Non-Bayesian Decision Theory: Beliefs and Desires as Reasons for Action (Theory and Decision Library A:, 44)

This book aims to present an account of rational choice from a non-Bayesian point of view. Rational agents maximize subjective expected utility, but contrary to what is claimed by Bayesians, the author argues that utility and subjective probability should not be defined in terms of preferences over uncertain prospects. To some extent, the author’s non-Bayesian view gives a modern account of what decision theory could have been like, had decision theorists not entered the Bayesian path discovered by Ramsey, Savage, and Jeffrey. The author argues that traditional Bayesian decision theory is unavailing from an action-guiding perspective. For the deliberating Bayesian agent, the output of decision theory is not a set of preferences over alternative acts - these preferences are on the contrary used as input to the theory. Instead, the output is a (set of) utility function(s) that can be used for describing the agent as an expected utility maximizer, which are of limited normative relevance. On the non-Bayesian view articulated by the author, utility and probability are defined in terms of preferences over certain outcomes. These utility and probability functions are then used for generating preferences over uncertain prospects, which conform to the principle of maximizing expected utility. It is argued that this approach offers more action guidance. 1402086989......Page 1 Contents......Page 8 1. Introduction......Page 10 1.1 The subjective non-Bayesian approach......Page 13 1.2 A criterion of rationality for ideal agents......Page 14 1.3 Basic concepts......Page 16 1.4 Preview......Page 20 2. Bayesian decision theory......Page 22 2.1 The basic idea......Page 23 2.2 From objective to subjective probability......Page 26 2.3 The purely subjective approach......Page 29 2.4 The propositional approach......Page 32 2.5 Do Bayesians put the cart before the horse?......Page 35 3. Choosing what to decide......Page 40 3.1 Transformative and effective rules defined......Page 42 3.2 A comparison structure for formal representations......Page 45 3.3 An axiomatic analysis of transformative decision rules......Page 46 3.4 Strong versus weak monotonicity......Page 49 3.5 Two notions of permutability......Page 52 3.6 More on iterativity......Page 57 3.7 Acyclicity......Page 61 3.8 Rival representations......Page 62 4. Indeterminate preferences......Page 69 4.1 Previous accounts of preferential indeterminacy......Page 70 4.2 What is a preference?......Page 72 4.3 Introduction to the probabilistic theory......Page 76 4.4 The probabilistic analysis of preference......Page 77 4.5 Reflexivity, symmetry, and transitivity......Page 78 4.6 The choice axiom is not universally valid......Page 81 4.7 Spohn and Levi on self-predicting probabilities......Page 82 4.8 Further remarks on indeterminate preferences......Page 87 5. Utility......Page 89 5.1 The classical theory......Page 90 5.2 The probabilistic theory......Page 95 5.3 A modified version of the probabilistic theory......Page 97 5.4 Can desires be reduced to beliefs?......Page 99 5.5 Second-order preferences......Page 100 6. Subjective probability......Page 103 6.1 Why not objective probability?......Page 104 6.2 Why not Bayesian subjective probability?......Page 107 6.3 Non-Bayesian subjective probability......Page 110 6.4 Subjective non-Bayesian probability and horse race lotteries......Page 113 6.5 Concluding remarks......Page 115 7. Expected utility......Page 117 7.1 From Pascal to Allais......Page 118 7.3 The rule-based axiomatisation......Page 120 7.4 The act-based axiomatisation......Page 126 7.5 The Allais paradox......Page 128 7.6 The independence axiom vs. the trade-off principle......Page 131 8. Risk aversion......Page 134 8.1 Beyond the Pratt-Arrow concept......Page 135 8.2 The first impossibility theorem......Page 137 8.3 The second impossibility theorem......Page 140 8.4 The precautionary principle......Page 141 8.5 The fourth impossibility theorem......Page 145 8.6 Risk aversion as an epistemic concept?......Page 147 Appendix A: Proofs......Page 150 References......Page 170 M......Page 175 Z......Page 176 For quite some time, philosophers, economists, and statisticians have endorsed a view on rational choice known as Bayesianism. The work on this book has grown out of a feeling that the Bayesian view has come to dominate the academic com- nitytosuchanextentthatalternative,non-Bayesianpositionsareseldomextensively researched. Needless to say, I think this is a pity. Non-Bayesian positions deserve to be examined with much greater care, and the present work is an attempt to defend what I believe to be a coherent and reasonably detailed non-Bayesian account of decision theory. The main thesis I defend can be summarised as follows. Rational agents m- imise subjective expected utility, but contrary to what is claimed by Bayesians, ut- ity and subjective probability should not be de?ned in terms of preferences over uncertain prospects. On the contrary, rational decision makers need only consider preferences over certain outcomes. It will be shown that utility and probability fu- tions derived in a non-Bayesian manner can be used for generating preferences over uncertain prospects, that support the principle of maximising subjective expected utility. To some extent, this non-Bayesian view gives an account of what modern - cision theory could have been like, had decision theorists not entered the Bayesian path discovered by Ramsey, de Finetti, Savage, and others. I will not discuss all previous non-Bayesian positions presented in the literature. This title presents an account of rational choice from a non-Bayesian point of view. Rational agents maximise subjective expected utility, but contrary to what is claimed by Bayesians, the author argues that utility and subjective probability should not be defined in terms of preferences over uncertain prospects