The purpose of this exercise is to illustrate the potential conflict between personal liberty and the Pareto principle (first studied by Sen). Assume there is a copy of Lady Chatterley's Lover available to be read by two persons, A and B. There are three possible options: (a) A reads the book and B does not; (b) B reads the book and A does not; (c) neither reads the book. The preference ordering of A (the prude) is c A a A b and the preference ordering of B (the lascivious) is a B bB c. Hence c is the worst option for one and the best option for the other; while both prefer a to b. Define the personal liberty rule as allowing everyone to choose freely on personal matters (like the color of one's own hair) with society as a whole accepting the choice, no matter what others think.
a. Apply the personal liberty rule to the example to derive social preferences b c and c a.
b. Show that by the Pareto principle we must have a social preference cycle a b c a.
c. Suppose that liberalism is constrained by the requirement that the prude A decides to respect B's preferences such that A's preference for c over b is ignored. Similarly for B, only his preference for b over c is relevant but not his preference for a over c. What are the modified preference orderings of each person? Show that it leads to acyclic (transitive) social preference.
d. The second possibility to solve the paradox is to suppose that each is willing to respect the other's choice. Thus A respects B's preference for b over c and B respects A's preference for c over a. What are the modified preference orderings of each person? Show that it leads to acyclic social preference. What is then the best social outcome?