Consider a society consisting of two individuals, Prude (7) and Lewd (A), and a book, Lady Chatterley's Lover. At most one individual may hold the book, so the only three available alternatives are that nobody reads the book (Ø), only Prude reads it ({a}), or only Lewd does ({A}). Lewd prefers to read the book than to not read it, but would prefer it even more if Prude read it instead. Prude, however, believes that nobody ought to read the book, but, if somebody must, he would be the better
Consider a society consisting of two individuals, Prude (7) and Lewd (A), and a book, Lady Chatterley's Lover. At most one individual may hold the book, so the only three available alternatives are that nobody reads the book (Ø), only Prude reads it ({a}), or only Lewd does ({A}). Lewd prefers to read the book than to not read it, but would prefer it even more if Prude read it instead. Prude, however, believes that nobody ought to read the book, but, if somebody must, he would be the better
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Transcribed Image Text:5. Consider a society consisting of two individuals, Prude (7) and Lewd (A), and a
book, Lady Chatterley's Lover. At most one individual may hold the book, so the
only three available alternatives are that nobody reads the book (Ø), only Prude reads
it ({7}), or only Lewd does ({A}). Lewd prefers to read the book than to not read
it, but would prefer it even more if Prude read it instead. Prude, however, believes
that nobody ought to read the book, but, if somebody must, he would be the better
choice of reader. Formally, {T}Px{\}P,Ø and ØPr{T}Pr{A}.
A social welfare function is liberal if, assuming that the book is given to Prude or
Lewd, society's preference over whether Prude or Lewd reads it agrees with the book
recipient's preference. Show that no social welfare function can be liberal, unanimous,
complete and quasi-transitive. (A binary relation is quasi-transitive if its asymmetric
part is transitive; its symmetric part need not be.)
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