The Logic of Decision

Preface

1. Deliberation: A Bayesian Framework
1.1. Acts, Conditions, Consequences
1.2. Desirabilities and Probabilities
1.3. Summary and Rationale
1.4. Incompletely Specified Desirabilities
1.5. Dominance, and a Fallacy
1.6. Problems
1.7. Ratifiability
1.8. Notes and References

2. Equivalent Scales
2.1. Equivalent Desirability Matrices
2.2. Conventions about Probabilities
2.3. A General Desirability Transformation
2.4. A Special Desirability Transformation
2.5. Problems
 
3. Ramsey's Theory
3.1. From Desirabilities to Probabilities
3.2. From Probabilities to Desirabilities
3.3. The von Neumann-Morgenstern Method
3.4. Ethical Neutrality; Probability 1/2
3.5. Calibrating the Desirability Scale
3.6. Measuring Probabilities
3.7. Conclusion
3.8. Problems
3.9. Notes and References
 
4. Propositional Attitudes
4.1. Belief and Desire
4.2. Justifying the Special Addition Law
4.3. Remarks on Fairness
4.4. Desirability
4.5. Sentences and Propositions
4.6. Notation
4.7. Belief versus Assent
4.8. Problems
4.9. References and Solutions
 
5. Preference
5.1. Computing Probabilities
5.2. The Propositions T and F
5.3. A Remark on Computing Probabilities
5.4. Computing Desirabilities
5.5. The Probability and Desirability Axioms
5.6. "Good," "Bad," "Indifferent"
5.7. Preference between News Items
5.8. Acts as Propositions
5.9. Desirabilities Determine Probabilities
5.10. Problems
5.11. Notes and References

6. Equivalence, Perspectives, Quantization
6.1. Bolker's Equivalence Theorem
6.2. Zero and Unit
6.3. Bounds on Desirabilities
6.4. Bounds on c
6.5. Perspective Transformations of Desirability
6.6. Probability Quantization
6.7. Problems
6.8. Acknowledgment
 
7. From Preference to Probability
7.1. The Existence, Closure, G, and Splitting Conditions
7.2. Determining Ratios of Probabilities
7.3. A Probability Scale for Indifferent Propositions
7.4. Nullity
7.5. A General Technique
7.6. Measuring Probabilities of Indifferent Propositions
7.7. Problems
 
8. Uniqueness
8.1. Uniqueness of Probabilities
8.2. A Scale of Desirabilities between 0 and 1
8.3. Uniqueness of the Scale
8.4. Uniqueness of Desirabilities in the Unit Interval
8.5. Uniqueness of Negative Desirabilities
8.6. Completing the Uniqueness Proof
8.7. Problems
8.8. Notes and References

9. Existence: Bolker's Axioms
9.1. Preference-or-Indifference as a Primitive
9.2. Prospects as Propositions
9.3. Averaging, Nullity, and Impartiality
9.4. Completeness, Atomlessness, Continuity
9.5. Notes and References
 
10. Boundedness; Causality
10.1. The St. Petersburg Paradox
10.2. Resolving the Paradox
10.3. Gambles as Causal Relationships
10.4. Our Theory Is Noncausal
10.5. Further Comparison with Ramsey's Theory
10.6. Justifying Quantization
10.7. Notes and References

11. Probability Kinematics
11.1. Conditionalization and Its Limits
11.2. The Problem
11.3. Solution for n = 2
11.4. Relevance
11.5. Comparison with Conditionalization
11.6. Solution for Finite n
11.7. Origination, Closure
11.8. The Continuous Case
11.9. Probabilistic Acts; Trying
11.10. Observation; Meaning
11.11. Notes and References

12. Induction and Objectification
12.1. Belief: Reasons versus Causes
12.2. Bayes's Theorem
12.3. Simple Induction
12.4. Confirming Generalizations
12.5. Objectivity and Learning
12.6. De Finetti's Representation Theorem
12.7. Objectification
12.8. Conclusion
12.9. Notes and References

Appendix: Preference among Preferences
Notes and References
Index