# The Logic of Decision

University of Chicago Press, Jul 15, 1990 - Mathematics - 231 pages
"[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

### What people are saying -Write a review

We haven't found any reviews in the usual places.

### 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 Copyright

### Popular passages

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.