NUMBER 4 MANIPULATION OF VOTING SCHEMES: A GENERAL RESULT BY ALLAN GIBBARD It has been conjectured that no system of voting can preclude strategic voting-the securing by a voter of an outcome he prefers through misrepresentation of his preferences. In this paper, for all significant systems of voting in which chance plays no role, the conjecture is verified. To prove the conjecture, a more general theorem in game theory is proved: a gameform is a game without utilities attached to outcomes; only a trivial game form, it is shown, can guarantee that whatever the utilities of the players may be, each player will have a dominant pure strategy.

MANIPULATION OF SCHEMES THAT MIX VOTING WITH CHANCE' BY ALLAN GIBBARD A decision scheme makes the probabilities of alternatives depend on individual strong orderings of them. It is strategy-proof if it logically precludes anyone's advantageously misrepresenting his preferences. It is unilateral if only one individual can affect the outcome, and duple if it restricts the final outcome to a fixed pair of alternatives. Any strategy-proof decision scheme, it is shown, is a probability mixture of schemes each of which is unilateral or duple. If it guarantees Pareto optimal outcomes, it is a probability mixture of dictatorial schemes. If it guarantees ex ante Pareto optimal lotteries, it is dictatorial. ' I have been helped in revising this paper by conversations with Mark Satterthwait Schwartz, and Hugo Sonnenschein, and by letters from Peter Fishburn and Richard Zeckhau grateful to the referee for remarkably detailed suggestions for shortening the proof of th theorem.

No abstract

No abstract