Part I:  Decision Problems

1 Introduction ............................................................................................................................ 11

2 Outcomes and Preferences ...................................................................................................  15

2.1 Preference relations
2.2 Rational choice under certainty 
2.3 Why completeness and transitivity?
2.4 Exercises
2.4.1 Exercises for Section 2.1: Preference relations
2.4.2 Exercises for Section 2.2: Rational choice under certainty
2.5 Solutions to Exercises 

3 States and Acts ....................................................................................................................... 27

3.1 Uncertainty, states and acts
3.2 Dominance
3.3 MaxiMin and LexiMin 34
3.3.1 MaxiMin
3.3.2 LexiMin 
3.4 Regret: a first attempt
3.5 Exercises
3.5.1 Exercises for Section 3.1: Uncertainty, states and acts 
3.5.2 Exercises for Section 3.2: Dominance
3.5.3 Exercises for Section 3.3: MaxiMin and LexiMin
3.5.4 Exercises for Section 3.4: Regret: a first attempt 
3.6 Solutions to Exercises 

4 Decision Trees ......................................................................................................................... 43

4.1 Decision trees
4.2 Money lotteries and risk neutrality
4.3 Backward induction
4.4 Beyond money lotteries and risk neutrality
4.5 Exercises
4.5.1 Exercises for Section 4.1: Decision Trees
4.5.2 Exercises for Section 4.2: Money lotteries and risk neutrality 
4.5.3 Exercises for Section 4.3: Backward induction
4.6 Solutions to Exercises 

Part II: Uncertainty and Decision Making

5 Expected Utility Theory ........................................................................................................ 71
5.1 Money lotteries and attitudes to risk
5.2 Expected utility: theorems 
5.3 Expected utility: the axioms
5.4 Exercises
5.4.1 Exercises for Section 5.1: Money lotteries and attitudes to risk
5.4.2 Exercises for Section 5.2: Expected utility theory
5.4.3 Exercises for Section 5.3: Expected utility axioms
5.5 Solutions to Exercises 

6 Applications of Expected Utility ..........................................................................................  95
6.1 States and acts revisited
6.2 Decision trees revisited
6.3 Regret
6.4 The Hurwicz index of pessimism
6.5 Exercises
6.5.1 Exercises for Section 6.1: States and acts revisited
6.5.2 Exercises for Section 6.2: Decision trees revisited
6.5.3 Exercises for Section 6.3: Regret
6.5.4 Exercises for Section 6.4: The Hurwicz index of pessimism 
6.6 Solutions to Exercises 

7 Conditional Reasoning ......................................................................................................... 123
7.1 Sets and probability: brief review
7.1.1 Sets
7.1.2 Probability
7.2 Conditional thinking
7.2.1 The natural frequencies approach
7.2.2 Conditional probability 
7.3 Simpson's paradox
7.3 Exercises
7.4.1 Exercises for Section 7.1: Sets and probability
7.4.2 Exercises for Section 7.2: Conditional thinking
7.5 Solutions to Exercises 

8 Information and Beliefs ....................................................................................................... 151
8.1 Uncertainty and information 
8.2 Updating beliefs
8.3 Belief revision
8.4 Information and truth
8.5 Exercises 
8.5.1 Exercises for Section 8.1: Uncertainty and information
8.5.2 Exercises for Section 8.2: Updating beliefs
8.5.3 Exercises for Section 8.3: Belief revision
8.6 Solutions to Exercises 

9 The Value of Information ...................................................................................................  169
9.1 When is information potentially valuable?
9.2 The value of information when outcomes are sums of money
9.2.1 Perfect information and risk neutrality
9.2.2 Perfect information and risk aversion
9.2.3 Imperfect information 
9.3 The general case
9.4 Different sources of information
9.5 Exercises
9.5.1 Exercises for Section 9.1: When is information potentially valuable?
9.5.2 Exercises for Section 9.2: The value of information when outcomes are sums of money
9.5.3 Exercises for Section 9.3: The general case 
9.5.4 Exercises for Section 9.4: Different sources of information
9.6 Solutions to Exercises

Part III: Thinking about Future Selves

10 Intertemporal Choice ......................................................................................................... 215
10.1 Introduction
10.2 Present value and discounting 
10.3 Exponential discounting
10.3.1 Time consistency
10.4 Hyperbolic discounting
10.4.1 Interpretation of the parameter b
10.5 Dealing with time inconsistency
10.6 Exercises
10.6.1 Exercises for Section 10.2: Present value and discounting 
10.6.2 Exercises for Section 10.3: Exponential discounting
10.6.3 Exercises for Section 10.4: Hyperbolic discounting
10.6.4 Exercises for Section 10.5: Dealing with time inconsistency
10.7 Solutions to Exercises 

Part IV: Group Decision Making

11 Aggregation of Preferences ............................................................................................... 245
11.1 Social preference functions
11.2 Arrow’s Impossibility Theorem
11.3 Illustration of the proof of Arrow’s theorem
11.4 Application of Arrow’s theorem to individual choice
11.5 Exercises 1
11.5.1 Exercises for Section 11.1: Social preference functions 
11.5.2 Exercises for Section 11.2: Arrow’s impossibility theorem
11.5.3 Exercises for Section 11.3: Illustration of the proof of Arrow’s theorem
11.5.4 Exercises for Section 11.4: Application of Arrow’s theorem to individual choice
11.6 Solutions to Exercises 

12 Misrepresentation of Preferences  ...................................................................................  275
12.1 Social choice functions 
12.2 Strategic voting
12.3 The Gibbard-Satterthwaite theorem
12.4 Illustration of the proof of the Gibbard-Satterthwaite theorem
12.5 Exercises
12.5.1 Exercises for Section 12.1:  Social choice functions
12.5.2 Exercises for Section 12.2: Strategic voting
12.5.3 Exercises for Section 12.3:  The Gibbard-Satterthwaite theorem
12.6 Solutions to Exercises .

Part V: Biases in Decision Making