On the manipulability of the fuzzy social choice functions

In many social decision-making contexts, a manipulator has incentives to change the social choice in his favor by strategically misrepresenting his preference. Gibbard [Manipulation of voting schemes: a general result, Econometrica 41(4) (1973) 587–601] and Satterthwaite [Strategy-proofness and Arrow's conditions: existence and correspondence theorems for voting procedures and social welfare functions. J. Econom. Theory 10 (1975) 187–217] have shown that any non-dictatorial voting choice procedure is vulnerable to strategic manipulation. This paper extends their result to the case of fuzzy weak preference relations. For this purpose, the best alternative set is defined in three ways and consequently three generalizations of the Gibbard–Satterthwaite theorem to the fuzzy context are provided.