# Decision Theory: a Brief Introduction

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...

References: 82

Chisholm, Roderick M and Ernest Sosa (1966) "On the Logic of 'Intrinsically Better '", American Philosophical Quarterly 3:244-249

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Fischhoff, Baruch and R Beyth (1975) "´I knew it would happen´ remembered probabilities of once-future things", Organizational Behavior and Human Performance 13:1-16

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Hansson, Bengt (1975), "The appropriateness of the expected utility model", Erkenntnis 9:175-193

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Hoerl, Arthur E and Herbert K Fallin (1974), "Reliability of Subjective Evaluations in a High Incentive Situation", Journal of the Royal Statistical Society 137, Part 2, 227-230

86

Levi, Isaac (1980), The enterprise of knowledge

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Murphy, AH and RL Winkler (1984) "Probability forecasting in meteorology", Journal of the American Statistical Association 79:489-500

88

Ruthen, Russell (1993) "Strange Matter", Scientific American August 1993, p

89

Skyrms, Brian (1980), "Higher order degrees of belief", pp

90

Wald, A (1950), Statistical Decision Functions

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