1. Gauthier maintains on page 39 that completeness is a relatively unproblematic necessary condition for rationality. Do you think he is right.

2. The claim that a preference ordering that is complete and transitive can be represented by an ordinal utility function is easily proven if there are only a finite number of alternatives. Can you sketch the proof?

3. What does the "money pump" argument discussed both in my book and Gauthier's show? How convincing do you find it?

4. What exactly is the relationship between utility and preference?

5. Why is it irrational to prefer A in figure 4.1.1 and D in figure 4.1.2? Would you be tempted to express these preferences? How are we to understand them? What can we learn from such experimental findings? Do they reveal a mistake in the standard theory of rationality?