Theory of decision under uncertainty:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge [u.a.]
Cambridge Univ. Press
2010
|
| Edition: | Reprinted |
| Series: | Econometric Society monographs
45 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis Klappentext |
| Physical Description: | XIV, 214 S. |
| ISBN: | 9780521517324 9780521741231 |
Staff View
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Record in the Search Index
| _version_ | 1804145584948379648 |
|---|---|
| adam_text | Contents
Preface
page
xiii
I Intuitive Definitions
1
1
Motivating Examples
3
2
Free Will and Determinism
5
2.1
Can Free Choice Be Predicted?
5
2.2
Is the World Deterministic?
6
2.3
Is Free Will Observable?
6
2.4
The Problem of Free Will
7
2.5
A Rational Illusion
10
2.6
Free Will and the Decision Matrix
12
3
The Principle of Indifference
14
3.1
Will a Canonical Space Help?
14
3.1.1
The Canonical State Space
14
3.1.2
Difficulties with a Uniform Prior on
[0, 1] 15
3.1.3
Conclusion
16
3.2
What s Special about the Coin?
17
3.2.1
Symmetry
17
3.2.2
Smooth Beliefs
18
4
Relative Frequencies
20
4.1
The Law of Large Numbers
20
4.2
The Problem of Induction
21
4.2.1
Hume s Critique
21
4.2.2
Goodman s Grue-Bleen Paradox
22
4.2.3
Kolmogorov Complexity and Its Dependence
of Language
23
4.2.4
Grue-Bleen Again
26
4.2.5
Evolutionary Explanations
31
4.3
Problems with the Frequentist Approach
34
Contents
і
Subjective
Probabilities
37
5.1
Linda
the Bank Teller
37
5.2
Pascal s Wager
38
5.3
Classical versus Bayesian Statistics
40
5.3.1
Basic Definitions
40
5.3.2
The Gambler Fallacy
41
5.3.3
Exchangeability
42
5.3.4
Confidence Is Not Probability
44
5.3.5
Classical Statistics Can Be Ridiculous
45
5.3.6
Different Methods for Different Goals
46
[
Behavioral Definitions
49
6
A Case Study
51
6.1
A Characterization Theorem for Maximization
of Utility
51
6.2
Proof
53
6.3
Interpretations
55
6.3.1
A Few Definitions
56
6.3.2
A Meta-Scientific Interpretation
59
6.3.3
A Normative Interpretation
62
6.3.4
A Descriptive Interpretation
63
6.4
Limitations
64
6.4.1
Sem
¡orders
65
6.4.2
Other Ways to Measure Utility
71
7
The Role of Theories
72
7.1
Theories Are Always Wrong
72
7.2
Theories and Conceptual Frameworks
74
7.3
Logical Positivism as a Metaphor
76
8 Von
Neumann-Morgenstem s Theorem
78
8.1
Background
78
8.2
The Theorem
79
8.3
Proofs
83
8.3.1
The Algebraic Approach
83
8.3.2
A Geometric Approach
84
8.3.3
A Separation Argument
85
8.4
The Three Interpretations
86
9 De
Finetti s Theorem
89
9.1
Motivation
89
9.2
The Theorem
90
9.3
A Proof
91
9.4
The Three Interoretatinn«
92
Contents
¡x
10
Savage s
Theorem 94
10.1
Background
94
10.2
States, Outcomes, and Acts
96
10.3
Axioms
97
10.3.1
PI
97
10.3.2
P2
97
10.3.3
Notation
99
10.3.4
Null Events
99
10.3.5
P3
100
10.3.6
P4
102
10.3.7
P5
102
10.3.8
P6
103
10.3.9
P7
104
10.4
The Result for a Finite Outcome Set
105
10.4.1
Finitely Additive Measures
105
10.4.2
Nonatomic Measures
107
10.4.3
The Theorem
108
10.5
The Case of a General Outcome Set
108
10.6
Interpretations
109
10.7
The Proof and Qualitative Probabilities
110
11
The Definition of States
113
11.1
Causality
113
11.1.1
Newcomb s Paradox
113
11.1.2
States as Functions from Acts to Outcomes
114
11.1.3
A Problem
115
11.2
Hempel s Paradox of Confirmation
116
11.2.1
Are All Ravens Black?
116
11.2.2
A State-Space Formulation
117
11.2.3
What Is a Confirmation?
117
11.2.4
A Resolution
118
11.2.5
Good s Variation
118
11.2.6
What Do We Learn from This?
119
11.3
Monty Hall Three-Door Game
120
12
A Critique of Savage
123
12.1
Criticizing Critiques
123
12.1.1
An Example
123
12.1.2
The General Lesson
124
12.2
Critique of P3 and P4
125
12.2.1
Example
125
12.2.2
Defense
126
12.2.3
State-Dependent Utility
127
12.2.4
The Definition of Subjective Probability
128
12.2.5
When Is State Dependence Necessary?
129
к
Contents
12.3
Critique
of
Pl
and P2
ì
30
12.3.1
The Basic
Problem 13°
12.3.2
Reasoned Choice versus Raw Preferences
131
12.3.3
Schmeidler s Critique and Ellsberg s
Paradox 132
12.3.4
Observability of States
136
12.3.5
Problems of Complexity
137
13
Objectivity and Rationality 138
13.1
Subjectivity and Objectivity 138
13.2
Objective and Subjective Rationality
139
14
Anscombe-Aumann s Theorem
142
III Alternative Behavioral Theories I45
15
Choquet Expected Utility I47
15.1
Schmeidler s Intuition I47
15.2
Choquet Integral I49
15.3
Comonotonicity I50
15.4
Axioms and Result
151
16
Prospect Theory I54
16.1
Background I54
16.2
Gain-Loss Asymmetry
154
16.3
Distortion of Probabilities
156
16.4
Rank-Dependent Probabilities and Choquet
Integration
158
17
Maxmin Expected Utility I60
17.1
Convex Games
160
17.2
A Cognitive Interpretation of
CEU
1
6
17.3
Axioms and Result I63
17.4
Interpretation of MMEU
163
17.5
Generalizations and Variations
165
17.6
Bewley s Alternative Approach
165
17.7
Combining Objective and Subjective Rationality
166
17.8
Applications
168
TV Cognitive Origins
171
18
Case-Based Qualitative Beliefs 173
18.1
Axioms and Result
173
18.2
Four Known Techniques
175
18.3
The Combination Axiom in General Analogical
Reasoning
177
18.4
Violations of the Combination Axiom l79
Contents xi
19 Frequentism
Revisited
180
19.1
Similarity-Weighted Empirical Frequencies
180
19.2
Intuition
181
19.3
Axiomatization
182
19.4
Empirical Similarity and Objective Probabilities
184
20
Future Research
188
References
191
Index
199
Theory of Decision under Uncertainty
This book describes the classical axiomatic theories of decision under uncertainty,
as well as critiques thereof and alternative theories. It focuses on the meaning of
probability, discussing some definitions and surveying their scope of applicability.
The behavioral definition of subjective probability serves as a way to present the
classical theories, culminating in Savage s theorem. The limitations of this result as
a definition of probability lead to two directions
-
first, similar behavioral definitions
of more general theories, such as
nonadditive
probabilities and multiple priors, and
second, cognitive derivations based on case-based techniques.
Itzhak
Gilboa is a professor in the Berglas School of Economics, Tel-Aviv Uni¬
versity, Israel, and a professor in the newly established Department of Economics
and Decision Science,
НЕС,
Paris. Earlier, he became a chaired professor at North¬
western University in
1992,
visited at the Department of Economics, University of
Pennsylvania
( 1995-1997),
and was a professor at Boston University
( 1997-1999).
Professor Gilboa also served as a Fellow at the Cowles Foundation at Yale Univer¬
sity from
2001
to
2007.
The recipient of a Sloan Fellowship, among other awards,
he has published articles in the leading economic theory journals, primarily on
decision under uncertainty. Professor Gilboa coauthored A Theory of Case-Based
Decisions with David Schmeidler (Cambridge University Press,
2001).
He received
his Ph.D. from Tel-Aviv University in
1987.
|
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| spelling | Gilboa, Itzhak 1963- Verfasser (DE-588)131540548 aut Theory of decision under uncertainty Itzhak Gilboa Reprinted Cambridge [u.a.] Cambridge Univ. Press 2010 XIV, 214 S. txt rdacontent n rdamedia nc rdacarrier Econometric Society monographs 45 Decision making Uncertainty (Information theory) Entscheidung bei Unsicherheit (DE-588)4070864-0 gnd rswk-swf Entscheidung bei Unsicherheit (DE-588)4070864-0 s DE-604 Econometric Society monographs 45 (DE-604)BV000018129 45 Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=022464553&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=022464553&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
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| subject_GND | (DE-588)4070864-0 |
| title | Theory of decision under uncertainty |
| title_auth | Theory of decision under uncertainty |
| title_exact_search | Theory of decision under uncertainty |
| title_full | Theory of decision under uncertainty Itzhak Gilboa |
| title_fullStr | Theory of decision under uncertainty Itzhak Gilboa |
| title_full_unstemmed | Theory of decision under uncertainty Itzhak Gilboa |
| title_short | Theory of decision under uncertainty |
| title_sort | theory of decision under uncertainty |
| topic | Decision making Uncertainty (Information theory) Entscheidung bei Unsicherheit (DE-588)4070864-0 gnd |
| topic_facet | Decision making Uncertainty (Information theory) Entscheidung bei Unsicherheit |
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