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Decision Theory A Brief Introduction

Decision theory in economics, psychology, philosophy, mathematics, and statistics is concerned with identifying the values, uncertainties and other issues relevant in a given decision, its rationality, and the resulting optimal decision. It is closely related to the field of game theory as to interactions of agents with at least partially conflicting interests whose decisions affect each other. | Decision Theory A Brief Introduction 1994-08-19 Minor revisions 2005-08-23 Sven Ove Hansson Department of Philosophy and the History of Technology Royal Institute of Technology KTH Stockholm 1 Contents Preface.4 1. What is decision theory .5 1.1 Theoretical questions about decisions.5 1.2 A truly interdisciplinary subject.6 1.3 Normative and descriptive theories.6 1.4 Outline of the following chapters.8 2. Decision processes.9 2.1 Condorcet.9 2.2 Modern sequential models.9 2.3 Non-sequential models.10 2.4 The phases of practical decisions - and of decision theory.12 3. Deciding and valuing.13 3.1 Relations and numbers.13 3.2 The comparative value terms.14 3.3 Completeness.16 3.4 Transitivity.17 3.5 Using preferences in decision-making.19 3.6 Numerical representation.20 3.7 Using utilities in decision-making.21 4. The standard representation of individual decisions.23 4.1 Alternatives.23 4.2 Outcomes and states of nature.24 4.3 Decision matrices.25 4.4 Information about states of nature.26 5. Expected utility.29 5.1 What is expected utility .29 5.2 Objective and subjective utility.30 5.3 Appraisal of EU.31 5.4 Probability estimates.34 6. Bayesianism.37 6.1 What is Bayesianism .37 6.2 Appraisal of Bayesianism.40 7. Variations of expected utility.45 7.1 Process utilities and regret theory.45 2 7.2 Prospect theory.47 8. Decision-making under uncertainty.50 8.1 Paradoxes of uncertainty.50 8.2 Measures of incompletely known probabilities.52 8.3 Decision criteria for uncertainty.55 9. Decision-making under ignorance.59 9.1 Decision rules for classical ignorance .59 9.2 Unknown possibilities.63 10. The demarcation of decisions.68 10.1 Unfinished list of alternatives.68 10.2 Indeterminate decision horizons.69 11. Decision instability.73 11.1 Conditionalized EU.73 11.2 Newcomb s paradox.74 11.3 Instability.76 12. Social decision theory.79 12.1 The basic insight.79 12.2 Arrow s theorem.81 References.82