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| Preface | |
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| Intuitive Definitions | |
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| Motivating Examples | |
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| Free Will and Determinism | |
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| Can Free Choice Be Predicted? | |
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| Is the World Deterministic? | |
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| Is Free Will Observable? | |
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| The Problem of Free Will | |
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| A Rational Illusion | |
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| Free Will and the Decision Matrix | |
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| The Principle of Indifference | |
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| Will a Canonical Space Help? | |
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| The Canonical State Space | |
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| Difficulties with a Uniform Prior on [0, 1] | |
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| Conclusion | |
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| What's Special about the Coin? | |
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| Symmetry | |
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| Smooth Beliefs | |
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| Relative Frequencies | |
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| The Law of Large Numbers | |
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| The Problem of Induction | |
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| Hume's Critique | |
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| Goodman's Grue-Bleen Paradox | |
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| Kolmogorov Complexity and Its Dependence of Language | |
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| Grue-Bleen Again | |
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| Evolutionary Explanations | |
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| Problems with the Frequentist Approach | |
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| Subjective Probabilities | |
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| Linda the Bank Teller | |
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| Pascal's Wager | |
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| Classical versus Bayesian Statistics | |
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| Basic Definitions | |
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| The Gambler Fallacy | |
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| Exchangeability | |
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| Confidence Is Not Probability | |
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| Classical Statistics Can Be Ridiculous | |
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| Different Methods for Different Goals | |
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| Behavioral Definitions | |
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| A Case Study | |
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| A Characterization Theorem for Maximization of Utility | |
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| Proof | |
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| Interpretations | |
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| A Few Definitions | |
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| A Meta-Scientific Interpretation | |
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| A Normative Interpretation | |
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| A Descriptive Interpretation | |
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| Limitations | |
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| Semiorders | |
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| Other Ways to Measure Utility | |
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| The Role of Theories | |
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| Theories Are Always Wrong | |
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| Theories and Conceptual Frameworks | |
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| Logical Positivism as a Metaphor | |
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| Von Neumann-Morgenstern's Theorem | |
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| Background | |
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| The Theorem | |
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| Proofs | |
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| The Algebraic Approach | |
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| A Geometric Approach | |
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| A Separation Argument | |
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| The Three Interpretations | |
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| De Finetti's Theorem | |
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| Motivation | |
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| The Theorem | |
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| A Proof | |
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| The Three Interpretations | |
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| Savage's Theorem | |
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| Background | |
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| States, Outcomes, and Acts | |
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| Axioms | |
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| P1 | |
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| P2 | |
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| Notation | |
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| Null Events | |
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| P3 | |
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| P4 | |
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| P5 | |
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| P6 | |
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| P7 | |
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| The Result for a Finite Outcome Set | |
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| Finitely Additive Measures | |
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| Nonatomic Measures | |
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| The Theorem | |
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| The Case of a General Outcome Set | |
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| Interpretations | |
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| The Proof and Qualitative Probabilities | |
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| The Definition of States | |
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| Causality | |
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| Newcomb's Paradox | |
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| States as Functions from Acts to Outcomes | |
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| A Problem | |
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| Hempel's Paradox of Confirmation | |
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| Are All Ravens Black? | |
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| A State-Space Formulation | |
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| What Is a Confirmation? | |
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| A Resolution | |
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| Good's Variation | |
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| What Do We Learn from This? | |
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| Monty Hall Three-Door Game | |
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| A Critique of Savage | |
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| Criticizing Critiques | |
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| An Example | |
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| The General Lesson | |
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| Critique of P3 and P4 | |
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| Example | |
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| Defense | |
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| State-Dependent Utility | |
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| The Definition of Subjective Probability | |
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| When Is State Dependence Necessary? | |
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| Critique of P1 and P2 | |
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| The Basic Problem | |
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| Reasoned Choice versus Raw Preferences | |
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| Schmeidler's Critique and Ellsberg's Paradox | |
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| Observability of States | |
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| Problems of Complexity | |
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| Objectivity and Rationality | |
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| Subjectivity and Objectivity | |
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| Objective and Subjective Rationality | |
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| Anscombe-Aumann's Theorem | |
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| Alternative Behavioral Theories | |
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| Choquet Expected Utility | |
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| Schmeidler's Intuition | |
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| Choquet Integral | |
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| Comonotonicity | |
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| Axioms and Result | |
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| Prospect Theory | |
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| Background | |
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| Gain-Loss Asymmetry | |
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| Distortion of Probabilities | |
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| Rank-Dependent Probabilities and Choquet Integration | |
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| Maxmin Expected Utility | |
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| Convex Games | |
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| A Cognitive Interpretation of CEU | |
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| Axioms and Result | |
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| Interpretation of MMEU | |
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| Generalizations and Variations | |
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| Bewley's Alternative Approach | |
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| Combining Objective and Subjective Rationality | |
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| Applications | |
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| Cognitive Origins | |
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| Case-Based Qualitative Beliefs | |
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| Axioms and Result | |
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| Four Known Techniques | |
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| The Combination Axiom in General Analogical Reasoning | |
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| Violations of the Combination Axiom | |
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| Frequentism Revisited | |
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| Similarity-Weighted Empirical Frequencies | |
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| Intuition | |
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| Axiomatization | |
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| Empirical Similarity and Objective Probabilities | |
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| Future Research | |
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| References | |
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| Index | |