decision theory A Brief Introduction.pdf

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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 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
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Preface
This text is a non-technical overview of modern decision theory. It is
intended for university students with no previous acquaintance with the
subject, and was primarily written for the participants of a course on risk
analysis at Uppsala University in 1994.
Some of the chapters are revised versions from a report written in
1990 for the Swedish National Board for Spent Nuclear Fuel.
Uppsala, August 1994
Sven Ove Hansson
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1. What is decision theory?
Decision theory is theory about decisions. The subject is not a very unified
one. To the contrary, there are many different ways to theorize about
decisions, and therefore also many different research traditions. This text
attempts to reflect some of the diversity of the subject. Its emphasis lies on
the less (mathematically) technical aspects of decision theory.
1.1 Theoretical questions about decisions
The following are examples of decisions and of theoretical problems that
they give rise to.
Shall I bring the umbrella today? – The decision depends on
something which I do not know, namely whether it will rain or not.
I am looking for a house to buy. Shall I buy this one? – This
house looks fine, but perhaps I will find a still better house for the
same price if I go on searching. When shall I stop the search
procedure?
Am I going to smoke the next cigarette? – One single cigarette is
no problem, but if I make the same decision sufficiently many times
it may kill me.
The court has to decide whether the defendent is guilty or not. –
There are two mistakes that the court can make, namely to convict
an innocent person and to acquit a guilty person. What principles
should the court apply if it considers the first of this mistakes to be
more serious than the second?
A committee has to make a decision, but its members have
different opinions . – What rules should they use to ensure that they
can reach a conclusion even if they are in disagreement?
Almost everything that a human being does involves decisions. Therefore,
to theorize about decisions is almost the same as to theorize about human
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