Decision Theory: a Brief Introduction

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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

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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

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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...
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