the agent should maximizeexpected utility with respect to the known or subjectiveprobability

I This is the accepted view of economic theoryI or majority of economic theorists and game theorists.

Rationality

I Economic decision is rational if it optimizes the agent’spreferences,

I As long as the preferences are consistent

I De gustibus non est disputandumI In case of risk or uncertainty the agent should maximizeexpected utility with respect to the known or subjectiveprobability

I This is the accepted view of economic theoryI or majority of economic theorists and game theorists.

Rationality

I Economic decision is rational if it optimizes the agent’spreferences,

I As long as the preferences are consistentI De gustibus non est disputandum

I In case of risk or uncertainty the agent should maximizeexpected utility with respect to the known or subjectiveprobability

I This is the accepted view of economic theoryI or majority of economic theorists and game theorists.

Rationality

I Economic decision is rational if it optimizes the agent’spreferences,

I As long as the preferences are consistentI De gustibus non est disputandumI In case of risk or uncertainty the agent should maximizeexpected utility with respect to the known or subjectiveprobability

I This is the accepted view of economic theoryI or majority of economic theorists and game theorists.

Rationality

I Economic decision is rational if it optimizes the agent’spreferences,

I As long as the preferences are consistentI De gustibus non est disputandumI In case of risk or uncertainty the agent should maximizeexpected utility with respect to the known or subjectiveprobability

I This is the accepted view of economic theory

I or majority of economic theorists and game theorists.

Rationality

I Economic decision is rational if it optimizes the agent’spreferences,

I As long as the preferences are consistentI De gustibus non est disputandumI In case of risk or uncertainty the agent should maximizeexpected utility with respect to the known or subjectiveprobability

I This is the accepted view of economic theoryI or majority of economic theorists and game theorists.

Rationality and Objectivity

I The definition 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 thenexposed to the analysis of her behavior, she regrets it (feelsembarrassed).

I In other words, an act is rational (or objectively rational) ifthe decision maker can convince others that she optimized hergoals.

I Like Objectivity this is an interpersonal concept —convincingothers

I An act is subjectively rational if the decision maker can not beconvinced by others that she failed to optimize her goals.

Rationality and Objectivity

I The definition 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 thenexposed to the analysis of her behavior, she regrets it (feelsembarrassed).

I In other words, an act is rational (or objectively rational) ifthe decision maker can convince others that she optimized hergoals.

I Like Objectivity this is an interpersonal concept —convincingothers

I An act is subjectively rational if the decision maker can not beconvinced by others that she failed to optimize her goals.

Rationality and Objectivity

I The definition 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 thenexposed to the analysis of her behavior, she regrets it (feelsembarrassed).

I In other words, an act is rational (or objectively rational) ifthe decision maker can convince others that she optimized hergoals.

I Like Objectivity this is an interpersonal concept —convincingothers

I An act is subjectively rational if the decision maker can not beconvinced by others that she failed to optimize her goals.

Rationality and Objectivity

I The definition 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 thenexposed to the analysis of her behavior, she regrets it (feelsembarrassed).

I In other words, an act is rational (or objectively rational) ifthe decision maker can convince others that she optimized hergoals.

I Like Objectivity this is an interpersonal concept —convincingothers

I An act is subjectively rational if the decision maker can not beconvinced by others that she failed to optimize her goals.

Rationality and Objectivity

I The definition 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 thenexposed to the analysis of her behavior, she regrets it (feelsembarrassed).

I In other words, an act is rational (or objectively rational) ifthe decision maker can convince others that she optimized hergoals.

I Like Objectivity this is an interpersonal concept —convincingothers

I An act is subjectively rational if the decision maker can not beconvinced by others that she failed to optimize her goals.

The Bayesian approach

I Four tenets of Bayesianism in economic theory

I Formulation of a state space, where each state “resolves alluncertainty”

I Prior Probability: (i) Whenever a fact is not known, oneshould have probabilistic beliefs about its possible values.

I (ii) These beliefs should be given by a single probabilitymeasure defined over the state space

I Updating of the prior according to Bayes ruleI When facing a decision problem, one should maximizeexpected utility

I (ii)* Sometimes the prior is posited on the consequences.

The Bayesian approach

I Four tenets of Bayesianism in economic theoryI Formulation of a state space, where each state “resolves alluncertainty”

I Prior Probability: (i) Whenever a fact is not known, oneshould have probabilistic beliefs about its possible values.

I (ii) These beliefs should be given by a single probabilitymeasure defined over the state space

I Updating of the prior according to Bayes ruleI When facing a decision problem, one should maximizeexpected utility

I (ii)* Sometimes the prior is posited on the consequences.

The Bayesian approach

I Four tenets of Bayesianism in economic theoryI Formulation of a state space, where each state “resolves alluncertainty”

I Prior Probability: (i) Whenever a fact is not known, oneshould have probabilistic beliefs about its possible values.

I (ii) These beliefs should be given by a single probabilitymeasure defined over the state space

I Updating of the prior according to Bayes ruleI When facing a decision problem, one should maximizeexpected utility

I (ii)* Sometimes the prior is posited on the consequences.

The Bayesian approach

I Four tenets of Bayesianism in economic theoryI Formulation of a state space, where each state “resolves alluncertainty”

I Prior Probability: (i) Whenever a fact is not known, oneshould have probabilistic beliefs about its possible values.

I (ii) These beliefs should be given by a single probabilitymeasure defined over the state space

I Updating of the prior according to Bayes ruleI When facing a decision problem, one should maximizeexpected utility

I (ii)* Sometimes the prior is posited on the consequences.

The Bayesian approach

I Four tenets of Bayesianism in economic theoryI Formulation of a state space, where each state “resolves alluncertainty”

I Prior Probability: (i) Whenever a fact is not known, oneshould have probabilistic beliefs about its possible values.

I (ii) These beliefs should be given by a single probabilitymeasure defined over the state space

I Updating of the prior according to Bayes rule

I When facing a decision problem, one should maximizeexpected utility

I (ii)* Sometimes the prior is posited on the consequences.

The Bayesian approach

I Four tenets of Bayesianism in economic theoryI Formulation of a state space, where each state “resolves alluncertainty”

I Prior Probability: (i) Whenever a fact is not known, oneshould have probabilistic beliefs about its possible values.

I (ii) These beliefs should be given by a single probabilitymeasure defined over the state space

I Updating of the prior according to Bayes ruleI When facing a decision problem, one should maximizeexpected utility

I (ii)* Sometimes the prior is posited on the consequences.

The Bayesian approach

I Four tenets of Bayesianism in economic theoryI Formulation of a state space, where each state “resolves alluncertainty”

I Prior Probability: (i) Whenever a fact is not known, oneshould have probabilistic beliefs about its possible values.

I (ii) These beliefs should be given by a single probabilitymeasure defined over the state space

I Updating of the prior according to Bayes ruleI When facing a decision problem, one should maximizeexpected utility

I (ii)* Sometimes the prior is posited on the consequences.

Background

I Undoubtedly, the Bayesian approach is immensely powerfuland successful

I It is very good at representing knowledge, belief, and intuitionIndeed, it is a first 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 ofparameters does not grow with the database

I By contrast, in economics, it has been applied to very largespaces

Background

I Undoubtedly, the Bayesian approach is immensely powerfuland successful

I It is very good at representing knowledge, belief, and intuitionIndeed, it is a first 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 ofparameters does not grow with the database

I By contrast, in economics, it has been applied to very largespaces

Background

I Undoubtedly, the Bayesian approach is immensely powerfuland successful

I It is very good at representing knowledge, belief, and intuitionIndeed, it is a first 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 ofparameters does not grow with the database

I By contrast, in economics, it has been applied to very largespaces

Background

I Undoubtedly, the Bayesian approach is immensely powerfuland successful

I It is very good at representing knowledge, belief, and intuitionIndeed, it is a first 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 ofparameters does not grow with the database

I By contrast, in economics, it has been applied to very largespaces

Background

I Undoubtedly, the Bayesian approach is immensely powerfuland successful

I It is very good at representing knowledge, belief, and intuitionIndeed, it is a first 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 ofparameters does not grow with the database

I By contrast, in economics, it has been applied to very largespaces

Background

I Undoubtedly, the Bayesian approach is immensely powerfuland successful

I It is very good at representing knowledge, belief, and intuitionIndeed, it is a first 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 ofparameters does not grow with the database

I By contrast, in economics, it has been applied to very largespaces

Non-Bayesian decisions

I

A B = AC

a 7 0b 0 7c 3 3

Ellsberg’s Paradox

I One urn contains 50 black and 50 red ballsI Another contains 100 balls, each black or redI Do you prefer a bet on the known or the unknown urn?I Many prefer the known probabilities. People often preferknown to unknown probabilities

I This is inconsistent with the Bayesian approach

I Still, many insist on this choice even when the inconsistencyand Savage’s axioms are explained to them

Ellsberg’s Paradox

I One urn contains 50 black and 50 red ballsI Another contains 100 balls, each black or redI Do you prefer a bet on the known or the unknown urn?I Many prefer the known probabilities. People often preferknown to unknown probabilities

I This is inconsistent with the Bayesian approachI Still, many insist on this choice even when the inconsistencyand Savage’s axioms are explained to them

Symmetry and Reality

I Ellsberg’s paradox may be misleadingIf 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, stockmarket crashes, etc.

I Indeed, my critique was based on the cognitive implausibilityof the Bayesian approach, and not on the results of anexperiment

Symmetry and Reality

I Ellsberg’s paradox may be misleadingIf 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, stockmarket crashes, etc.

I Indeed, my critique was based on the cognitive implausibilityof the Bayesian approach, and not on the results of anexperiment

Symmetry and Reality

I Ellsberg’s paradox may be misleadingIf 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, stockmarket crashes, etc.

I Indeed, my critique was based on the cognitive implausibilityof the Bayesian approach, and not on the results of anexperiment