The Logic of Decision

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University of Chicago Press, Jul 15, 1990 - Mathematics - 231 pages
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"[This book] proposes new foundations for the Bayesian principle of rational action, and goes on to develop a new logic of desirability and probabtility."—Frederic Schick, Journal of Philosophy
 

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Contents

A Bayesian Framework
3
12 Desirabilities and Probabilities
4
13 Summary and Rationale
7
14 Incompletely Specified Desirabilities
8
15 Dominance and a Fallacy
10
16 Problems
12
17 Rat if lability
17
18 Notes and References
22
72 Determining Ratios of Probabilities
120
73 A Probability Scale for Indifferent Propositions
124
74 Nullity
125
75 A General Technique
127
76 Measuring Probabilities of Indifferent Propositions
128
77 Problems
131
8 Uniqueness
134
81 Uniqueness of Probabilities
135

Equivalent Scales
28
21 Equivalent Desirability Matrices
29
22 Conventions about Probabilities
33
23 A General Desirability Transformation
34
24 A Special Desirability Transformation
36
25 Problems
41
Ramseys Theory
43
32 From Probabilities to Desirabilities
44
33 The von NeumannMorgenstern Method
46
34 Ethical Neutrality Probability 12
48
35 Calibrating the Desirability Scale
51
36 Measuring Probabilities
52
37 Conclusion
53
38 Problems
55
39 Notes and References
57
4 Prepositional Attitudes
61
42 Justifying the Special Addition Law
62
43 Remarks on Fairness
63
44 Desirability
64
45 Sentences and Propositions
66
46 Notation
67
47 Belief versus Assent
70
48 Problems
72
49 References and Solutions
74
Preference
76
52 The Propositions T and F
78
54 Computing Desirabilities
80
55 The Probability and Desirability Axioms
82
56 Good Bad Indifferent
83
57 Preference between News Items
84
58 Acts as Propositions
85
59 Desirabilities Determine Probabilities
87
510 Problems
89
511 Notes and References
93
Equivalence Perspectives Quantization
97
61 Bolkers Equivalence Theorem
98
62 Zero and Unit
101
63 Bounds on Desirabilities
102
64 Bounds on c
104
65 Perspective Transformations of Desirability
105
66 Probability Quantization
108
67 Problems
113
68 Acknowledgment
114
From Preference to Probability
115
71 The Existence Closure G and Splitting Conditions
118
82 A Scale of Desirabilities between 0 and 1
136
83 Uniqueness of the Scale
138
84 Uniqueness of Desirabilities in the Unit Interval
139
85 Uniqueness of Negative Desirabilities
141
86 Completing the Uniqueness Proof
142
87 Problems
143
88 Notes and References
144
Bolkers Axioms
146
92 Prospects as Propositions
147
93 Averaging Nullity and Impartiality
148
94 Completeness Atomlessness Continuity
149
95 Notes and References
151
10 Boundedness Causality
152
101 The St Petersburg Paradox
153
102 Resolving the Paradox
156
103 Gambles as Causal Relationships
158
104 Our Theory Is Noncausal
159
105 Further Comparison with Ramseys Theory
160
106 Justifying Quantization
163
107 Notes and References
164
Probability Kinematics
166
112 The Problem
168
113 Solution for n 2
170
114 Relevance
172
115 Comparison with Conditionalization
173
116 Solution for Finite n
174
117 Origination Closure
175
118 The Continuous Case
177
119 Probabilistic Acts Trying
179
1110 Observation Meaning
181
1111 Notes and References
182
Induction and Objectification
186
122 Bayess Theorem
187
123 Simple Induction
189
124 Confirming Generalizations
192
125 Objectivity and Learning
197
126 De Fincttis Representation Theorem
201
127 Objectification
204
128 Conclusion
210
129 Notes and References
213
Preference among Preferences
216
Notes and References
226
Index
231
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Page 1 - In order to judge," they say, "of what we ought to do in order to obtain a good and to avoid an evil, it is necessary to consider not only the good and evil in themselves, but also the probability of their happening and not happening, and to regard geometrically the proportion which all these things have, taken together.

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