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An Introduction to Decision Theory

Book Description

This introduction to decision theory offers comprehensive and accessible discussions of decision-making under ignorance and risk, the foundations of utility theory, the debate over subjective and objective probability, Bayesianism, causal decision theory, game theory, and social choice theory. No mathematical skills are assumed, and all concepts and results are explained in non-technical and intuitive as well as more formal ways. There are over 100 exercises with solutions, and a glossary of key terms and concepts. An emphasis on foundational aspects of normative decision theory (rather than descriptive decision theory) makes the book particularly useful for philosophy students, but it will appeal to readers in a range of disciplines including economics, psychology, political science and computer science.

Table of Contents

  1. Coverpage
  2. An Introduction to Decision Theory
  3. Title page
  4. Copyright page
  5. Contents
  6. Preface
  7. 1 Introduction
    1. 1.1 Normative and descriptive decision theory
    2. 1.2 Rational and right decisions
    3. 1.3 Risk, ignorance and uncertainty
    4. 1.4 Social choice theory and game theory
    5. 1.5 A very brief history of decision theory
  8. 2 The decision matrix
    1. 2.1 States
    2. 2.2 Outcomes
    3. 2.3 Acts
    4. 2.4 Rival formalisations
  9. 3 Decisions under ignorance
    1. 3.1 Dominance
    2. 3.2 Maximin and leximin
    3. 3.3 Maximax and the optimism–pessimism rule
    4. 3.4 Minimax regret
    5. 3.5 The principle of insufficient reason
    6. 3.6 Randomised acts
  10. 4 Decisions under risk
    1. 4.1 Maximising what?
    2. 4.2 Why is it rational to maximise expected utility?
    3. 4.3 The axiomatic approach
    4. 4.4 Allais’ paradox
    5. 4.5 Ellsberg’s paradox
    6. 4.6 The St Petersburg paradox
    7. 4.7 The two-envelope paradox
  11. 5 Utility
    1. 5.1 How to construct an ordinal scale
    2. 5.2 von Neumann and Morgenstern’s interval scale
    3. 5.3 Can utility be measured on a ratio scale?
    4. 5.4 Can we define utility without being able to measure it?
  12. 6 The mathematics of probability
    1. 6.1 The probability calculus
    2. 6.2 Conditional probability
    3. 6.3 Bayes’ theorem
    4. 6.4 The problem of unknown priors
  13. 7 The philosophy of probability
    1. 7.1 The classical interpretation
    2. 7.2 The frequency interpretation
    3. 7.3 The propensity interpretation
    4. 7.4 Logical and epistemic interpretations
    5. 7.5 Subjective probability
  14. 8 Why should we accept the preference axioms?
    1. 8.1 Must a rational preference be transitive?
    2. 8.2 Must a rational preference be complete?
    3. 8.3 The multi-attribute approach
    4. 8.4 Must a rational preference satisfy the independence axiom?
    5. 8.5 Risk aversion
  15. 9 Causal vs. evidential decision theory
    1. 9.1 Newcomb’s problem
    2. 9.2 Causal decision theory
    3. 9.3 Evidential decision theory
  16. 10 Bayesian vs. non-Bayesian decision theory
    1. 10.1 What is Bayesianism?
    2. 10.2 Arguments for and against Bayesianism
    3. 10.3 Non-Bayesian approaches
  17. 11 Game theory I: Basic concepts and zero-sum games
    1. 11.1 The prisoner’s dilemma
    2. 11.2 A taxonomy of games
    3. 11.3 Common knowledge and dominance reasoning
    4. 11.4 Two-person zero-sum games
    5. 11.5 Mixed strategies and the minimax theorem
  18. 12 Game theory II: Nonzero-sum and cooperative games
    1. 12.1 The Nash equilibrium
    2. 12.2 The battle of the sexes and chicken
    3. 12.3 The bargaining problem
    4. 12.4 Iterated games
    5. 12.5 Game theory and evolution
    6. 12.6 Game theory and ethics
  19. 13 Social choice theory
    1. 13.1 The social choice problem
    2. 13.2 Arrow’s impossibility theorem
    3. 13.3 Sen on liberalism and the Pareto principle
    4. 13.4 Harsanyi’s utilitarian theorems
  20. 14 Overview of descriptive decision theory
    1. 14.1 Observed violations of the expected utility principle
    2. 14.2 Prospect theory
    3. 14.3 Violations of transitivity and completeness
    4. 14.4 The relevance of descriptive decision theory
  21. Appendix A: Glossary
  22. Appendix B: Proof of the von Neumann–Morgenstern theorem
  23. Further reading
  24. Index