ABSTRACT
The problem of strategic manipulation of social decision rules has been extensively discussed in recent years. The major contributions on this problem are those of Gibbard (1973), Pattanaik (1973, 1974, 1975) and Satterthwaite (1975). Gibbard and Satterthwaite are concerned with the stability of voting schemes which yield one and only one social alternative as the outcome for any given set of individual orderings. Voting schemes can be viewed as social decision rules. Then a voting scheme is a social decision rule whose structure is such that for every situation it yields a social preference relation such that the choice set (the set of best elements) contains exactly one element. It can be easily seen that every voting scheme which satisfies the condition of independence of irrelevant alternatives is either dictatorial or violates the weak Pareto criterion. So, the Gibbard–Satterthwaite theorem essentially considers the stability of a class of non-binary social decision rules.
